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class="vector-toc-link" href="#Derivation_and_characteristics"> <div class="vector-toc-text"> 1.1 Derivation and characteristics </div> </a> <ul id="toc-Derivation_and_characteristics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Modelling_and_validation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Modelling_and_validation"> <div class="vector-toc-text"> 2 Modelling and validation </div> </a> <button aria-controls="toc-Modelling_and_validation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Modelling and validation subsection </button> <ul id="toc-Modelling_and_validation-sublist" class="vector-toc-list"> <li id="toc-Superconducting_memristor_component" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Superconducting_memristor_component"> <div class="vector-toc-text"> 2.1 Superconducting memristor component </div> </a> <ul id="toc-Superconducting_memristor_component-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memristor_circuits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memristor_circuits"> <div class="vector-toc-text"> 2.2 Memristor circuits </div> </a> <ul id="toc-Memristor_circuits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Criticisms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Criticisms"> <div class="vector-toc-text"> 2.3 Criticisms </div> </a> <ul id="toc-Criticisms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experimental_tests" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Experimental_tests"> <div class="vector-toc-text"> 2.4 Experimental tests </div> </a> <ul id="toc-Experimental_tests-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Theory" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Theory"> <div class="vector-toc-text"> 3 Theory </div> </a> <button aria-controls="toc-Theory-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Theory subsection </button> <ul id="toc-Theory-sublist" class="vector-toc-list"> <li id="toc-Operation_as_a_switch" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Operation_as_a_switch"> <div class="vector-toc-text"> 3.1 Operation as a switch </div> </a> <ul id="toc-Operation_as_a_switch-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memristive_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memristive_systems"> <div class="vector-toc-text"> 3.2 Memristive systems </div> </a> <ul id="toc-Memristive_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pinched_hysteresis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pinched_hysteresis"> <div class="vector-toc-text"> 3.3 Pinched hysteresis </div> </a> <ul id="toc-Pinched_hysteresis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memristive_networks_and_mathematical_models_of_circuit_interactions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memristive_networks_and_mathematical_models_of_circuit_interactions"> <div class="vector-toc-text"> 3.4 Memristive networks and mathematical models of circuit interactions </div> </a> <ul id="toc-Memristive_networks_and_mathematical_models_of_circuit_interactions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Extended_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Extended_systems"> <div class="vector-toc-text"> 3.5 Extended systems </div> </a> <ul id="toc-Extended_systems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Implementation_of_hysteretic_current-voltage_memristors" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Implementation_of_hysteretic_current-voltage_memristors"> <div class="vector-toc-text"> 4 Implementation of hysteretic current-voltage memristors </div> </a> <button aria-controls="toc-Implementation_of_hysteretic_current-voltage_memristors-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Implementation of hysteretic current-voltage memristors subsection </button> <ul id="toc-Implementation_of_hysteretic_current-voltage_memristors-sublist" class="vector-toc-list"> <li id="toc-Titanium_dioxide_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Titanium_dioxide_memristor"> <div class="vector-toc-text"> 4.1 Titanium dioxide memristor </div> </a> <ul id="toc-Titanium_dioxide_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Silicon_dioxide_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Silicon_dioxide_memristor"> <div class="vector-toc-text"> 4.2 Silicon dioxide memristor </div> </a> <ul id="toc-Silicon_dioxide_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polymeric_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polymeric_memristor"> <div class="vector-toc-text"> 4.3 Polymeric memristor </div> </a> <ul id="toc-Polymeric_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Layered_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Layered_memristor"> <div class="vector-toc-text"> 4.4 Layered memristor </div> </a> <ul id="toc-Layered_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Atomristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Atomristor"> <div class="vector-toc-text"> 4.5 Atomristor </div> </a> <ul id="toc-Atomristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferroelectric_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferroelectric_memristor"> <div class="vector-toc-text"> 4.6 Ferroelectric memristor </div> </a> <ul id="toc-Ferroelectric_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Carbon_nanotube_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Carbon_nanotube_memristor"> <div class="vector-toc-text"> 4.7 Carbon nanotube memristor </div> </a> <ul id="toc-Carbon_nanotube_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Biomolecular_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Biomolecular_memristor"> <div class="vector-toc-text"> 4.8 Biomolecular memristor </div> </a> <ul id="toc-Biomolecular_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spin_memristive_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spin_memristive_systems"> <div class="vector-toc-text"> 4.9 Spin memristive systems </div> </a> <ul id="toc-Spin_memristive_systems-sublist" class="vector-toc-list"> <li id="toc-Spintronic_memristor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Spintronic_memristor"> <div class="vector-toc-text"> 4.9.1 Spintronic memristor </div> </a> <ul id="toc-Spintronic_memristor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memristance_in_a_magnetic_tunnel_junction" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Memristance_in_a_magnetic_tunnel_junction"> <div class="vector-toc-text"> 4.9.2 Memristance in a magnetic tunnel junction </div> </a> <ul id="toc-Memristance_in_a_magnetic_tunnel_junction-sublist" class="vector-toc-list"> <li id="toc-Extrinsic_mechanism" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Extrinsic_mechanism"> <div class="vector-toc-text"> 4.9.2.1 Extrinsic mechanism </div> </a> <ul id="toc-Extrinsic_mechanism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Intrinsic_mechanism" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Intrinsic_mechanism"> <div class="vector-toc-text"> 4.9.2.2 Intrinsic mechanism </div> </a> <ul id="toc-Intrinsic_mechanism-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Spin_memristive_system" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Spin_memristive_system"> <div class="vector-toc-text"> 4.9.3 Spin memristive system </div> </a> <ul id="toc-Spin_memristive_system-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Self-directed_channel_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Self-directed_channel_memristor"> <div class="vector-toc-text"> 4.10 Self-directed channel memristor </div> </a> <ul id="toc-Self-directed_channel_memristor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Implementation_of_hysteretic_flux-charge_memristors" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Implementation_of_hysteretic_flux-charge_memristors"> <div class="vector-toc-text"> 5 Implementation of hysteretic flux-charge memristors </div> </a> <button aria-controls="toc-Implementation_of_hysteretic_flux-charge_memristors-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Implementation of hysteretic flux-charge memristors subsection </button> <ul id="toc-Implementation_of_hysteretic_flux-charge_memristors-sublist" class="vector-toc-list"> <li id="toc-Time-integrated_Formingfree_memristor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Time-integrated_Formingfree_memristor"> <div class="vector-toc-text"> 5.1 Time-integrated Formingfree memristor </div> </a> <ul id="toc-Time-integrated_Formingfree_memristor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Potential_applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Potential_applications"> <div class="vector-toc-text"> 6 Potential applications </div> </a> <ul id="toc-Potential_applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Derivative_devices" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Derivative_devices"> <div class="vector-toc-text"> 7 Derivative devices </div> </a> <button aria-controls="toc-Derivative_devices-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Derivative devices subsection </button> <ul id="toc-Derivative_devices-sublist" class="vector-toc-list"> <li id="toc-Memistor_and_memtransistor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memistor_and_memtransistor"> <div class="vector-toc-text"> 7.1 Memistor and memtransistor </div> </a> <ul id="toc-Memistor_and_memtransistor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memcapacitors_and_meminductors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memcapacitors_and_meminductors"> <div class="vector-toc-text"> 7.2 Memcapacitors and meminductors </div> </a> <ul id="toc-Memcapacitors_and_meminductors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memfractance_and_memfractor,_2nd-_and_3rd-order_memristor,_memcapacitor_and_meminductor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memfractance_and_memfractor,_2nd-_and_3rd-order_memristor,_memcapacitor_and_meminductor"> <div class="vector-toc-text"> 7.3 Memfractance and memfractor, 2nd- and 3rd-order memristor, memcapacitor and meminductor </div> </a> <ul id="toc-Memfractance_and_memfractor,_2nd-_and_3rd-order_memristor,_memcapacitor_and_meminductor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> 8 History </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle History subsection </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Precursors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Precursors"> <div class="vector-toc-text"> 8.1 Precursors </div> </a> <ul id="toc-Precursors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theoretical_description" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Theoretical_description"> <div class="vector-toc-text"> 8.2 Theoretical description </div> </a> <ul id="toc-Theoretical_description-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Twenty-first_century" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Twenty-first_century"> <div class="vector-toc-text"> 8.3 Twenty-first century </div> </a> <ul id="toc-Twenty-first_century-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 9 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> 10 Footnotes </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 11 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 12 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 13 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Memristor</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox 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Available in 37 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-37" aria-hidden="true" > 37 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%82%D8%A7%D9%88%D9%85%D8%A9_%D8%B0%D8%A7%D9%83%D8%B1%D9%8A%D8%A9" title="مقاومة ذاكرية – Arabic" lang="ar" hreflang="ar" data-title="مقاومة ذاكرية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A7%87%E0%A6%AE%E0%A6%B0%E0%A6%BF%E0%A6%B8%E0%A7%8D%E0%A6%9F%E0%A6%B0" title="মেমরিস্টর – Bangla" lang="bn" hreflang="bn" data-title="মেমরিস্টর" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B5%D0%BC%D1%80%D0%B8%D1%81%D1%82%D0%BE%D1%80" title="Мемристор – Bulgarian" lang="bg" hreflang="bg" data-title="Мемристор" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Memristor" title="Memristor – Catalan" lang="ca" hreflang="ca" data-title="Memristor" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Memristor" title="Memristor – Czech" lang="cs" hreflang="cs" data-title="Memristor" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Memristor" title="Memristor – Danish" lang="da" hreflang="da" data-title="Memristor" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Memristor" title="Memristor – German" lang="de" hreflang="de" data-title="Memristor" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Memristor" title="Memristor – Estonian" lang="et" hreflang="et" data-title="Memristor" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Memristor" title="Memristor – Spanish" lang="es" hreflang="es" data-title="Memristor" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Memristore" title="Memristore – Basque" lang="eu" hreflang="eu" data-title="Memristore" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%85%D8%B1%DB%8C%D8%B3%D8%AA%D9%88%D8%B1" title="ممریستور – Persian" lang="fa" hreflang="fa" data-title="ممریستور" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Memristor" title="Memristor – French" lang="fr" hreflang="fr" data-title="Memristor" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A9%A4%EB%A6%AC%EC%8A%A4%ED%84%B0" title="멤리스터 – Korean" lang="ko" hreflang="ko" data-title="멤리스터" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Memristor" title="Memristor – Indonesian" lang="id" hreflang="id" data-title="Memristor" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Memristore" title="Memristore – Italian" lang="it" hreflang="it" data-title="Memristore" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9E%D7%A8%D7%99%D7%A1%D7%98%D7%95%D7%A8" title="ממריסטור – Hebrew" lang="he" hreflang="he" data-title="ממריסטור" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Memrisztor" title="Memrisztor – Hungarian" lang="hu" hreflang="hu" data-title="Memrisztor" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Memristor" title="Memristor – Dutch" lang="nl" hreflang="nl" data-title="Memristor" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A1%E3%83%A2%E3%83%AA%E3%82%B9%E3%82%BF" title="メモリスタ – Japanese" lang="ja" hreflang="ja" data-title="メモリスタ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Memristor" title="Memristor – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Memristor" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Memrystor" title="Memrystor – Polish" lang="pl" hreflang="pl" data-title="Memrystor" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Memristor" title="Memristor – Portuguese" lang="pt" hreflang="pt" data-title="Memristor" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Memristor" title="Memristor – Romanian" lang="ro" hreflang="ro" data-title="Memristor" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D0%BC%D1%80%D0%B8%D1%81%D1%82%D0%BE%D1%80" title="Мемристор – Russian" lang="ru" hreflang="ru" data-title="Мемристор" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Nonlinear two-terminal fundamental circuit element</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Memistor" title="Memistor">Memistor</a> or <a href="/wiki/Memtransistor" title="Memtransistor">Memtransistor</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><caption class="infobox-title">Memristor</caption><tbody><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Memristor_(50665029093)_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Memristor_%2850665029093%29_%28cropped%29.jpg/220px-Memristor_%2850665029093%29_%28cropped%29.jpg" decoding="async" width="220" height="228" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Memristor_%2850665029093%29_%28cropped%29.jpg/330px-Memristor_%2850665029093%29_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Memristor_%2850665029093%29_%28cropped%29.jpg/440px-Memristor_%2850665029093%29_%28cropped%29.jpg 2x" data-file-width="4079" data-file-height="4225" /></a><div class="infobox-caption">Memristor developed by the <a href="/wiki/University_of_Illinois_at_Urbana-Champaign" class="mw-redirect" title="University of Illinois at Urbana-Champaign">University of Illinois at Urbana-Champaign</a> and <a href="/wiki/National_Energy_Technology_Laboratory" title="National Energy Technology Laboratory">National Energy Technology Laboratory</a></div></td></tr><tr><th scope="row" class="infobox-label">Working principle‍</th><td class="infobox-data">Relating electric charge and magnetic flux linkage</td></tr><tr><th scope="row" class="infobox-label">Inventor</th><td class="infobox-data"><a href="/wiki/Leon_Chua" class="mw-redirect" title="Leon Chua">Leon Chua</a></td></tr><tr><th scope="row" class="infobox-label">Invention year</th><td class="infobox-data">1971; 54 years ago (1971)</td></tr><tr><th scope="row" class="infobox-label">Number of <a href="/wiki/Terminal_(electronics)" title="Terminal (electronics)">terminals</a></th><td class="infobox-data">2</td></tr><tr><th scope="row" class="infobox-label">Linear?</th><td class="infobox-data">No</td></tr><tr><th colspan="2" class="infobox-header"><a href="/wiki/Electronic_symbol" title="Electronic symbol">Electronic symbol</a></th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/File:Memristor-Symbol.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Memristor-Symbol.svg/35px-Memristor-Symbol.svg.png" decoding="async" width="35" height="71" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Memristor-Symbol.svg/53px-Memristor-Symbol.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Memristor-Symbol.svg/70px-Memristor-Symbol.svg.png 2x" data-file-width="35" data-file-height="71" /></a></td></tr></tbody></table> A memristor (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ˈmɛmrɪstər/</a>; a <a href="/wiki/Portmanteau" class="mw-redirect" title="Portmanteau">portmanteau</a> of memory resistor) is a non-linear <a href="/wiki/Terminal_(electronics)" title="Terminal (electronics)">two-terminal</a> <a href="/wiki/Electronic_component" title="Electronic component">electrical component</a> relating <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> and magnetic <a href="/wiki/Flux_linkage" title="Flux linkage">flux linkage</a>. It was described and named in 1971 by <a href="/wiki/Leon_Chua" class="mw-redirect" title="Leon Chua">Leon Chua</a>, completing a theoretical quartet of fundamental electrical components which also comprises the <a href="/wiki/Resistor" title="Resistor">resistor</a>, <a href="/wiki/Capacitor" title="Capacitor">capacitor</a> and <a href="/wiki/Inductor" title="Inductor">inductor</a>.<a href="#cite_note-chua71-1">[1]</a> Chua and Kang later generalized the concept to memristive systems.<a href="#cite_note-chua76-2">[2]</a> Such a system comprises a circuit, of multiple conventional components, which mimics key properties of the ideal memristor component and is also commonly referred to as a memristor. Several such memristor system technologies have been developed, notably <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>. The identification of memristive properties in electronic devices has attracted controversy. Experimentally, the ideal memristor has yet to be demonstrated.<a href="#cite_note-Pershin_2018-3">[3]</a><a href="#cite_note-Kim_2019-4">[4]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="As_a_fundamental_electrical_component">As a fundamental electrical component</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=1" title="Edit section: As a fundamental electrical component">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Two-terminal_non-linear_circuit_elements.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Two-terminal_non-linear_circuit_elements.svg/220px-Two-terminal_non-linear_circuit_elements.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Two-terminal_non-linear_circuit_elements.svg/330px-Two-terminal_non-linear_circuit_elements.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Two-terminal_non-linear_circuit_elements.svg/440px-Two-terminal_non-linear_circuit_elements.svg.png 2x" data-file-width="1024" data-file-height="1024" /></a><figcaption>Conceptual symmetries of resistor, capacitor, inductor, and memristor</figcaption></figure> Chua in his 1971 paper identified a theoretical symmetry between the non-linear resistor (voltage vs. current), non-linear capacitor (voltage vs. charge), and non-linear inductor (magnetic flux linkage vs. current). From this symmetry he inferred the characteristics of a fourth fundamental non-linear circuit element, linking magnetic flux and charge, which he called the memristor. In contrast to a linear (or non-linear) resistor, the memristor has a dynamic relationship between current and voltage, including a memory of past voltages or currents. Other scientists had proposed dynamic memory resistors such as the <a href="/wiki/Memistor" title="Memistor">memistor</a> of Bernard Widrow, but Chua introduced a mathematical generality. <div class="mw-heading mw-heading3"><h3 id="Derivation_and_characteristics">Derivation and characteristics</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=2" title="Edit section: Derivation and characteristics">edit</a>]</div> The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage Φm(t) and the amount of electric charge that has flowed, q(t):<a href="#cite_note-chua71-1">[1]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(\mathrm {\Phi } _{\mathrm {m} }(t),q(t))=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Φ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(\mathrm {\Phi } _{\mathrm {m} }(t),q(t))=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96fff63491f64261d6ee1df829d4d3746af4fe32" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.029ex; height:2.843ex;" alt="{\displaystyle f(\mathrm {\Phi } _{\mathrm {m} }(t),q(t))=0}"> The magnetic <a href="/wiki/Flux_linkage" title="Flux linkage">flux linkage</a>, Φm, is generalized from the circuit characteristic of an inductor. It does not represent a magnetic field here. Its physical meaning is discussed below. The symbol Φm may be regarded as the integral of voltage over time.<a href="#cite_note-5">[5]</a> In the relationship between Φm and q, the derivative of one with respect to the other depends on the value of one or the other, and so each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M(q)={\frac {\mathrm {d} \Phi _{\rm {m}}}{\mathrm {d} q}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M(q)={\frac {\mathrm {d} \Phi _{\rm {m}}}{\mathrm {d} q}}\,.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50065bf6c9ea9104a967fd396bbf39cb4ae95f00" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.861ex; height:5.843ex;" alt="{\displaystyle M(q)={\frac {\mathrm {d} \Phi _{\rm {m}}}{\mathrm {d} q}}\,.}"> Substituting the flux as the time integral of the voltage, and charge as the time integral of current, the more convenient forms are: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M(q(t))={\cfrac {\mathrm {d} \Phi _{\rm {}}/\mathrm {d} t}{\mathrm {d} q/\mathrm {d} t}}={\frac {V(t)}{I(t)}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>I</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M(q(t))={\cfrac {\mathrm {d} \Phi _{\rm {}}/\mathrm {d} t}{\mathrm {d} q/\mathrm {d} t}}={\frac {V(t)}{I(t)}}\,.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93b4372535c28a6de5b653a10e99f56e0b1924ab" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:27.574ex; height:7.176ex;" alt="{\displaystyle M(q(t))={\cfrac {\mathrm {d} \Phi _{\rm {}}/\mathrm {d} t}{\mathrm {d} q/\mathrm {d} t}}={\frac {V(t)}{I(t)}}\,.}"> To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term M(q), which characterizes the device, and write it as a differential equation. <table class="wikitable"> <caption>Differential equation relationships between resistance, capacitance, inductance, and memristance </caption> <tbody><tr> <th scope="col">Device </th> <th scope="col">Symbol </th> <th scope="col">Characteristic property </th> <th scope="col">Units </th> <th scope="col">Unit ratio (V, A, C, Wb) </th> <th scope="col">Differential equation </th></tr> <tr> <th scope="row"><a href="/wiki/Resistor" title="Resistor">Resistor</a> </th> <td>R</td> <td><a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">Resistance</a></td> <td><a href="/wiki/Ohm" title="Ohm">ohm</a> (Ω)</td> <td><a href="/wiki/Volt" title="Volt">volts</a> per <a href="/wiki/Ampere" title="Ampere">ampere</a> (V / A)</td> <td>R = dV / dI </td></tr> <tr> <th scope="row"><a href="/wiki/Capacitor" title="Capacitor">Capacitor</a> </th> <td>C</td> <td><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></td> <td><a href="/wiki/Farad" title="Farad">farad</a> (F)</td> <td><a href="/wiki/Coulomb" title="Coulomb">coulombs</a> per volt (C / V)</td> <td>C = dq / dV </td></tr> <tr> <th scope="row"><a href="/wiki/Inductor" title="Inductor">Inductor</a> </th> <td>L</td> <td><a href="/wiki/Inductance" title="Inductance">Inductance</a></td> <td><a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a> (H)</td> <td><a href="/wiki/Weber_(unit)" title="Weber (unit)">webers</a> per ampere (Wb / A)</td> <td>L = dΦm / dI </td></tr> <tr> <th scope="row">Memristor </th> <td>M</td> <td>Memristance</td> <td>ohm (Ω)</td> <td>webers per coulomb (Wb / C)</td> <td>M = dΦm / dq </td></tr></tbody></table> The above table covers all meaningful ratios of differentials of I, q, Φm, and V. No device can relate dI to dq, or dΦm to dV, because I is the time derivative of q and Φm is the integral of V with respect to time. It can be inferred from this that memristance is charge-dependent <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a>. If M(q(t)) is a constant, then we obtain <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>, R(t) = V(t)/I(t). If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) can vary with time. Solving for voltage as a function of time produces <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V(t)=\ M(q(t))I(t)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mtext> </mtext> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mi>I</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(t)=\ M(q(t))I(t)\,.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80cbbc5ba0bdc971b4a39fa14b98de412cfab355" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.94ex; height:2.843ex;" alt="{\displaystyle V(t)=\ M(q(t))I(t)\,.}"> This equation reveals that memristance defines a linear relationship between current and voltage, as long as M does not vary with charge. Nonzero current implies time varying charge. <a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a>, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement—as long as the maximum change in q does not cause <a href="/wiki/Small_signal_model" class="mw-redirect" title="Small signal model">much</a> change in M. Furthermore, the memristor is static if no current is applied. If I(t) = 0, we find V(t) = 0 and M(t) is constant. This is the essence of the memory effect. Analogously, we can define a W(ϕ(t)) as memductance:<a href="#cite_note-chua71-1">[1]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i(t)=W(\phi (t))v(t)\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>W</mi> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i(t)=W(\phi (t))v(t)\,.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d5255b6040886a237c524c0eeee157a762e0451" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.639ex; height:2.843ex;" alt="{\displaystyle i(t)=W(\phi (t))v(t)\,.}"> The <a href="/wiki/Power_consumption" class="mw-redirect" title="Power consumption">power consumption</a> characteristic recalls that of a resistor, I2R: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(t)=\ I(t)V(t)=\ I^{2}(t)M(q(t))\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mtext> </mtext> <mi>I</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mtext> </mtext> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(t)=\ I(t)V(t)=\ I^{2}(t)M(q(t))\,.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6773f3bd2379c93f6b93ae78532163f79f05777b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.933ex; height:3.176ex;" alt="{\displaystyle P(t)=\ I(t)V(t)=\ I^{2}(t)M(q(t))\,.}"> As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a constant resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop. M(q) is physically restricted to be positive for all values of q (assuming the device is passive and does not become <a href="/wiki/Superconductive" class="mw-redirect" title="Superconductive">superconductive</a> at some q). A negative value would mean that it would perpetually supply energy when operated with alternating current. <div class="mw-heading mw-heading2"><h2 id="Modelling_and_validation">Modelling and validation</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=3" title="Edit section: Modelling and validation">edit</a>]</div> In order to understand the nature of memristor function, some knowledge of fundamental circuit theoretic concepts is useful, starting with the concept of <a href="/wiki/Semiconductor_device_modeling" title="Semiconductor device modeling">device modeling</a>.<a href="#cite_note-muthuswamyBanerjee2019-6">[6]</a> Engineers and scientists seldom analyze a physical system in its original form. Instead, they construct a model which approximates the behaviour of the system. By analyzing the behaviour of the model, they hope to predict the behaviour of the actual system. The primary reason for constructing models is that physical systems are usually too complex to be amenable to a practical analysis. In the 20th century, work was done on devices where researchers did not recognize the memristive characteristics. This has raised the suggestion that such devices should be recognised as memristors.<a href="#cite_note-muthuswamyBanerjee2019-6">[6]</a> Pershin and Di Ventra<a href="#cite_note-Pershin_2018-3">[3]</a> have proposed a test that can help to resolve some of the long-standing controversies about whether an ideal memristor does actually exist or is a purely mathematical concept. The rest of this article primarily addresses memristors as related to <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a> devices, since the majority of work since 2008 has been concentrated in this area. <div class="mw-heading mw-heading3"><h3 id="Superconducting_memristor_component">Superconducting memristor component</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=4" title="Edit section: Superconducting memristor component">edit</a>]</div> Dr. Paul Penfield, in a 1974 MIT technical report<a href="#cite_note-penfield1974-7">[7]</a> mentions the memristor in connection with <a href="/wiki/Josephson_junctions" class="mw-redirect" title="Josephson junctions">Josephson junctions</a>. This was an early use of the word "memristor" in the context of a circuit device. One of the terms in the current through a Josephson junction is of the form: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}i_{M}(v)&=\epsilon \cos(\phi _{0})v\\&=W(\phi _{0})v\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>ϵ</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>v</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>W</mi> <mo stretchy="false">(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>v</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}i_{M}(v)&=\epsilon \cos(\phi _{0})v\\&=W(\phi _{0})v\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7b49b69e591e0e3135ab04d28a41d22231c4cc2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.367ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}i_{M}(v)&=\epsilon \cos(\phi _{0})v\\&=W(\phi _{0})v\end{aligned}}}"> where ϵ is a constant based on the physical superconducting materials, v is the voltage across the junction and iM is the current through the junction. Through the late 20th century, research regarding this phase-dependent conductance in Josephson junctions was carried out.<a href="#cite_note-langenberg74-8">[8]</a><a href="#cite_note-pedersen1972-9">[9]</a><a href="#cite_note-pedersen1974-10">[10]</a><a href="#cite_note-thompson1973-11">[11]</a> A more comprehensive approach to extracting this phase-dependent conductance appeared with Peotta and Di Ventra's seminal paper in 2014.<a href="#cite_note-peottaDiVentra2014-12">[12]</a> <div class="mw-heading mw-heading3"><h3 id="Memristor_circuits">Memristor circuits</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=5" title="Edit section: Memristor circuits">edit</a>]</div> Due to the practical difficulty of studying the ideal memristor, we will discuss other electrical devices which can be modelled using memristors. For a mathematical description of a memristive device (systems), see <a href="#Theory">§ Theory</a>. A discharge tube can be modelled as a memristive device, with resistance being a function of the number of conduction electrons ne.<a href="#cite_note-chua76-2">[2]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}v_{\mathrm {M} }&=R(n_{\mathrm {e} })i_{\mathrm {M} }\\{\frac {\mathrm {d} n_{\mathrm {e} }}{\mathrm {d} t}}&=\beta n+\alpha R(n_{\mathrm {e} })i_{\mathrm {M} }^{2}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>R</mi> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>β</mi> <mi>n</mi> <mo>+</mo> <mi>α</mi> <mi>R</mi> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}v_{\mathrm {M} }&=R(n_{\mathrm {e} })i_{\mathrm {M} }\\{\frac {\mathrm {d} n_{\mathrm {e} }}{\mathrm {d} t}}&=\beta n+\alpha R(n_{\mathrm {e} })i_{\mathrm {M} }^{2}\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/565a477b4efca4842b07e0f86ed9290341168a44" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:23.862ex; height:8.509ex;" alt="{\displaystyle {\begin{aligned}v_{\mathrm {M} }&=R(n_{\mathrm {e} })i_{\mathrm {M} }\\{\frac {\mathrm {d} n_{\mathrm {e} }}{\mathrm {d} t}}&=\beta n+\alpha R(n_{\mathrm {e} })i_{\mathrm {M} }^{2}\end{aligned}}}"> vM is the voltage across the discharge tube, iM is the current flowing through it, andne is the number of conduction electrons. A simple memristance function is R(ne) = F/ne. The parameters α, β, and F depend on the dimensions of the tube and the gas fillings. An <a href="#Experimental_tests">experimental</a> identification of memristive behaviour is the "pinched hysteresis loop" in the v-i plane.<a href="#cite_note-13">[a]</a><a href="#cite_note-muthuswamy2014-14">[13]</a><a href="#cite_note-sah2015-15">[14]</a> Thermistors can be modeled as memristive devices:<a href="#cite_note-sah2015-15">[14]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}v&=R_{0}(T_{0})\exp \left[\beta \left({\frac {1}{T}}-{\frac {1}{T_{0}}}\right)\right]i\\&\equiv R(T)i\\{\frac {\mathrm {d} T}{\mathrm {d} t}}&={\frac {1}{C}}\left[-\delta \cdot (T-T_{0})+R(T)i^{2}\right]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>v</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <mi>β</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mi>i</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>≡</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mi>i</mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>C</mi> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mi>δ</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}v&=R_{0}(T_{0})\exp \left[\beta \left({\frac {1}{T}}-{\frac {1}{T_{0}}}\right)\right]i\\&\equiv R(T)i\\{\frac {\mathrm {d} T}{\mathrm {d} t}}&={\frac {1}{C}}\left[-\delta \cdot (T-T_{0})+R(T)i^{2}\right]\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc0aa313843800d30c361de2cf8d2d50fd0c8944" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.588ex; margin-bottom: -0.25ex; width:35.684ex; height:14.843ex;" alt="{\displaystyle {\begin{aligned}v&=R_{0}(T_{0})\exp \left[\beta \left({\frac {1}{T}}-{\frac {1}{T_{0}}}\right)\right]i\\&\equiv R(T)i\\{\frac {\mathrm {d} T}{\mathrm {d} t}}&={\frac {1}{C}}\left[-\delta \cdot (T-T_{0})+R(T)i^{2}\right]\end{aligned}}}"> β is a material constant, T is the absolute body temperature of the thermistor, T0 is the ambient temperature (both temperatures in Kelvin), R0(T0) denotes the cold temperature resistance at T = T0, C is the heat capacitance and δ is the dissipation constant for the thermistor. A fundamental phenomenon that has hardly been studied is memristive behaviour in <a href="/wiki/P-n_junctions" class="mw-redirect" title="P-n junctions">p-n junctions</a>.<a href="#cite_note-chuaTseng74-16">[15]</a> The memristor plays a crucial role in mimicking the charge storage effect in the diode base, and is also responsible for the conductivity modulation phenomenon (that is so important during forward transients). <div class="mw-heading mw-heading3"><h3 id="Criticisms">Criticisms</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=6" title="Edit section: Criticisms">edit</a>]</div> In 2008, a team at <a href="/wiki/HP_Labs" title="HP Labs">HP Labs</a> found experimental evidence for the Chua's memristor based on an analysis of a <a href="/wiki/Thin_film" title="Thin film">thin film</a> of <a href="/wiki/Titanium_dioxide" title="Titanium dioxide">titanium dioxide</a>, thus connecting the operation of <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a> devices to the memristor concept. According to HP Labs, the memristor would operate in the following way: the memristor's <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">electrical resistance</a> is not constant but depends on the current that had previously flowed through the device, i.e., its present resistance depends on how much electric charge has previously flowed through it and in what direction; the device remembers its history—the so-called <dfn>non-volatility property</dfn>.<a href="#cite_note-chua11-17">[16]</a> When the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again.<a href="#cite_note-Williams08-18">[17]</a><a href="#cite_note-19">[18]</a> The HP Labs result was published in the scientific journal <a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a>.<a href="#cite_note-Williams08-18">[17]</a><a href="#cite_note-Williams_-_Spectrum_2008-12-20">[19]</a> Following this claim, Leon Chua has argued that the memristor definition could be generalized to cover all forms of two-terminal non-volatile memory devices based on resistance switching effects.<a href="#cite_note-chua11-17">[16]</a> Chua also argued that the memristor is the oldest known <a href="/wiki/Circuit_element" class="mw-redirect" title="Circuit element">circuit element</a>, with its effects predating the <a href="/wiki/Resistor" title="Resistor">resistor</a>, <a href="/wiki/Capacitor" title="Capacitor">capacitor</a>, and <a href="/wiki/Inductor" title="Inductor">inductor</a>.<a href="#cite_note-Memristor200yearsold-21">[20]</a> However, there are doubts as to whether a memristor can actually exist in physical reality.<a href="#cite_note-Meuffels_2012-22">[21]</a><a href="#cite_note-DiVentra_2013-23">[22]</a><a href="#cite_note-Sundqvist_2017-24">[23]</a><a href="#cite_note-25">[24]</a> Additionally, some experimental evidence contradicts Chua's generalization since a non-passive <a href="/wiki/Nanobatteries" title="Nanobatteries">nanobattery</a> effect is observable in resistance switching memory.<a href="#cite_note-memristor_nanobattery-26">[25]</a> A simple test has been proposed by Pershin and Di Ventra<a href="#cite_note-Pershin_2018-3">[3]</a> to analyze whether such an ideal or generic memristor does actually exist or is a purely mathematical concept. Up to now,[<a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers">when?</a>] there seems to be no experimental resistance switching device (<a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>) which can pass the test.<a href="#cite_note-Pershin_2018-3">[3]</a><a href="#cite_note-Kim_2019-4">[4]</a> These devices are intended for applications in <a href="/wiki/Nanoelectronic" class="mw-redirect" title="Nanoelectronic">nanoelectronic</a> memory devices, computer logic, and <a href="/wiki/Neuromorphic" class="mw-redirect" title="Neuromorphic">neuromorphic</a>/neuromemristive computer architectures.<a href="#cite_note-27">[26]</a><a href="#cite_note-28">[27]</a> In 2013, Hewlett-Packard CTO Martin Fink suggested that memristor memory may become commercially available as early as 2018.<a href="#cite_note-memristor2018-29">[28]</a> In March 2012, a team of researchers from <a href="/wiki/HRL_Laboratories" title="HRL Laboratories">HRL Laboratories</a> and the <a href="/wiki/University_of_Michigan" title="University of Michigan">University of Michigan</a> announced the first functioning memristor array built on a <a href="/wiki/CMOS" title="CMOS">CMOS</a> chip.<a href="#cite_note-HRLmemristor-30">[29]</a> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Memristor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/9/9f/Memristor.jpg/225px-Memristor.jpg" decoding="async" width="225" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/9/9f/Memristor.jpg 1.5x" data-file-width="324" data-file-height="308" /></a><figcaption>An array of 17 purpose-built <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>-depleted <a href="/wiki/Titanium_dioxide" title="Titanium dioxide">titanium dioxide</a> memristors built at <a href="/wiki/HP_Labs" title="HP Labs">HP Labs</a>, imaged by an <a href="/wiki/Atomic_force_microscope" class="mw-redirect" title="Atomic force microscope">atomic force microscope</a>. The wires are about 50 nm, or 150 atoms, wide.<a href="#cite_note-31">[30]</a> <a href="/wiki/Electric_current" title="Electric current">Electric current</a> through the memristors shifts the oxygen vacancies, causing a gradual and persistent change in <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">electrical resistance</a>.<a href="#cite_note-Kanellos-32">[31]</a></figcaption></figure> According to the original 1971 definition, the memristor is the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage. In 2011, <a href="/wiki/Leon_Chua" class="mw-redirect" title="Leon Chua">Chua</a> argued for a broader definition that includes all two-terminal non-volatile memory devices based on resistance switching.<a href="#cite_note-chua11-17">[16]</a> Williams argued that <a href="/wiki/Magnetoresistive_RAM" title="Magnetoresistive RAM">MRAM</a>, <a href="/wiki/Phase-change_memory" title="Phase-change memory">phase-change memory</a> and <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a> are memristor technologies.<a href="#cite_note-Mellor2011-33">[32]</a> Some researchers argued that biological structures such as blood<a href="#cite_note-Courtland2011-34">[33]</a> and skin<a href="#cite_note-G_K_Johnsen_et_al-35">[34]</a><a href="#cite_note-McAlpine2011-36">[35]</a> fit the definition. Others argued that the memory device under development by <a href="/wiki/HP_Labs" title="HP Labs">HP Labs</a> and other forms of <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a> are not memristors, but rather part of a broader class of variable-resistance systems,<a href="#cite_note-Clarke2012-37">[36]</a> and that a broader definition of memristor is a scientifically unjustifiable <a href="/wiki/Land_grabbing" title="Land grabbing">land grab</a> that favored HP's memristor patents.<a href="#cite_note-PaulMarks2012-38">[37]</a> In 2011, Meuffels and Schroeder noted that one of the early memristor papers included a mistaken assumption regarding ionic conduction.<a href="#cite_note-Meuffels_2011-39">[38]</a> In 2012, Meuffels and Soni discussed some fundamental issues and problems in the realization of memristors.<a href="#cite_note-Meuffels_2012-22">[21]</a> They indicated inadequacies in the electrochemical modeling presented in the <a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a> article "The missing memristor found"<a href="#cite_note-Williams08-18">[17]</a> because the impact of <a href="/wiki/Concentration_polarization" title="Concentration polarization">concentration polarization</a> effects on the behavior of metal−<a href="/wiki/TiO2" class="mw-redirect" title="TiO2">TiO2−x</a>−metal structures under voltage or current stress was not considered.<a href="#cite_note-memristor_nanobattery-26">[25]</a> In a kind of <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a>, Meuffels and Soni<a href="#cite_note-Meuffels_2012-22">[21]</a> furthermore revealed a severe inconsistency: If a current-controlled memristor with the so-called <dfn>non-volatility property</dfn><a href="#cite_note-chua11-17">[16]</a> exists in physical reality, its behavior would violate <a href="/wiki/Landauer%27s_principle" title="Landauer's principle">Landauer's principle</a>, which places a limit on the minimum amount of energy required to change "information" states of a system. This critique was finally adopted by <a href="/wiki/Di_Ventra" class="mw-redirect" title="Di Ventra">Di Ventra</a> and Pershin<a href="#cite_note-DiVentra_2013-23">[22]</a> in 2013. Within this context, Meuffels and Soni<a href="#cite_note-Meuffels_2012-22">[21]</a> pointed to a fundamental thermodynamic principle: Non-volatile information storage requires the existence of <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free-energy</a> barriers that separate the distinct internal memory states of a system from each other; otherwise, one would be faced with an "indifferent" situation, and the system would arbitrarily fluctuate from one memory state to another just under the influence of <a href="/wiki/Thermal_fluctuations" title="Thermal fluctuations">thermal fluctuations</a>. When unprotected against <a href="/wiki/Thermal_fluctuations" title="Thermal fluctuations">thermal fluctuations</a>, the internal memory states exhibit some diffusive dynamics, which causes state degradation.<a href="#cite_note-DiVentra_2013-23">[22]</a> The free-energy barriers must therefore be high enough to ensure a low <a href="/wiki/Bit_error_rate" title="Bit error rate">bit-error probability</a> of bit operation.<a href="#cite_note-Kish_2014-40">[39]</a> Consequently, there is always a lower limit of energy requirement – depending on the required <a href="/wiki/Bit_error_rate" title="Bit error rate">bit-error probability</a> – for intentionally changing a bit value in any memory device.<a href="#cite_note-Kish_2014-40">[39]</a><a href="#cite_note-Kish_2015-41">[40]</a> In the general concept of memristive system the defining equations are (see <a href="#Theory">§ Theory</a>): <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}y(t)&=g(\mathbf {x} ,u,t)u(t),\\{\dot {\mathbf {x} }}&=f(\mathbf {x} ,u,t),\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y(t)&=g(\mathbf {x} ,u,t)u(t),\\{\dot {\mathbf {x} }}&=f(\mathbf {x} ,u,t),\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3eb0482fb035232369677e2d157ac4074123699b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.853ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}y(t)&=g(\mathbf {x} ,u,t)u(t),\\{\dot {\mathbf {x} }}&=f(\mathbf {x} ,u,t),\end{aligned}}}"> where u(t) is an input signal, and y(t) is an output signal. The vector <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32adf004df5eb0a8c7fd8c0b6b7405183c5a5ef2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {x} }"> represents a set of n state variables describing the different internal memory states of the device. <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\mathbf {x} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\mathbf {x} }}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fce8ab3723fe7f431534391268cdaa9010b2ede3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:2.176ex;" alt="{\displaystyle {\dot {\mathbf {x} }}}"> is the time-dependent rate of change of the state vector <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32adf004df5eb0a8c7fd8c0b6b7405183c5a5ef2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {x} }"> with time. When one wants to go beyond mere <a href="/wiki/Curve_fitting" title="Curve fitting">curve fitting</a> and aims at a real physical modeling of non-volatile memory elements, e.g., <a href="/wiki/Resistive_random-access_memory" title="Resistive random-access memory">resistive random-access memory</a> devices, one has to keep an eye on the aforementioned physical correlations. To check the adequacy of the proposed model and its resulting state equations, the input signal u(t) can be superposed with a stochastic term ξ(t), which takes into account the existence of inevitable <a href="/wiki/Thermal_fluctuations" title="Thermal fluctuations">thermal fluctuations</a>. The dynamic state equation in its general form then finally reads: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\mathbf {x} }}=f(\mathbf {x} ,u(t)+\xi (t),t),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\mathbf {x} }}=f(\mathbf {x} ,u(t)+\xi (t),t),}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfbdffb087463be2785af07c96676857c438b859" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.061ex; height:2.843ex;" alt="{\displaystyle {\dot {\mathbf {x} }}=f(\mathbf {x} ,u(t)+\xi (t),t),}"> where ξ(t) is, e.g., white <a href="/wiki/Gaussian_noise" title="Gaussian noise">Gaussian</a> <a href="/wiki/Noise_(electronics)" title="Noise (electronics)">current or voltage noise</a>. On the basis of an analytical or numerical analysis of the time-dependent response of the system towards noise, a decision on the physical validity of the modeling approach can be made, e.g., whether the system would be able to retain its memory states in power-off mode. Such an analysis was performed by Di Ventra and Pershin<a href="#cite_note-DiVentra_2013-23">[22]</a> with regard to the genuine current-controlled memristor. As the proposed dynamic state equation provides no physical mechanism enabling such a memristor to cope with inevitable thermal fluctuations, a current-controlled memristor would erratically change its state in course of time just under the influence of current noise.<a href="#cite_note-DiVentra_2013-23">[22]</a><a href="#cite_note-Slipko_2013-42">[41]</a> Di Ventra and Pershin<a href="#cite_note-DiVentra_2013-23">[22]</a> thus concluded that memristors whose resistance (memory) states depend solely on the current or voltage history would be unable to protect their memory states against unavoidable <a href="/wiki/Johnson%E2%80%93Nyquist_noise" title="Johnson–Nyquist noise">Johnson–Nyquist noise</a> and permanently suffer from information loss, a so-called "stochastic catastrophe". A current-controlled memristor can thus not exist as a solid-state device in physical reality. The above-mentioned thermodynamic principle furthermore implies that the operation of two-terminal non-volatile memory devices (e.g. "resistance-switching" memory devices (<a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>)) cannot be associated with the memristor concept, i.e., such devices cannot by itself remember their current or voltage history. Transitions between distinct internal memory or resistance states are of <a href="/wiki/Probability" title="Probability">probabilistic</a> nature. The probability for a transition from state {i} to state {j} depends on the height of the free-energy barrier between both states. The transition probability can thus be influenced by suitably driving the memory device, i.e., by "lowering" the free-energy barrier for the transition {i}→{j} by means of, for example, an externally applied bias. A "resistance switching" event can simply be enforced by setting the external bias to a value above a certain threshold value. This is the trivial case, i.e., the free-energy barrier for the transition {i}→{j} is reduced to zero. In case one applies biases below the threshold value, there is still a finite probability that the device will switch in course of time (triggered by a random thermal fluctuation), but – as one is dealing with probabilistic processes – it is impossible to predict when the switching event will occur. That is the basic reason for the stochastic nature of all observed resistance-switching (<a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>) processes. If the free-energy barriers are not high enough, the memory device can even switch without having to do anything. When a two-terminal non-volatile memory device is found to be in a distinct resistance state {j} , there exists therefore no physical one-to-one relationship between its present state and its foregoing voltage history. The switching behavior of individual non-volatile memory devices thus cannot be described within the mathematical framework proposed for memristor/memristive systems. An extra thermodynamic curiosity arises from the definition that memristors/memristive devices should energetically act like resistors. The instantaneous electrical power entering such a device is completely dissipated as <a href="/wiki/Joule_heating" title="Joule heating">Joule heat</a> to the surrounding, so no extra energy remains in the system after it has been brought from one resistance state xi to another one xj. Thus, the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of the memristor device in state xi, U(V, T, xi), would be the same as in state xj, U(V, T, xj), even though these different states would give rise to different device's resistances, which itself must be caused by physical alterations of the device's material. Other researchers noted that memristor models based on the assumption of linear <a href="/wiki/Ionic_mobility" class="mw-redirect" title="Ionic mobility">ionic drift</a> do not account for asymmetry between set time (high-to-low resistance switching) and reset time (low-to-high resistance switching) and do not provide ionic mobility values consistent with experimental data. Non-linear ionic-drift models have been proposed to compensate for this deficiency.<a href="#cite_note-Mitre_2012-43">[42]</a> A 2014 article from researchers of <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a> concluded that Strukov's (HP's) initial/basic memristor modeling equations do not reflect the actual device physics well, whereas subsequent (physics-based) models such as Pickett's model or Menzel's ECM model (Menzel is a co-author of that article) have adequate predictability, but are computationally prohibitive. As of 2014, the search continues for a model that balances these issues; the article identifies Chang's and Yakopcic's models as potentially good compromises.<a href="#cite_note-E._Linn_et_al-44">[43]</a> Martin Reynolds, an electrical engineering analyst with research outfit <a href="/wiki/Gartner" title="Gartner">Gartner</a>, commented that while HP was being sloppy in calling their device a memristor, critics were being pedantic in saying that it was not a memristor.<a href="#cite_note-Martin_Reynolds-45">[44]</a> <div class="mw-heading mw-heading3"><h3 id="Experimental_tests">Experimental tests</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=7" title="Edit section: Experimental tests">edit</a>]</div> <a href="/wiki/Leon_Chua" class="mw-redirect" title="Leon Chua">Chua</a> suggested experimental tests to determine if a device may properly be categorized as a memristor:<a href="#cite_note-chua76-2">[2]</a> <ul><li>The <a href="/wiki/Lissajous_curve" title="Lissajous curve">Lissajous curve</a> in the voltage–current plane is a pinched <a href="/wiki/Hysteresis" title="Hysteresis">hysteresis</a> loop when driven by any bipolar periodic voltage or current without respect to initial conditions.</li> <li>The area of each lobe of the pinched hysteresis loop shrinks as the frequency of the forcing signal increases.</li> <li>As the frequency tends to infinity, the hysteresis loop degenerates to a straight line through the origin, whose slope depends on the amplitude and shape of the forcing signal.</li></ul> According to Chua<a href="#cite_note-MemristorExperimentalTests-46">[45]</a><a href="#cite_note-MemristorExperimentalTests2-47">[46]</a> all resistive switching memories including <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>, <a href="/wiki/Magnetoresistive_RAM" title="Magnetoresistive RAM">MRAM</a> and <a href="/wiki/Phase-change_memory" title="Phase-change memory">phase-change memory</a> meet these criteria and are memristors. However, the lack of data for the Lissajous curves over a range of initial conditions or over a range of frequencies complicates assessments of this claim. Experimental evidence shows that redox-based resistance memory (<a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>) includes a <a href="/wiki/Nanobatteries" title="Nanobatteries">nanobattery</a> effect that is contrary to Chua's memristor model. This indicates that the memristor theory needs to be extended or corrected to enable accurate ReRAM modeling.<a href="#cite_note-memristor_nanobattery-26">[25]</a> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=8" title="Edit section: Theory">edit</a>]</div> In 2008, researchers from <a href="/wiki/HP_Labs" title="HP Labs">HP Labs</a> introduced a model for a memristance function based on thin films of <a href="/wiki/Titanium_dioxide" title="Titanium dioxide">titanium dioxide</a>.<a href="#cite_note-Williams08-18">[17]</a> For Ron ≪ Roff the memristance function was determined to be <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M(q(t))=R_{\mathrm {off} }\cdot \left(1-{\frac {\mu _{v}R_{\mathrm {on} }}{D^{2}}}q(t)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mrow> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M(q(t))=R_{\mathrm {off} }\cdot \left(1-{\frac {\mu _{v}R_{\mathrm {on} }}{D^{2}}}q(t)\right)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7060d65101744cc5471c35f27dbdd6eed621c1dc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.931ex; height:6.176ex;" alt="{\displaystyle M(q(t))=R_{\mathrm {off} }\cdot \left(1-{\frac {\mu _{v}R_{\mathrm {on} }}{D^{2}}}q(t)\right)}"> where Roff represents the high resistance state, Ron represents the low resistance state, μv represents the mobility of dopants in the thin film, and D represents the film thickness. The HP Labs group noted that "window functions" were necessary to compensate for differences between experimental measurements and their memristor model due to non-linear ionic drift and boundary effects. <div class="mw-heading mw-heading3"><h3 id="Operation_as_a_switch">Operation as a switch</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=9" title="Edit section: Operation as a switch">edit</a>]</div> For some memristors, applied current or voltage causes substantial change in resistance. Such devices may be characterized as switches by investigating the time and energy that must be spent to achieve a desired change in resistance. This assumes that the applied voltage remains constant. Solving for energy dissipation during a single switching event reveals that for a memristor to switch from Ron to Roff in time Ton to Toff, the charge must change by ΔQ = Qon − Qoff. <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}E_{\mathrm {switch} }&=V^{2}\int _{T_{\mathrm {off} }}^{T_{\mathrm {on} }}{\frac {\mathrm {d} t}{M(q(t))}}\\&=V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{I(q)M(q)}}\\&=V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{V(q)}}\\&=V\Delta Q\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">h</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> <mrow> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> </mrow> <mrow> <mi>I</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mi>M</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> </mrow> <mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>V</mi> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}E_{\mathrm {switch} }&=V^{2}\int _{T_{\mathrm {off} }}^{T_{\mathrm {on} }}{\frac {\mathrm {d} t}{M(q(t))}}\\&=V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{I(q)M(q)}}\\&=V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{V(q)}}\\&=V\Delta Q\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83a4f653e2941423dd5e60f28cca4aaf596b3995" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -11.171ex; width:29.896ex; height:23.509ex;" alt="{\displaystyle {\begin{aligned}E_{\mathrm {switch} }&=V^{2}\int _{T_{\mathrm {off} }}^{T_{\mathrm {on} }}{\frac {\mathrm {d} t}{M(q(t))}}\\&=V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{I(q)M(q)}}\\&=V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{V(q)}}\\&=V\Delta Q\end{aligned}}}"> Substituting V = I(q)M(q), and then ∫ dq/V = ∆Q/V for constant V to produces the final expression. This power characteristic differs fundamentally from that of a <a href="/wiki/Metal_oxide_semiconductor" class="mw-redirect" title="Metal oxide semiconductor">metal oxide semiconductor</a> <a href="/wiki/Transistor" title="Transistor">transistor</a>, which is capacitor-based. Unlike the transistor, the final state of the memristor in terms of charge does not depend on bias voltage. The type of memristor described by Williams ceases to be ideal after switching over its entire resistance range, creating <a href="/wiki/Hysteresis" title="Hysteresis">hysteresis</a>, also called the "hard-switching regime".<a href="#cite_note-Williams08-18">[17]</a> Another kind of switch would have a cyclic M(q) so that each off-on event would be followed by an on-off event under constant bias. Such a device would act as a memristor under all conditions, but would be less practical. <div class="mw-heading mw-heading3"><h3 id="Memristive_systems">Memristive systems</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=10" title="Edit section: Memristive systems">edit</a>]</div> In the more general concept of an n-th order memristive system the defining equations are <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}y(t)&=g({\textbf {x}},u,t)u(t),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u,t)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y(t)&=g({\textbf {x}},u,t)u(t),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u,t)\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/783a4ac19fa5bb889d478ebcfe31b3dc993613f6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.853ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}y(t)&=g({\textbf {x}},u,t)u(t),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u,t)\end{aligned}}}"> where u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and g and f are <a href="/wiki/Continuous_functions" class="mw-redirect" title="Continuous functions">continuous functions</a>. For a current-controlled memristive system the signal u(t) represents the current signal i(t) and the signal y(t) represents the voltage signal v(t). For a voltage-controlled memristive system the signal u(t) represents the voltage signal v(t) and the signal y(t) represents the current signal i(t). The pure memristor is a particular case of these equations, namely when x depends only on charge (x = q) and since the charge is related to the current via the time derivative dq/dt = i(t). Thus for pure memristors f (i.e. the rate of change of the state) must be equal or proportional to the current i(t). <div class="mw-heading mw-heading3"><h3 id="Pinched_hysteresis">Pinched hysteresis</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=11" title="Edit section: Pinched hysteresis">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pinched_crossing_hysteresis.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Pinched_crossing_hysteresis.png/220px-Pinched_crossing_hysteresis.png" decoding="async" width="220" height="143" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/0c/Pinched_crossing_hysteresis.png 1.5x" data-file-width="302" data-file-height="196" /></a><figcaption>Example of pinched hysteresis curve, V versus I</figcaption></figure> One of the resulting properties of memristors and memristive systems is the existence of a pinched <a href="/wiki/Hysteresis" title="Hysteresis">hysteresis</a> effect.<a href="#cite_note-DiVentraPershin2011-48">[47]</a> For a current-controlled memristive system, the input u(t) is the current i(t), the output y(t) is the voltage v(t), and the slope of the curve represents the electrical resistance. The change in slope of the pinched hysteresis curves demonstrates switching between different resistance states which is a phenomenon central to <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a> and other forms of two-terminal resistance memory. At high frequencies, memristive theory predicts the pinched hysteresis effect will degenerate, resulting in a straight line representative of a linear resistor. It has been proven that some types of non-crossing pinched hysteresis curves (denoted Type-II) cannot be described by memristors.<a href="#cite_note-Biolek2011-49">[48]</a> <div class="mw-heading mw-heading3"><h3 id="Memristive_networks_and_mathematical_models_of_circuit_interactions">Memristive networks and mathematical models of circuit interactions</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=12" title="Edit section: Memristive networks and mathematical models of circuit interactions">edit</a>]</div> The concept of memristive networks was first introduced by Leon Chua in his 1965 paper "Memristive Devices and Systems." Chua proposed the use of memristive devices as a means of building artificial neural networks that could simulate the behavior of the human brain. In fact, memristive devices in circuits have complex interactions due to Kirchhoff's laws. A memristive network is a type of artificial neural network that is based on memristive devices, which are electronic components that exhibit the property of memristance. In a memristive network, the memristive devices are used to simulate the behavior of neurons and synapses in the human brain. The network consists of layers of memristive devices, each of which is connected to other layers through a set of weights. These weights are adjusted during the training process, allowing the network to learn and adapt to new input data. One advantage of memristive networks is that they can be implemented using relatively simple and inexpensive hardware, making them an attractive option for developing low-cost artificial intelligence systems. They also have the potential to be more energy efficient than traditional artificial neural networks, as they can store and process information using less power. However, the field of memristive networks is still in the early stages of development, and more research is needed to fully understand their capabilities and limitations. For the simplest model with only memristive devices with voltage generators in series, there is an exact and in closed form equation (<a href="/wiki/Caravelli-Traversa-Di_Ventra_equation" title="Caravelli-Traversa-Di Ventra equation">Caravelli–Traversa–Di Ventra equation</a>, CTDV)<a href="#cite_note-50">[49]</a> which describes the evolution of the internal memory of the network for each device. For a simple memristor model (but not realistic) of a switch between two resistance values, given by the Williams-Strukov model <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R(x)=R_{off}(1-x)+R_{on}x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>n</mi> </mrow> </msub> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R(x)=R_{off}(1-x)+R_{on}x}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/971a2bea93def4d901f39ef68bf812539df58d3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.695ex; height:3.009ex;" alt="{\displaystyle R(x)=R_{off}(1-x)+R_{on}x}">, with <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dx/dt=I/\beta -\alpha x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>β</mi> <mo>−</mo> <mi>α</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx/dt=I/\beta -\alpha x}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c44a625ab56c0df067efb4788110b4c9235ae6fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.186ex; height:2.843ex;" alt="{\displaystyle dx/dt=I/\beta -\alpha x}">, there is a set of nonlinearly coupled differential equations that takes the form: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d{\vec {x}}}{dt}}=-\alpha {\vec {x}}+{\frac {1}{\beta }}(I-\chi \Omega X)^{-1}\Omega {\vec {S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>β</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>I</mi> <mo>−</mo> <mi>χ</mi> <mi mathvariant="normal">Ω</mi> <mi>X</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d{\vec {x}}}{dt}}=-\alpha {\vec {x}}+{\frac {1}{\beta }}(I-\chi \Omega X)^{-1}\Omega {\vec {S}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f8f1d3088cb456d246d646dc97fe050f1bc401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.598ex; height:5.843ex;" alt="{\displaystyle {\frac {d{\vec {x}}}{dt}}=-\alpha {\vec {x}}+{\frac {1}{\beta }}(I-\chi \Omega X)^{-1}\Omega {\vec {S}}}"></dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"> is the diagonal matrix with elements <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}"> on the diagonal, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ,\beta ,\chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ,\beta ,\chi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e96a1425ab129ea3d883276563102044ae5c344f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.343ex; height:2.509ex;" alt="{\displaystyle \alpha ,\beta ,\chi }"> are based on the memristors physical parameters. The vector <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {S}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c71a6b104c40975c738d5f0e22d445ebd509eb81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.538ex; height:3.009ex;" alt="{\displaystyle {\vec {S}}}"> is the vector of voltage generators in series to the memristors. The circuit topology enters only in the projector operator <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega ^{2}=\Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega ^{2}=\Omega }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b3b54e74f9031fe9986bc3834ad73d29723caa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.509ex; height:2.676ex;" alt="{\displaystyle \Omega ^{2}=\Omega }">, defined in terms of the cycle matrix of the graph. The equation provides a concise mathematical description of the interactions due to Kirchhoff 's laws. Interestingly, the equation shares many properties in common with a <a href="/wiki/Hopfield_network" title="Hopfield network">Hopfield network</a>, such as the existence of Lyapunov functions and classical tunnelling phenomena.<a href="#cite_note-51">[50]</a> In the context of memristive networks, the CTD equation may be used to predict the behavior of memristive devices under different operating conditions, or to design and optimize memristive circuits for specific applications. <div class="mw-heading mw-heading3"><h3 id="Extended_systems">Extended systems</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=13" title="Edit section: Extended systems">edit</a>]</div> Some researchers have raised the question of the scientific legitimacy of HP's memristor models in explaining the behavior of <a href="/wiki/ReRAM" class="mw-redirect" title="ReRAM">ReRAM</a>.<a href="#cite_note-Clarke2012-37">[36]</a><a href="#cite_note-PaulMarks2012-38">[37]</a> and have suggested extended memristive models to remedy perceived deficiencies.<a href="#cite_note-memristor_nanobattery-26">[25]</a> One example<a href="#cite_note-memresistor-52">[51]</a> attempts to extend the memristive systems framework by including dynamic systems incorporating higher-order derivatives of the input signal u(t) as a series expansion <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)u(t)+g_{1}({\textbf {x}},u){\operatorname {d} ^{2}u \over \operatorname {d} t^{2}}+g_{2}({\textbf {x}},u){\operatorname {d} ^{4}u \over \operatorname {d} t^{4}}+\ldots +g_{m}({\textbf {x}},u){\operatorname {d} ^{2m}u \over \operatorname {d} t^{2m}},\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>⁡</mo> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>…</mo> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>m</mi> </mrow> </msup> <mo>⁡</mo> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)u(t)+g_{1}({\textbf {x}},u){\operatorname {d} ^{2}u \over \operatorname {d} t^{2}}+g_{2}({\textbf {x}},u){\operatorname {d} ^{4}u \over \operatorname {d} t^{4}}+\ldots +g_{m}({\textbf {x}},u){\operatorname {d} ^{2m}u \over \operatorname {d} t^{2m}},\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e25128f3a4a38cede40af83ab0acc65a51aeff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.681ex; margin-bottom: -0.324ex; width:74.116ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)u(t)+g_{1}({\textbf {x}},u){\operatorname {d} ^{2}u \over \operatorname {d} t^{2}}+g_{2}({\textbf {x}},u){\operatorname {d} ^{4}u \over \operatorname {d} t^{4}}+\ldots +g_{m}({\textbf {x}},u){\operatorname {d} ^{2m}u \over \operatorname {d} t^{2m}},\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}"></dd></dl> where m is a positive integer, u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and the functions g and f are <a href="/wiki/Continuous_function" title="Continuous function">continuous functions</a>. This equation produces the same zero-crossing hysteresis curves as memristive systems but with a different <a href="/wiki/Frequency_response" title="Frequency response">frequency response</a> than that predicted by memristive systems. Another example suggests including an offset value <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"> to account for an observed nanobattery effect which violates the predicted zero-crossing pinched hysteresis effect.<a href="#cite_note-memristor_nanobattery-26">[25]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)(u(t)-a),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">x</mtext> </mrow> </mrow> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)(u(t)-a),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d63c91907666526775ed2924a48c922e884396b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.906ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)(u(t)-a),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}"></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Implementation_of_hysteretic_current-voltage_memristors">Implementation of hysteretic current-voltage memristors</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=14" title="Edit section: Implementation of hysteretic current-voltage memristors">edit</a>]</div> There exist implementations of memristors with a hysteretic current-voltage curve or with both hysteretic current-voltage curve and hysteretic flux-charge curve [arXiv:2403.20051]. Memristors with hysteretic current-voltage curve use a resistance dependent on the history of the current and voltage and bode well for the future of memory technology due to their simple structure, high energy efficiency, and high integration [DOI: 10.1002/aisy.202200053]. <div class="mw-heading mw-heading3"><h3 id="Titanium_dioxide_memristor">Titanium dioxide memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=15" title="Edit section: Titanium dioxide memristor">edit</a>]</div> Interest in the memristor revived when an experimental solid-state version was reported by <a href="/wiki/R._Stanley_Williams" title="R. Stanley Williams">R. Stanley Williams</a> of <a href="/wiki/Hewlett_Packard" class="mw-redirect" title="Hewlett Packard">Hewlett Packard</a> in 2007.<a href="#cite_note-53">[52]</a><a href="#cite_note-54">[53]</a><a href="#cite_note-55">[54]</a> The article was the first to demonstrate that a solid-state device could have the characteristics of a memristor based on the behavior of <a href="/wiki/Nanoscopic_scale" class="mw-redirect" title="Nanoscopic scale">nanoscale</a> thin films. The device neither uses magnetic flux as the theoretical memristor suggested, nor stores charge as a capacitor does, but instead achieves a resistance dependent on the history of current. Although not cited in HP's initial reports on their <a href="/wiki/TiO2" class="mw-redirect" title="TiO2">TiO2</a> memristor, the resistance switching characteristics of titanium dioxide were originally described in the 1960s.<a href="#cite_note-Argall1968-56">[55]</a> The HP device is composed of a thin (50 <a href="/wiki/Nanometer" class="mw-redirect" title="Nanometer">nm</a>) <a href="/wiki/Titanium_dioxide" title="Titanium dioxide">titanium dioxide</a> film between two 5 nm thick <a href="/wiki/Electrode" title="Electrode">electrodes</a>, one <a href="/wiki/Titanium" title="Titanium">titanium</a>, the other <a href="/wiki/Platinum" title="Platinum">platinum</a>. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> atoms. The oxygen vacancies act as <a href="/wiki/Charge_carrier" title="Charge carrier">charge carriers</a>, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift (see <a href="/wiki/Fast-ion_conductor" title="Fast-ion conductor">Fast-ion conductor</a>), changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current.<a href="#cite_note-Williams08-18">[17]</a> Since the HP device displays fast-ion conduction at nanoscale, it is considered a <a href="/wiki/Nanoionic_device" class="mw-redirect" title="Nanoionic device">nanoionic device</a>.<a href="#cite_note-Terabe2007-57">[56]</a> Memristance is displayed only when both the doped layer and depleted layer contribute to resistance. When enough charge has passed through the memristor that the ions can no longer move, the device enters <a href="/wiki/Hysteresis" title="Hysteresis">hysteresis</a>. It ceases to integrate q=∫I dt, but rather keeps q at an upper bound and M fixed, thus acting as a constant resistor until current is reversed. Memory applications of thin-film oxides had been an area of active investigation for some time. <a href="/wiki/IBM" title="IBM">IBM</a> published an article in 2000 regarding structures similar to that described by Williams.<a href="#cite_note-Beck2000-58">[57]</a> <a href="/wiki/Samsung" title="Samsung">Samsung</a> has a U.S. patent for oxide-vacancy based switches similar to that described by Williams.<a href="#cite_note-59">[58]</a> In April 2010, HP labs announced that they had practical memristors working at 1 <a href="/wiki/Nanosecond" title="Nanosecond">ns</a> (~1 GHz) switching times and 3 nm by 3 nm sizes,<a href="#cite_note-60">[59]</a> which bodes well for the future of the technology.<a href="#cite_note-61">[60]</a> At these densities it could easily rival the current sub-25 nm <a href="/wiki/Flash_memory" title="Flash memory">flash memory</a> technology. <div class="mw-heading mw-heading3"><h3 id="Silicon_dioxide_memristor">Silicon dioxide memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=16" title="Edit section: Silicon dioxide memristor">edit</a>]</div> It seems that memristance has been reported in <a href="/wiki/Nanoscale" class="mw-redirect" title="Nanoscale">nanoscale</a> thin films of silicon dioxide as early as the 1960s .<a href="#cite_note-62">[61]</a> However, hysteretic conductance in silicon was associated to memristive effects only in 2009.<a href="#cite_note-63">[62]</a> More recently, beginning in 2012, Tony Kenyon, Adnan Mehonic and their group clearly demonstrated that the resistive switching in silicon oxide thin films is due to the formation of oxygen vacancy filaments in defect-engineered silicon dioxide, having probed directly the movement of oxygen under electrical bias, and imaged the resultant conductive filaments using conductive atomic force microscopy. <a href="#cite_note-64">[63]</a> <div class="mw-heading mw-heading3"><h3 id="Polymeric_memristor">Polymeric memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=17" title="Edit section: Polymeric memristor">edit</a>]</div> In 2004, Krieger and Spitzer described dynamic doping of polymer and inorganic dielectric-like materials that improved the switching characteristics and retention required to create functioning nonvolatile memory cells.<a href="#cite_note-65">[64]</a> They used a passive layer between electrode and active thin films, which enhanced the extraction of ions from the electrode. It is possible to use <a href="/wiki/Fast-ion_conductor" title="Fast-ion conductor">fast-ion conductor</a> as this passive layer, which allows a significant reduction of the ionic extraction field. In July 2008, Erokhin and Fontana claimed to have developed a polymeric memristor before the more recently announced titanium dioxide memristor.<a href="#cite_note-Erokhin2008-66">[65]</a> In 2010, Alibart, Gamrat, Vuillaume et al.<a href="#cite_note-67">[66]</a> introduced a new hybrid organic/<a href="/wiki/Nanoparticle" title="Nanoparticle">nanoparticle</a> device (the <a href="/wiki/NOMFET" title="NOMFET">NOMFET</a> : Nanoparticle Organic Memory Field Effect Transistor), which behaves as a memristor<a href="#cite_note-68">[67]</a> and which exhibits the main behavior of a biological spiking synapse. This device, also called a synapstor (synapse transistor), was used to demonstrate a neuro-inspired circuit (associative memory showing a pavlovian learning).<a href="#cite_note-69">[68]</a> In 2012, Crupi, Pradhan and Tozer described a proof of concept design to create neural synaptic memory circuits using organic ion-based memristors.<a href="#cite_note-70">[69]</a> The synapse circuit demonstrated <a href="/wiki/Long-term_potentiation" title="Long-term potentiation">long-term potentiation</a> for learning as well as inactivity based forgetting. Using a grid of circuits, a pattern of light was stored and later recalled. This mimics the behavior of the V1 neurons in the <a href="/wiki/Primary_visual_cortex" class="mw-redirect" title="Primary visual cortex">primary visual cortex</a> that act as spatiotemporal filters that process visual signals such as edges and moving lines. In 2012, Erokhin and co-authors have demonstrated a stochastic three-dimensional matrix with capabilities for learning and adapting based on polymeric memristor.<a href="#cite_note-71">[70]</a> <div class="mw-heading mw-heading3"><h3 id="Layered_memristor">Layered memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=18" title="Edit section: Layered memristor">edit</a>]</div> In 2014, Bessonov et al. reported a flexible memristive device comprising a <a href="/wiki/Molybdenum_oxide" title="Molybdenum oxide">MoOx</a>/<a href="/wiki/MoS2" class="mw-redirect" title="MoS2">MoS2</a> heterostructure sandwiched between silver electrodes on a plastic foil.<a href="#cite_note-flexible_memristor-72">[71]</a> The fabrication method is entirely based on printing and solution-processing technologies using two-dimensional layered <a href="/wiki/Transition_metal_dichalcogenides" class="mw-redirect" title="Transition metal dichalcogenides">transition metal dichalcogenides</a> (TMDs). The memristors are mechanically flexible, <a href="/wiki/Transparency_and_translucency" title="Transparency and translucency">optically transparent</a> and produced at low cost. The memristive behaviour of switches was found to be accompanied by a prominent memcapacitive effect. High switching performance, demonstrated synaptic plasticity and sustainability to mechanical deformations promise to emulate the appealing characteristics of biological neural systems in novel computing technologies. <div class="mw-heading mw-heading3"><h3 id="Atomristor">Atomristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=19" title="Edit section: Atomristor">edit</a>]</div> Atomristor is defined as the electrical devices showing memristive behavior in atomically thin <a href="/wiki/Nanomaterials" title="Nanomaterials">nanomaterials</a> or atomic sheets. In 2018, Ge and Wu et al.<a href="#cite_note-73">[72]</a> in the <a href="/wiki/Deji_Akinwande" title="Deji Akinwande">Akinwande</a> group at the University of Texas, first reported a universal memristive effect in single-layer <a href="/wiki/Transition_metal_dichalcogenide_monolayers" title="Transition metal dichalcogenide monolayers">TMD</a> (MX2, M = Mo, W; and X = S, Se) atomic sheets based on vertical <a href="/wiki/Metal-insulator-metal" class="mw-redirect" title="Metal-insulator-metal">metal-insulator-metal</a> (MIM) device structure. The work was later extended to monolayer <a href="/wiki/Boron_nitride" title="Boron nitride">hexagonal boron nitride</a>, which is the thinnest memory material of around 0.33 nm.<a href="#cite_note-74">[73]</a> These atomristors offer forming-free switching and both unipolar and bipolar operation. The switching behavior is found in single-crystalline and poly-crystalline films, with various conducting electrodes (gold, silver and graphene). Atomically thin TMD sheets are prepared via <a href="/wiki/Chemical_vapor_deposition" title="Chemical vapor deposition">CVD</a>/<a href="/wiki/MOCVD" class="mw-redirect" title="MOCVD">MOCVD</a>, enabling low-cost fabrication. Afterwards, taking advantage of the low "on" resistance and large on/off ratio, a high-performance zero-power <a href="/wiki/RF_switch" title="RF switch">RF switch</a> is proved based on MoS2 or h-BN atomristors, indicating a new application of memristors for <a href="/wiki/5G" title="5G">5G</a>, <a href="/wiki/6G_(network)" class="mw-redirect" title="6G (network)">6G</a> and THz communication and connectivity systems.<a href="#cite_note-75">[74]</a><a href="#cite_note-76">[75]</a> In 2020, atomistic understanding of the conductive virtual point mechanism was elucidated in an article in nature nanotechnology.<a href="#cite_note-77">[76]</a> <div class="mw-heading mw-heading3"><h3 id="Ferroelectric_memristor">Ferroelectric memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=20" title="Edit section: Ferroelectric memristor">edit</a>]</div> The <a href="/wiki/Ferroelectric" class="mw-redirect" title="Ferroelectric">ferroelectric</a> memristor<a href="#cite_note-78">[77]</a> is based on a thin ferroelectric barrier sandwiched between two metallic electrodes. Switching the polarization of the <a href="/wiki/Ferroelectric" class="mw-redirect" title="Ferroelectric">ferroelectric</a> material by applying a positive or negative voltage across the junction can lead to a two order of magnitude resistance variation: ROFF ≫ RON (an effect called Tunnel Electro-Resistance). In general, the polarization does not switch abruptly. The reversal occurs gradually through the nucleation and growth of ferroelectric domains with opposite polarization. During this process, the resistance is neither RON or ROFF, but in between. When the voltage is cycled, the ferroelectric domain configuration evolves, allowing a fine tuning of the resistance value. The ferroelectric memristor's main advantages are that ferroelectric domain dynamics can be tuned, offering a way to engineer the memristor response, and that the resistance variations are due to purely electronic phenomena, aiding device reliability, as no deep change to the material structure is involved. <div class="mw-heading mw-heading3"><h3 id="Carbon_nanotube_memristor">Carbon nanotube memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=21" title="Edit section: Carbon nanotube memristor">edit</a>]</div> In 2013, Ageev, Blinov et al.<a href="#cite_note-Rubashkina2013-79">[78]</a> reported observing memristor effect in structure based on vertically aligned carbon nanotubes studying bundles of CNT by <a href="/wiki/Scanning_tunneling_microscope" title="Scanning tunneling microscope">scanning tunneling microscope</a>. Later it was found<a href="#cite_note-80">[79]</a> that CNT memristive switching is observed when a nanotube has a non-uniform elastic strain ΔL0. It was shown that the memristive switching mechanism of strained СNT is based on the formation and subsequent redistribution of non-uniform elastic strain and piezoelectric field Edef in the nanotube under the influence of an external electric field E(x,t). <div class="mw-heading mw-heading3"><h3 id="Biomolecular_memristor">Biomolecular memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=22" title="Edit section: Biomolecular memristor">edit</a>]</div> Biomaterials have been evaluated for use in artificial synapses and have shown potential for application in neuromorphic systems.<a href="#cite_note-81">[80]</a> In particular, the feasibility of using a collagen‐based biomemristor as an artificial synaptic device has been investigated,<a href="#cite_note-82">[81]</a> whereas a synaptic device based on lignin demonstrated rising or lowering current with consecutive voltage sweeps depending on the sign of the voltage<a href="#cite_note-83">[82]</a> furthermore a natural silk fibroin demonstrated memristive properties;<a href="#cite_note-84">[83]</a> spin-memristive systems based on biomolecules are also being studied.<a href="#cite_note-85">[84]</a> In 2012, <a href="/wiki/Sandro_Carrara" title="Sandro Carrara">Sandro Carrara</a> and co-authors have proposed the first biomolecular memristor with aims to realize highly sensitive biosensors.<a href="#cite_note-86">[85]</a> Since then, several memristive <a href="/wiki/Sensors" class="mw-redirect" title="Sensors">sensors</a> have been demonstrated.<a href="#cite_note-87">[86]</a> <div class="mw-heading mw-heading3"><h3 id="Spin_memristive_systems">Spin memristive systems</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=23" title="Edit section: Spin memristive systems">edit</a>]</div> <div class="mw-heading mw-heading4"><h4 id="Spintronic_memristor">Spintronic memristor</h4>[<a href="/w/index.php?title=Memristor&action=edit&section=24" title="Edit section: Spintronic memristor">edit</a>]</div> Chen and Wang, researchers at disk-drive manufacturer <a href="/wiki/Seagate_Technology" title="Seagate Technology">Seagate Technology</a> described three examples of possible magnetic memristors.<a href="#cite_note-Xiaobin2009-88">[87]</a> In one device resistance occurs when the spin of electrons in one section of the device points in a different direction from those in another section, creating a "domain wall", a boundary between the two sections. Electrons flowing into the device have a certain spin, which alters the device's magnetization state. Changing the magnetization, in turn, moves the domain wall and changes the resistance. The work's significance led to an interview by <a href="/wiki/IEEE_Spectrum" title="IEEE Spectrum">IEEE Spectrum</a>.<a href="#cite_note-Neil2009-89">[88]</a> A first experimental proof of the <a href="/wiki/Spintronic" class="mw-redirect" title="Spintronic">spintronic</a> memristor based on domain wall motion by spin currents in a magnetic tunnel junction was given in 2011.<a href="#cite_note-Chanthbouala2011-90">[89]</a> <div class="mw-heading mw-heading4"><h4 id="Memristance_in_a_magnetic_tunnel_junction">Memristance in a magnetic tunnel junction</h4>[<a href="/w/index.php?title=Memristor&action=edit&section=25" title="Edit section: Memristance in a magnetic tunnel junction">edit</a>]</div> The <a href="/wiki/Magnetic_tunnel_junction" class="mw-redirect" title="Magnetic tunnel junction">magnetic tunnel junction</a> has been proposed to act as a memristor through several potentially complementary mechanisms, both extrinsic (redox reactions, charge trapping/detrapping and electromigration within the barrier) and intrinsic (<a href="/wiki/Spin-transfer_torque" title="Spin-transfer torque">spin-transfer torque</a>). <div class="mw-heading mw-heading5"><h5 id="Extrinsic_mechanism">Extrinsic mechanism</h5>[<a href="/w/index.php?title=Memristor&action=edit&section=26" title="Edit section: Extrinsic mechanism">edit</a>]</div> Based on research performed between 1999 and 2003, Bowen et al. published experiments in 2006 on a <a href="/wiki/Magnetic_tunnel_junction" class="mw-redirect" title="Magnetic tunnel junction">magnetic tunnel junction</a> (MTJ) endowed with bi-stable spin-dependent states<a href="#cite_note-BowenAPL2006-91">[90]</a>(<a href="/wiki/Resistive_random-access_memory" title="Resistive random-access memory">resistive switching</a>). The MTJ consists in a SrTiO3 (STO) tunnel barrier that separates <a href="/wiki/Half-metal" title="Half-metal">half-metallic oxide</a> LSMO and ferromagnetic metal CoCr electrodes. The MTJ's usual two device resistance states, characterized by a parallel or antiparallel alignment of electrode magnetization, are altered by applying an electric field. When the electric field is applied from the CoCr to the LSMO electrode, the <a href="/wiki/Tunnel_magnetoresistance" title="Tunnel magnetoresistance">tunnel magnetoresistance</a> (TMR) ratio is positive. When the direction of electric field is reversed, the TMR is negative. In both cases, large amplitudes of TMR on the order of 30% are found. Since a fully spin-polarized current flows from the <a href="/wiki/Half-metal" title="Half-metal">half-metallic</a> LSMO electrode, within the <a href="/wiki/Tunnel_magnetoresistance" title="Tunnel magnetoresistance">Julliere model</a>, this sign change suggests a sign change in the effective spin polarization of the STO/CoCr interface. The origin to this multistate effect lies with the observed migration of Cr into the barrier and its state of oxidation. The sign change of TMR can originate from modifications to the STO/CoCr interface density of states, as well as from changes to the tunneling landscape at the STO/CoCr interface induced by CrOx redox reactions. Reports on MgO-based memristive switching within MgO-based MTJs appeared starting in 2008<a href="#cite_note-HalleyAPL2008-92">[91]</a> and 2009.<a href="#cite_note-krzysteczko2009apl-93">[92]</a> While the drift of oxygen vacancies within the insulating MgO layer has been proposed to describe the observed memristive effects,<a href="#cite_note-krzysteczko2009apl-93">[92]</a> another explanation could be charge trapping/detrapping on the localized states of oxygen vacancies<a href="#cite_note-BertinJAP2011-94">[93]</a> and its impact<a href="#cite_note-schleicherNC2014-95">[94]</a> on spintronics. This highlights the importance of understanding what role oxygen vacancies play in the memristive operation of devices that deploy complex oxides with an intrinsic property such as ferroelectricity<a href="#cite_note-garciaS2010-96">[95]</a> or multiferroicity.<a href="#cite_note-pantelAM2012-97">[96]</a> <div class="mw-heading mw-heading5"><h5 id="Intrinsic_mechanism">Intrinsic mechanism</h5>[<a href="/w/index.php?title=Memristor&action=edit&section=27" title="Edit section: Intrinsic mechanism">edit</a>]</div> The magnetization state of a MTJ can be controlled by <a href="/wiki/Spin-transfer_torque" title="Spin-transfer torque">Spin-transfer torque</a>, and can thus, through this intrinsic physical mechanism, exhibit memristive behavior. This spin torque is induced by current flowing through the junction, and leads to an efficient means of achieving a <a href="/wiki/Magnetoresistive_RAM" title="Magnetoresistive RAM">MRAM</a>. However, the length of time the current flows through the junction determines the amount of current needed, i.e., charge is the key variable.<a href="#cite_note-98">[97]</a> The combination of intrinsic (spin-transfer torque) and extrinsic (resistive switching) mechanisms naturally leads to a second-order memristive system described by the state vector x = (x1,x2), where x1 describes the magnetic state of the electrodes and x2 denotes the resistive state of the MgO barrier. In this case the change of x1 is current-controlled (spin torque is due to a high current density) whereas the change of x2 is voltage-controlled (the drift of oxygen vacancies is due to high electric fields). The presence of both effects in a memristive magnetic tunnel junction led to the idea of a nanoscopic synapse-neuron system.<a href="#cite_note-krzysteczko2012advmat-99">[98]</a> <div class="mw-heading mw-heading4"><h4 id="Spin_memristive_system">Spin memristive system</h4>[<a href="/w/index.php?title=Memristor&action=edit&section=28" title="Edit section: Spin memristive system">edit</a>]</div> A fundamentally different mechanism for memristive behavior has been proposed by Pershin and <a href="/wiki/Di_Ventra" class="mw-redirect" title="Di Ventra">Di Ventra</a>.<a href="#cite_note-100">[99]</a><a href="#cite_note-Pershin2008-101">[100]</a> The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang.<a href="#cite_note-chua76-2">[2]</a> The mechanism of memristive behavior in such structures is based entirely on the electron spin degree of freedom which allows for a more convenient control than the ionic transport in nanostructures. When an external control parameter (such as voltage) is changed, the adjustment of electron spin polarization is delayed because of the diffusion and relaxation processes causing hysteresis. This result was anticipated in the study of spin extraction at semiconductor/ferromagnet interfaces,<a href="#cite_note-102">[101]</a> but was not described in terms of memristive behavior. On a short time scale, these structures behave almost as an ideal memristor.<a href="#cite_note-chua71-1">[1]</a> This result broadens the possible range of applications of semiconductor spintronics and makes a step forward in future practical applications. <div class="mw-heading mw-heading3"><h3 id="Self-directed_channel_memristor">Self-directed channel memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=29" title="Edit section: Self-directed channel memristor">edit</a>]</div> In 2017, Kris Campbell formally introduced the self-directed channel (SDC) memristor.<a href="#cite_note-103">[102]</a> The SDC device is the first memristive device available commercially to researchers, students and electronics enthusiast worldwide.<a href="#cite_note-104">[103]</a> The SDC device is operational immediately after fabrication. In the Ge2Se3 active layer, Ge-Ge homopolar bonds are found and switching occurs. The three layers consisting of Ge2Se3/Ag/Ge2Se3, directly below the top tungsten electrode, mix together during deposition and jointly form the silver-source layer. A layer of SnSe is between these two layers ensuring that the silver-source layer is not in direct contact with the active layer. Since silver does not migrate into the active layer at high temperatures, and the active layer maintains a high glass transition temperature of about 350 °C (662 °F), the device has significantly higher processing and operating temperatures at 250 °C (482 °F) and at least 150 °C (302 °F), respectively. These processing and operating temperatures are higher than most ion-conducting chalcogenide device types, including the S-based glasses (e.g. GeS) that need to be photodoped or thermally annealed. These factors allow the SDC device to operate over a wide range of temperatures, including long-term continuous operation at 150 °C (302 °F). <div class="mw-heading mw-heading2"><h2 id="Implementation_of_hysteretic_flux-charge_memristors">Implementation of hysteretic flux-charge memristors</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=30" title="Edit section: Implementation of hysteretic flux-charge memristors">edit</a>]</div> There exist implementations of memristors with both hysteretic current-voltage curve and hysteretic flux-charge curve [arXiv:2403.20051]. Memristors with both hysteretic current-voltage curve and hysteretic flux-charge curve use a memristance dependent on the history of the flux and charge. Those memristors can merge the functionality of the arithmetic logic unit and of the memory unit without data transfer [DOI: 10.1002/adfm.201303365].  <div class="mw-heading mw-heading3"><h3 id="Time-integrated_Formingfree_memristor">Time-integrated Formingfree memristor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=31" title="Edit section: Time-integrated Formingfree memristor">edit</a>]</div> Time-integrated Formingfree (TiF) memristors reveal a hysteretic flux-charge curve with two distinguishable branches in the positive bias range and with two distinguishable branches in the negative bias range. And TiF memristors also reveal a hysteretic current-voltage curve with two distinguishable branches in the positive bias range and with two distinguishable branches in the negative bias range. The memristance state of a TiF memristor can be controlled by both the flux and the charge [DOI: 10.1063/1.4775718]. A TiF memristor was first demonstrated by <a href="/wiki/Heidemarie_Schmidt" title="Heidemarie Schmidt">Heidemarie Schmidt</a> and her team in 2011 [DOI: 10.1063/1.3601113]. This TiF memristor is composed of a BiFeO3 thin film between metallically conducting electrodes, one gold, the other platinum. The hysteretic flux-charge curve of the TiF memristor changes its slope continuously in one branch in the positive and in one branch in the negative bias range (write branches) and has a constant slope in one branch in the positive and in one branch in the negative bias range (read branches) [arXiv:2403.20051]. According to Leon O. Chua [Reference 1: 10.1.1.189.3614] the slope of the flux-charge curve corresponds to the memristance of a memristor or to its internal state variables. The TiF memristors can be considered as memristors with a constant memristance in the two read branches and with a reconfigurable memristance in the two write branches. The physical memristor model which describes the hysteretic current-voltage curves of the TiF memristor implements static and dynamic internal state variables in the two read branches and in the two write branches [arXiv:2402.10358]. The static and dynamic internal state variables of a non-linear memristors can be used to implement operations on non-linear memristors representing linear, non-linear, and even transcendental, e.g. exponential or logarithmic, input-output functions. The transport characteristics of the TiF memristor in the small current – small voltage range are non-linear. This non-linearity well compares to the non-linear characteristics in the small current – small voltage range of the basic former and present building blocks in the arithmetic logic unit of von-Neumann computers, i.e. of vacuum tubes and of transistors. In contrast to vacuum tubes and transistors, the signal output of hysteretic flux-charge memristors, i.e. of TiF memristors, is not lost when the operation power is switched off before storing the signal output to the memory. Therefore, hysteretic flux-charge memristors are said to merge the functionality of the arithmetic logic unit and of the memory unit without data transfer [DOI: 10.1002/adfm.201303365]. The transport characteristics in the small current – small voltage range of hysteretic current-voltage memristors are linear. This explains why hysteretic current-voltage memristors are well established memory units and why they can not merge the functionality of the arithmetic logic unit and of the memory unit without data transfer [arXiv:2403.20051]. <div class="mw-heading mw-heading2"><h2 id="Potential_applications">Potential applications</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=32" title="Edit section: Potential applications">edit</a>]</div> Memristors remain a laboratory curiosity, as yet made in insufficient numbers to gain any commercial applications. A potential application of memristors is in analog memories for superconducting quantum computers.<a href="#cite_note-peottaDiVentra2014-12">[12]</a> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output 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href="/wiki/Computer_memory" title="Computer memory">Computer memory</a> and <a href="/wiki/Computer_data_storage" title="Computer data storage">data storage</a> types</th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">General</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li> <li><a href="/wiki/Memory_coherence" title="Memory coherence">Memory coherence</a></li> <li><a href="/wiki/Cache_coherence" title="Cache coherence">Cache coherence</a></li> <li><a href="/wiki/Memory_hierarchy" title="Memory hierarchy">Memory hierarchy</a></li> <li><a href="/wiki/Memory_access_pattern" title="Memory access pattern">Memory access pattern</a></li> <li><a href="/wiki/Memory_map" title="Memory map">Memory map</a></li> <li><a href="/wiki/Computer_data_storage#Secondary_storage" 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integrity</a></li> <li><a href="/wiki/Data_security" title="Data security">Data security</a></li> <li><a href="/wiki/Data_validation" title="Data validation">Data validation</a></li> <li><a href="/wiki/Data_validation_and_reconciliation" title="Data validation and reconciliation">Data validation and reconciliation</a></li> <li><a href="/wiki/Data_recovery" title="Data recovery">Data recovery</a></li> <li><a href="/wiki/Computer_data_storage" title="Computer data storage">Storage</a></li> <li><a href="/wiki/Data_cluster" class="mw-redirect" title="Data cluster">Data cluster</a></li> <li><a href="/wiki/Directory_(computing)" title="Directory (computing)">Directory</a></li> <li><a href="/wiki/Shared_resource" title="Shared resource">Shared resource</a></li> <li><a href="/wiki/File_sharing" title="File sharing">File sharing</a></li> <li><a href="/wiki/File_system" title="File system">File system</a></li> <li><a href="/wiki/Clustered_file_system" title="Clustered file system">Clustered file system</a></li> <li><a href="/wiki/Clustered_file_system#Distributed_file_systems" title="Clustered file system">Distributed file system</a></li> <li><a href="/wiki/Distributed_file_system_for_cloud" title="Distributed file system for cloud">Distributed file system for cloud</a></li> <li><a href="/wiki/Distributed_data_store" title="Distributed data store">Distributed data store</a></li> <li><a href="/wiki/Distributed_database" title="Distributed database">Distributed database</a></li> <li><a href="/wiki/Database" title="Database">Database</a></li> <li><a href="/wiki/Data_bank" title="Data bank">Data bank</a></li> <li><a href="/wiki/Data_storage" title="Data storage">Data storage</a></li> <li><a href="/wiki/Data_store" title="Data store">Data store</a></li> <li><a href="/wiki/Data_deduplication" title="Data deduplication">Data deduplication</a></li> <li><a href="/wiki/Data_structure" title="Data structure">Data structure</a></li> <li><a href="/wiki/Data_redundancy" title="Data redundancy">Data redundancy</a></li> <li><a href="/wiki/Replication_(computing)" title="Replication (computing)">Replication (computing)</a></li> <li><a href="/wiki/Memory_refresh" title="Memory refresh">Memory refresh</a></li> <li><a href="/wiki/Storage_record" title="Storage record">Storage record</a></li> <li><a href="/wiki/Information_repository" title="Information repository">Information repository</a></li> <li><a href="/wiki/Knowledge_base" title="Knowledge base">Knowledge base</a></li> <li><a href="/wiki/Computer_file" title="Computer file">Computer file</a></li> <li><a href="/wiki/Object_file" title="Object file">Object file</a></li> <li><a href="/wiki/File_deletion" title="File deletion">File deletion</a></li> <li><a href="/wiki/File_copying" title="File copying">File copying</a></li> <li><a href="/wiki/Backup" title="Backup">Backup</a></li> <li><a href="/wiki/Core_dump" title="Core dump">Core dump</a></li> <li><a href="/wiki/Hex_dump" title="Hex dump">Hex dump</a></li> <li><a href="/wiki/Data_communication" title="Data communication">Data communication</a></li> <li><a href="/wiki/Information_transfer" title="Information transfer">Information transfer</a></li> <li><a href="/wiki/Temporary_file" title="Temporary file">Temporary file</a></li> <li><a href="/wiki/Copy_protection" title="Copy protection">Copy protection</a></li> <li><a href="/wiki/Digital_rights_management" title="Digital rights management">Digital rights management</a></li> <li><a href="/wiki/Volume_(computing)" title="Volume (computing)">Volume (computing)</a></li> <li><a href="/wiki/Boot_sector" title="Boot sector">Boot sector</a></li> <li><a href="/wiki/Master_boot_record" title="Master boot record">Master boot record</a></li> <li><a href="/wiki/Volume_boot_record" title="Volume boot record">Volume boot record</a></li> <li><a href="/wiki/Disk_array" title="Disk array">Disk array</a></li> <li><a href="/wiki/Disk_image" title="Disk image">Disk image</a></li> <li><a href="/wiki/Disk_mirroring" title="Disk mirroring">Disk mirroring</a></li> <li><a href="/wiki/Disk_aggregation" title="Disk aggregation">Disk aggregation</a></li> <li><a href="/wiki/Disk_partitioning" title="Disk partitioning">Disk partitioning</a></li> <li><a href="/wiki/Memory_segmentation" title="Memory segmentation">Memory segmentation</a></li> <li><a href="/wiki/Locality_of_reference" title="Locality of reference">Locality of reference</a></li> <li><a href="/wiki/Logical_disk" title="Logical disk">Logical disk</a></li> <li><a href="/wiki/Storage_virtualization" title="Storage virtualization">Storage virtualization</a></li> <li><a href="/wiki/Virtual_memory" title="Virtual memory">Virtual memory</a></li> <li><a href="/wiki/Memory-mapped_file" title="Memory-mapped file">Memory-mapped file</a></li> <li><a href="/wiki/Software_entropy" class="mw-redirect" title="Software entropy">Software entropy</a></li> <li><a href="/wiki/Software_rot" title="Software rot">Software rot</a></li> <li><a href="/wiki/In-memory_database" title="In-memory database">In-memory database</a></li> <li><a href="/wiki/In-memory_processing" title="In-memory processing">In-memory processing</a></li> <li><a href="/wiki/Persistence_(computer_science)" title="Persistence (computer science)">Persistence (computer science)</a></li> <li><a href="/wiki/Persistent_data_structure" title="Persistent data structure">Persistent data structure</a></li> <li><a href="/wiki/RAID" title="RAID">RAID</a></li> <li><a href="/wiki/Non-RAID_drive_architectures" title="Non-RAID drive architectures">Non-RAID drive architectures</a></li> <li><a href="/wiki/Memory_paging" title="Memory paging">Memory paging</a></li> <li><a href="/wiki/Bank_switching" title="Bank switching">Bank switching</a></li> <li><a href="/wiki/Grid_computing" title="Grid computing">Grid computing</a></li> <li><a href="/wiki/Cloud_computing" title="Cloud computing">Cloud computing</a></li> <li><a href="/wiki/Cloud_storage" title="Cloud storage">Cloud storage</a></li> <li><a href="/wiki/Fog_computing" title="Fog computing">Fog computing</a></li> <li><a href="/wiki/Edge_computing" title="Edge computing">Edge computing</a></li> <li><a href="/wiki/Dew_computing" title="Dew computing">Dew computing</a></li> <li><a href="/wiki/Amdahl%27s_law" title="Amdahl's law">Amdahl's law</a></li> <li><a href="/wiki/Moore%27s_law" title="Moore's law">Moore's law</a></li> <li><a href="/wiki/Mark_Kryder#Kryder's_law_projection" title="Mark Kryder">Kryder's law</a></li></ul></div></div></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Volatile_memory" title="Volatile memory">Volatile</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Random-access_memory" title="Random-access memory">RAM</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Cache_(computing)#HARDWARE" title="Cache (computing)">Hardware cache</a> <ul><li><a href="/wiki/CPU_cache" title="CPU cache">CPU cache</a></li> <li><a href="/wiki/Scratchpad_memory" title="Scratchpad memory">Scratchpad memory</a></li></ul></li> <li><a href="/wiki/Dynamic_random-access_memory" title="Dynamic random-access memory">DRAM</a> <ul><li><a href="/wiki/EDRAM" title="EDRAM">eDRAM</a></li> <li><a href="/wiki/Synchronous_dynamic_random-access_memory" title="Synchronous dynamic random-access memory">SDRAM</a></li> <li><a href="/wiki/Synchronous_dynamic_random-access_memory#Synchronous_Graphics_RAM_(SGRAM)" title="Synchronous dynamic random-access memory">SGRAM</a></li> <li><a href="/wiki/DDR_SDRAM" title="DDR SDRAM">DDR</a></li> <li><a href="/wiki/GDDR_SDRAM" title="GDDR SDRAM">GDDR</a></li> <li><a href="/wiki/LPDDR" title="LPDDR">LPDDR</a></li> <li><a href="/wiki/Quad_Data_Rate_SRAM" title="Quad Data Rate SRAM">QDRSRAM</a></li> <li><a href="/wiki/Dynamic_random-access_memory#Extended_data_out_DRAM" title="Dynamic random-access memory">EDO DRAM</a></li> <li><a href="/wiki/XDR_DRAM" title="XDR DRAM">XDR DRAM</a></li> <li><a href="/wiki/RDRAM" title="RDRAM">RDRAM</a></li> <li><a href="/wiki/High_Bandwidth_Memory" title="High Bandwidth Memory">HBM</a></li></ul></li> <li><a href="/wiki/Static_random-access_memory" title="Static random-access memory">SRAM</a> <ul><li><a href="/wiki/1T-SRAM" title="1T-SRAM">1T-SRAM</a></li></ul></li> <li><a href="/wiki/Resistive_random-access_memory" title="Resistive random-access memory">ReRAM</a></li> <li><a href="/wiki/Quantum_memory" title="Quantum memory">QRAM</a></li> <li><a href="/wiki/Content-addressable_memory" title="Content-addressable memory">Content-addressable memory</a> (CAM)</li> <li><a href="/wiki/Computational_RAM" title="Computational RAM">Computational RAM</a></li> <li><a href="/wiki/Video_random_access_memory" class="mw-redirect" title="Video random access memory">VRAM</a></li> <li><a href="/wiki/Dual-ported_RAM" title="Dual-ported RAM">Dual-ported RAM</a> <ul><li><a href="/wiki/Video_RAM_(dual-ported_DRAM)" class="mw-redirect" title="Video RAM (dual-ported DRAM)">Video RAM (dual-ported DRAM)</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Historical</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Williams_tube" title="Williams tube">Williams–Kilburn tube</a> (1946–1947)</li> <li><a href="/wiki/Delay-line_memory" title="Delay-line memory">Delay-line memory</a> (1947)</li> <li><a href="/wiki/Mellon_optical_memory" title="Mellon optical memory">Mellon optical memory</a> (1951)</li> <li><a href="/wiki/Selectron_tube" title="Selectron tube">Selectron tube</a> (1952)</li> <li><a href="/wiki/Dekatron" title="Dekatron">Dekatron</a></li> <li><a href="/wiki/T-RAM" title="T-RAM">T-RAM</a> (2009)</li> <li><a href="/wiki/Z-RAM" title="Z-RAM">Z-RAM</a> (2002–2010)</li></ul></div></div></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Non-volatile_memory" title="Non-volatile memory">Non-volatile</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Read-only_memory" title="Read-only memory">ROM</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Diode_matrix" title="Diode matrix">Diode matrix</a></li> <li><a href="/wiki/Read-only_memory#Factory-programmed" title="Read-only memory">MROM</a></li> <li><a href="/wiki/Programmable_ROM" title="Programmable ROM">PROM</a> <ul><li><a href="/wiki/EPROM" title="EPROM">EPROM</a></li> <li><a href="/wiki/EEPROM" title="EEPROM">EEPROM</a></li></ul></li> <li><a href="/wiki/ROM_cartridge" title="ROM cartridge">ROM cartridge</a></li> <li><a href="/wiki/Solid-state_storage" title="Solid-state storage">Solid-state storage</a> (SSS) <ul><li><a href="/wiki/Flash_memory" title="Flash memory">Flash memory</a> is used in:</li> <li><a href="/wiki/Solid-state_drive" title="Solid-state drive">Solid-state drive</a> (SSD)</li> <li><a href="/wiki/Solid-state_hybrid_drive" class="mw-redirect" title="Solid-state hybrid drive">Solid-state hybrid drive</a> (SSHD)</li> <li><a href="/wiki/USB_flash_drive" title="USB flash drive">USB flash drive</a></li> <li><a href="/wiki/IBM_FlashSystem" title="IBM FlashSystem">IBM FlashSystem</a></li> <li><a href="/wiki/Flash_Core_Module" title="Flash Core Module">Flash Core Module</a></li></ul></li> <li><a href="/wiki/Memory_card" title="Memory card">Memory card</a> <ul><li><a href="/wiki/Memory_Stick" title="Memory Stick">Memory Stick</a></li> <li><a href="/wiki/CompactFlash" title="CompactFlash">CompactFlash</a></li> <li><a href="/wiki/PC_Card" title="PC Card">PC Card</a></li> <li><a href="/wiki/MultiMediaCard" title="MultiMediaCard">MultiMediaCard</a></li> <li><a href="/wiki/SD_card" title="SD card">SD card</a></li> <li><a href="/wiki/SIM_card" title="SIM card">SIM card</a></li> <li><a href="/wiki/SmartMedia" title="SmartMedia">SmartMedia</a></li> <li><a href="/wiki/Universal_Flash_Storage" title="Universal Flash Storage">Universal Flash Storage</a></li> <li><a href="/wiki/SxS" title="SxS">SxS</a></li> <li><a href="/wiki/MicroP2" title="MicroP2">MicroP2</a></li> <li><a href="/wiki/XQD_card" title="XQD card">XQD card</a></li></ul></li> <li><a href="/wiki/Programmable_metallization_cell" title="Programmable metallization cell">Programmable metallization cell</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Non-volatile_random-access_memory" title="Non-volatile random-access memory">NVRAM</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Memistor" title="Memistor">Memistor</a></li> <li><a class="mw-selflink selflink">Memristor</a></li> <li><a href="/wiki/Phase-change_memory" title="Phase-change memory">PCM</a> (<a href="/wiki/3D_XPoint" title="3D XPoint">3D XPoint</a>)</li> <li><a href="/wiki/Magnetoresistive_RAM" title="Magnetoresistive RAM">MRAM</a></li> <li><a href="/wiki/Electrochemical_RAM" title="Electrochemical RAM">Electrochemical RAM</a> (ECRAM)</li> <li><a href="/wiki/Nano-RAM" title="Nano-RAM">Nano-RAM</a></li> <li><a href="/wiki/Programmable_metallization_cell" title="Programmable metallization cell">CBRAM</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Early-stage <a href="/wiki/Non-volatile_random-access_memory" title="Non-volatile random-access memory">NVRAM</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Ferroelectric_RAM" title="Ferroelectric RAM">FeRAM</a></li> <li><a href="/wiki/Resistive_random-access_memory" title="Resistive random-access memory">ReRAM</a></li> <li><a href="/wiki/Fe_FET" title="Fe FET">FeFET memory</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Analog_recording" title="Analog recording">Analog recording</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Phonograph_cylinder" title="Phonograph cylinder">Phonograph cylinder</a></li> <li><a href="/wiki/Phonograph_record" title="Phonograph record">Phonograph record</a></li> <li><a href="/wiki/Quadruplex_videotape" title="Quadruplex videotape">Quadruplex videotape</a></li> <li><a href="/wiki/Vision_Electronic_Recording_Apparatus" title="Vision Electronic Recording Apparatus">Vision Electronic Recording Apparatus</a></li> <li><a href="/wiki/Magnetic_recording" class="mw-redirect" title="Magnetic recording">Magnetic recording</a> <ul><li><a href="/wiki/Magnetic_storage" title="Magnetic storage">Magnetic storage</a></li> <li><a href="/wiki/Magnetic_tape" title="Magnetic tape">Magnetic tape</a></li> <li><a href="/wiki/Magnetic-tape_data_storage" title="Magnetic-tape data storage">Magnetic-tape data storage</a></li> <li><a href="/wiki/Tape_drive" title="Tape drive">Tape drive</a></li> <li><a href="/wiki/Tape_library" title="Tape library">Tape library</a></li> <li><a href="/wiki/Digital_Data_Storage" title="Digital Data Storage">Digital Data Storage</a> (DDS)</li> <li><a href="/wiki/Videotape" title="Videotape">Videotape</a></li> <li><a href="/wiki/Videocassette" class="mw-redirect" title="Videocassette">Videocassette</a></li> <li><a href="/wiki/Cassette_tape" title="Cassette tape">Cassette tape</a></li> <li><a href="/wiki/Linear_Tape-Open" title="Linear Tape-Open">Linear Tape-Open</a></li> <li><a href="/wiki/Betamax" title="Betamax">Betamax</a></li> <li><a href="/wiki/8_mm_video_format" title="8 mm video format">8 mm video format</a></li> <li><a href="/wiki/DV_(video_format)" title="DV (video format)">DV</a></li> <li><a href="/wiki/MiniDV" class="mw-redirect" title="MiniDV">MiniDV</a></li> <li><a href="/wiki/MicroMV" title="MicroMV">MicroMV</a></li> <li><a href="/wiki/U-matic" title="U-matic">U-matic</a></li> <li><a href="/wiki/VHS" title="VHS">VHS</a></li> <li><a href="/wiki/S-VHS" title="S-VHS">S-VHS</a></li> <li><a href="/wiki/VHS-C" title="VHS-C">VHS-C</a></li> <li><a href="/wiki/D-VHS" title="D-VHS">D-VHS</a></li></ul></li> <li><a href="/wiki/Hard_disk_drive" title="Hard disk drive">Hard disk drive</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Optical_storage" title="Optical storage">Optical</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/3D_optical_data_storage" title="3D optical data storage">3D optical data storage</a> <ul><li><a href="/wiki/Optical_disc" title="Optical disc">Optical disc</a></li> <li><a href="/wiki/LaserDisc" title="LaserDisc">LaserDisc</a></li> <li><a href="/wiki/Compact_Disc_Digital_Audio" title="Compact Disc Digital Audio">Compact Disc Digital Audio</a> (CDDA)</li> <li><a href="/wiki/Compact_disc" title="Compact disc">CD</a></li> <li><a href="/wiki/CD_Video" title="CD Video">CD Video</a></li> <li><a href="/wiki/CD-R" title="CD-R">CD-R</a></li> <li><a href="/wiki/CD-RW" title="CD-RW">CD-RW</a></li> <li><a href="/wiki/Video_CD" title="Video CD">Video CD</a></li> <li><a href="/wiki/Super_Video_CD" title="Super Video CD">Super Video CD</a></li> <li><a href="/wiki/Mini_CD" title="Mini CD">Mini CD</a></li> <li><a href="/wiki/Nintendo_optical_discs" title="Nintendo optical discs">Nintendo optical discs</a></li> <li><a href="/wiki/CD-ROM" title="CD-ROM">CD-ROM</a></li> <li><a href="/wiki/Hyper_CD-ROM" title="Hyper CD-ROM">Hyper CD-ROM</a></li> <li><a href="/wiki/DVD" title="DVD">DVD</a></li> <li><a href="/wiki/DVD_recordable#DVD+R_and_DVD+RW_(DVD_"plus")" title="DVD recordable">DVD+R</a></li> <li><a href="/wiki/DVD-Video" title="DVD-Video">DVD-Video</a></li> <li><a href="/wiki/DVD_card" title="DVD card">DVD card</a></li> <li><a href="/wiki/DVD-RAM" title="DVD-RAM">DVD-RAM</a></li> <li><a href="/wiki/MiniDVD" title="MiniDVD">MiniDVD</a></li> <li><a href="/wiki/HD_DVD" title="HD DVD">HD DVD</a></li> <li><a href="/wiki/Blu-ray" title="Blu-ray">Blu-ray</a></li> <li><a href="/wiki/Ultra_HD_Blu-ray" title="Ultra HD Blu-ray">Ultra HD Blu-ray</a></li> <li><a href="/wiki/Holographic_Versatile_Disc" title="Holographic Versatile Disc">Holographic Versatile Disc</a></li></ul></li> <li><a href="/wiki/Write_once_read_many" title="Write once read many">WORM</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">In development</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Programmable_metallization_cell" title="Programmable metallization cell">CBRAM</a></li> <li><a href="/wiki/Racetrack_memory" title="Racetrack memory">Racetrack memory</a></li> <li><a href="/wiki/Nano-RAM" title="Nano-RAM">NRAM</a></li> <li><a href="/wiki/Millipede_memory" title="Millipede memory">Millipede memory</a></li> <li><a href="/wiki/Electrochemical_RAM" title="Electrochemical RAM">ECRAM</a></li> <li><a href="/wiki/Patterned_media" title="Patterned media">Patterned media</a></li> <li><a href="/wiki/Holographic_data_storage" title="Holographic data storage">Holographic data storage</a> <ul><li><a href="/wiki/Electronic_quantum_holography" title="Electronic quantum holography">Electronic quantum holography</a></li></ul></li> <li><a href="/wiki/5D_optical_data_storage" title="5D optical data storage">5D optical data storage</a></li> <li><a href="/wiki/DNA_digital_data_storage" title="DNA digital data storage">DNA digital data storage</a></li> <li><a href="/wiki/Universal_memory" title="Universal memory">Universal memory</a></li> <li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li> <li><a href="/wiki/Quantum_memory" title="Quantum memory">Quantum memory</a></li> <li><a href="/wiki/UltraRAM" title="UltraRAM">UltraRAM</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Historical</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Paper_data_storage" title="Paper data storage">Paper data storage</a> (1725)</li> <li><a href="/wiki/Punched_card" title="Punched card">Punched card</a> (1725)</li> <li><a href="/wiki/Punched_tape" title="Punched tape">Punched tape</a> (1725)</li> <li><a href="/wiki/Plugboard" title="Plugboard">Plugboard</a></li> <li><a href="/wiki/Drum_memory" title="Drum memory">Drum memory</a> (1932)</li> <li><a href="/wiki/Magnetic-core_memory" title="Magnetic-core memory">Magnetic-core memory</a> (1949)</li> <li><a href="/wiki/Plated-wire_memory" title="Plated-wire memory">Plated-wire memory</a> (1957)</li> <li><a href="/wiki/Core_rope_memory" title="Core rope memory">Core rope memory</a> (1960s)</li> <li><a href="/wiki/Thin-film_memory" title="Thin-film memory">Thin-film memory</a> (1962)</li> <li><a href="/wiki/Disk_pack" title="Disk pack">Disk pack</a> (1962)</li> <li><a href="/wiki/Twistor_memory" title="Twistor memory">Twistor memory</a> (~1968)</li> <li><a href="/wiki/Bubble_memory" title="Bubble memory">Bubble memory</a> (~1970)</li> <li><a href="/wiki/Floppy_disk" title="Floppy disk">Floppy disk</a> (1971)</li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Memory_types" title="Template:Memory types"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Memory_types" title="Template talk:Memory types"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Memory_types" title="Special:EditPage/Template:Memory types"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> Memristors can potentially be fashioned into <a href="/wiki/Non-volatile_memory" title="Non-volatile memory">non-volatile solid-state memory</a>, which could allow greater data density than hard drives with access times similar to <a href="/wiki/Dynamic_random-access_memory" title="Dynamic random-access memory">DRAM</a>, replacing both components.<a href="#cite_note-Kanellos-32">[31]</a> HP prototyped a crossbar latch memory that can fit 100 <a href="/wiki/Gigabit" class="mw-redirect" title="Gigabit">gigabits</a> in a square centimeter,<a href="#cite_note-EETimes-105">[104]</a> and proposed a scalable 3D design (consisting of up to 1000 layers or 1 <a href="/wiki/Petabit" class="mw-redirect" title="Petabit">petabit</a> per cm3).<a href="#cite_note-106">[105]</a> In May 2008 HP reported that its device reaches currently about one-tenth the speed of DRAM.<a href="#cite_note-107">[106]</a> The devices' resistance would be read with <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> so that the stored value would not be affected.<a href="#cite_note-108">[107]</a> In May 2012, it was reported that the access time had been improved to 90 nanoseconds, which is nearly one hundred times faster than the contemporaneous Flash memory. At the same time, the energy consumption was just one percent of that consumed by Flash memory.<a href="#cite_note-109">[108]</a> Memristors have applications in <a href="/wiki/Programmable_logic_device" title="Programmable logic device">programmable logic</a><a href="#cite_note-110">[109]</a> <a href="/wiki/Signal_processing" title="Signal processing">signal processing</a>,<a href="#cite_note-111">[110]</a> <a href="/wiki/Super-resolution_imaging" title="Super-resolution imaging">super-resolution imaging</a><a href="#cite_note-112">[111]</a> <a href="/wiki/Physical_neural_network" title="Physical neural network">physical neural networks</a>,<a href="#cite_note-113">[112]</a> <a href="/wiki/Control_theory" title="Control theory">control systems</a>,<a href="#cite_note-114">[113]</a> <a href="/wiki/Reconfigurable_computing" title="Reconfigurable computing">reconfigurable computing</a>,<a href="#cite_note-115">[114]</a> <a href="/wiki/In-memory_computing" class="mw-redirect" title="In-memory computing">in-memory computing</a>,<a href="#cite_note-116">[115]</a> <a href="/wiki/Brain%E2%80%93computer_interfaces" class="mw-redirect" title="Brain–computer interfaces">brain–computer interfaces</a><a href="#cite_note-117">[116]</a> and <a href="/wiki/RFID" class="mw-redirect" title="RFID">RFID</a>.<a href="#cite_note-118">[117]</a> Memristive devices are potentially used for stateful logic implication, allowing a replacement for CMOS-based logic computation<a href="#cite_note-119">[118]</a> Several early works have been reported in this direction.<a href="#cite_note-120">[119]</a><a href="#cite_note-121">[120]</a> In 2009, a simple electronic circuit<a href="#cite_note-122">[121]</a> consisting of an LC network and a memristor was used to model experiments on adaptive behavior of unicellular organisms.<a href="#cite_note-amoebaexp-123">[122]</a> It was shown that subjected to a train of periodic pulses, the circuit learns and anticipates the next pulse similar to the behavior of slime molds <a href="/wiki/Physarum_polycephalum" title="Physarum polycephalum">Physarum polycephalum</a> where the viscosity of channels in the cytoplasm responds to periodic environment changes.<a href="#cite_note-amoebaexp-123">[122]</a> Applications of such circuits may include, e.g., <a href="/wiki/Pattern_recognition" title="Pattern recognition">pattern recognition</a>. The <a href="/wiki/DARPA" title="DARPA">DARPA</a> <a href="/wiki/SyNAPSE" title="SyNAPSE">SyNAPSE</a> project funded HP Labs, in collaboration with the <a href="/wiki/Boston_University" title="Boston University">Boston University</a> Neuromorphics Lab, has been developing neuromorphic architectures which may be based on memristive systems. In 2010, <a href="/wiki/Massimiliano_Versace" title="Massimiliano Versace">Versace</a> and Chandler described the MoNETA (Modular Neural Exploring Traveling Agent) model.<a href="#cite_note-124">[123]</a> MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent using memristive hardware.<a href="#cite_note-125">[124]</a> Application of the memristor crossbar structure in the construction of an analog soft computing system was demonstrated by Merrikh-Bayat and Shouraki.<a href="#cite_note-126">[125]</a> In 2011, they showed<a href="#cite_note-127">[126]</a> how memristor crossbars can be combined with <a href="/wiki/Fuzzy_logic" title="Fuzzy logic">fuzzy logic</a> to create an analog memristive <a href="/wiki/Neuro-fuzzy" title="Neuro-fuzzy">neuro-fuzzy</a> computing system with fuzzy input and output terminals. Learning is based on the creation of fuzzy relations inspired from <a href="/wiki/Hebbian_theory" title="Hebbian theory">Hebbian learning rule</a>. In 2013 Leon Chua published a tutorial underlining the broad span of complex phenomena and applications that memristors span and how they can be used as non-volatile analog memories and can mimic classic habituation and learning phenomena.<a href="#cite_note-128">[127]</a> <div class="mw-heading mw-heading2"><h2 id="Derivative_devices">Derivative devices</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=33" title="Edit section: Derivative devices">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Memistor_and_memtransistor">Memistor and memtransistor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=34" title="Edit section: Memistor and memtransistor">edit</a>]</div> The <a href="/wiki/Memistor" title="Memistor">memistor</a> and <a href="/wiki/Memtransistor" title="Memtransistor">memtransistor</a> are transistor-based devices which include memristor function. <div class="mw-heading mw-heading3"><h3 id="Memcapacitors_and_meminductors">Memcapacitors and meminductors</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=35" title="Edit section: Memcapacitors and meminductors">edit</a>]</div> In 2009, <a href="/wiki/Massimiliano_Di_Ventra" title="Massimiliano Di Ventra">Di Ventra</a>, Pershin, and Chua extended<a href="#cite_note-DiVentra2009-129">[128]</a> the notion of memristive systems to capacitive and inductive elements in the form of memcapacitors and meminductors, whose properties depend on the state and history of the system, further extended in 2013 by Di Ventra and Pershin.<a href="#cite_note-DiVentra_2013-23">[22]</a> <div class="mw-heading mw-heading3"><h3 id="Memfractance_and_memfractor,_2nd-_and_3rd-order_memristor,_memcapacitor_and_meminductor">Memfractance and memfractor, 2nd- and 3rd-order memristor, memcapacitor and meminductor</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=36" title="Edit section: Memfractance and memfractor, 2nd- and 3rd-order memristor, memcapacitor and meminductor">edit</a>]</div> In September 2014, <a href="/w/index.php?title=Mohamed-Salah_Abdelouahab&action=edit&redlink=1" class="new" title="Mohamed-Salah Abdelouahab (page does not exist)">Mohamed-Salah Abdelouahab</a>, <a href="/w/index.php?title=Rene_Lozi&action=edit&redlink=1" class="new" title="Rene Lozi (page does not exist)">Rene Lozi</a>, and <a href="/wiki/Leon_Chua" class="mw-redirect" title="Leon Chua">Leon Chua</a> published a general theory of 1st-, 2nd-, 3rd-, and nth-order memristive elements using <a href="/wiki/Fractional_calculus" title="Fractional calculus">fractional derivatives</a>.<a href="#cite_note-130">[129]</a> <div class="mw-heading mw-heading2"><h2 id="History">History</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=37" title="Edit section: History">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Precursors">Precursors</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=38" title="Edit section: Precursors">edit</a>]</div> <a href="/wiki/Sir_Humphry_Davy" class="mw-redirect" title="Sir Humphry Davy">Sir Humphry Davy</a> is said by some to have performed the first experiments which can be explained by memristor effects as long ago as 1808.<a href="#cite_note-Memristor200yearsold-21">[20]</a><a href="#cite_note-131">[130]</a> However the first device of a related nature to be constructed was the <a href="/wiki/Memistor" title="Memistor">memistor</a> (i.e. memory resistor), a term coined in 1960 by <a href="/wiki/Bernard_Widrow" title="Bernard Widrow">Bernard Widrow</a> to describe a circuit element of an early artificial neural network called <a href="/wiki/ADALINE" title="ADALINE">ADALINE</a>. A few years later, in 1968, Argall published an article showing the resistance switching effects of TiO2 which was later claimed by researchers from Hewlett Packard to be evidence of a memristor.<a href="#cite_note-Argall1968-56">[55]</a>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Theoretical_description">Theoretical description</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=39" title="Edit section: Theoretical description">edit</a>]</div> <a href="/wiki/Leon_Chua" class="mw-redirect" title="Leon Chua">Leon Chua</a> postulated his new two-terminal circuit element in 1971. It was characterized by a relationship between charge and flux linkage as a fourth fundamental circuit element.<a href="#cite_note-chua71-1">[1]</a> Five years later he and his student Sung Mo Kang generalized the theory of memristors and memristive systems including a property of zero crossing in the <a href="/wiki/Lissajous_curve" title="Lissajous curve">Lissajous curve</a> characterizing current vs. voltage behavior.<a href="#cite_note-chua76-2">[2]</a> <div class="mw-heading mw-heading3"><h3 id="Twenty-first_century">Twenty-first century</h3>[<a href="/w/index.php?title=Memristor&action=edit&section=40" title="Edit section: Twenty-first century">edit</a>]</div> On May 1, 2008, Strukov, Snider, Stewart, and Williams published an article in Nature identifying a link between the two-terminal resistance switching behavior found in nanoscale systems and memristors.<a href="#cite_note-Williams08-18">[17]</a> On 23 January 2009, <a href="/wiki/Di_Ventra" class="mw-redirect" title="Di Ventra">Di Ventra</a>, Pershin, and Chua extended the notion of memristive systems to capacitive and inductive elements, namely <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> and <a href="/wiki/Inductor" title="Inductor">inductors</a>, whose properties depend on the state and history of the system.<a href="#cite_note-DiVentra2009-129">[128]</a> In July 2014, the MeMOSat/<a href="/wiki/LabOSat" class="mw-redirect" title="LabOSat">LabOSat</a> group<a href="#cite_note-labosat1-132">[131]</a> (composed of researchers from <a href="/w/index.php?title=Universidad_Nacional_de_General_San_Mart%C3%ADn_(Argentina)&action=edit&redlink=1" class="new" title="Universidad Nacional de General San Martín (Argentina) (page does not exist)">Universidad Nacional de General San Martín (Argentina)</a>, INTI, <a href="/wiki/CNEA" class="mw-redirect" title="CNEA">CNEA</a>, and <a href="/wiki/CONICET" class="mw-redirect" title="CONICET">CONICET</a>) put memory devices into a <a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">Low Earth orbit</a>.<a href="#cite_note-133">[132]</a> Since then, seven missions with different devices<a href="#cite_note-labosat2-134">[133]</a> are performing experiments in low orbits, onboard <a href="/wiki/Satellogic" title="Satellogic">Satellogic</a>'s <a href="/w/index.php?title=%C3%91u-Sat&action=edit&redlink=1" class="new" title="Ñu-Sat (page does not exist)">Ñu-Sat</a> satellites.<a href="#cite_note-135">[134]</a><a href="#cite_note-136">[135]</a> [<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>] On 7 July 2015, Knowm Inc announced Self Directed Channel (SDC) memristors commercially.<a href="#cite_note-137">[136]</a> These devices remain available in small numbers. On 13 July 2018, MemSat (Memristor Satellite) was launched to fly a memristor evaluation payload.<a href="#cite_note-138">[137]</a> In 2021, <a href="/wiki/Jennifer_Rupp" title="Jennifer Rupp">Jennifer Rupp</a> and Martin Bazant of <a href="/wiki/MIT" class="mw-redirect" title="MIT">MIT</a> started a "Lithionics" research programme to investigate applications of <a href="/wiki/Lithium" title="Lithium">lithium</a> beyond their use in <a href="/wiki/Battery_electrode" class="mw-redirect" title="Battery electrode">battery electrodes</a>, including <a href="/wiki/Lithium_oxide" title="Lithium oxide">lithium oxide</a>-based memristors in <a href="/wiki/Neuromorphic_computing" title="Neuromorphic computing">neuromorphic computing</a>.<a href="#cite_note-139">[138]</a><a href="#cite_note-140">[139]</a> In May 2023, TECHiFAB GmbH [https://techifab.com/] announced TiF memristors commercially. [arXiv: 2403.20051, arXiv: 2402.10358] These TiF memristors remain available in small and medium numbers. In the September 2023 issue of <a href="/wiki/Science_(journal)" title="Science (journal)">Science Magazine</a>, Chinese scientists Wenbin Zhang et al. described the development and testing of a memristor-based <a href="/wiki/Integrated_circuit" title="Integrated circuit">integrated circuit</a>.<a href="#cite_note-141">[140]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=41" title="Edit section: See also">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output 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data-file-height="128" /></a><a href="/wiki/Portal:Electronics" title="Portal:Electronics">Electronics portal</a></li></ul> <ul><li><a href="/wiki/3D_XPoint" title="3D XPoint">3D XPoint</a></li> <li><a href="/wiki/Electrical_element" title="Electrical element">Electrical element</a></li> <li><a href="/wiki/Hybrid_Memory_Cube" title="Hybrid Memory Cube">Hybrid Memory Cube</a></li> <li><a href="/wiki/List_of_emerging_technologies" title="List of emerging technologies">List of emerging technologies</a></li> <li><a href="/wiki/Neuromorphic_engineering" class="mw-redirect" title="Neuromorphic engineering">Neuromorphic engineering</a></li> <li><a href="/wiki/Trancitor" title="Trancitor">Trancitor</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=42" title="Edit section: Footnotes">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-13"><a href="#cite_ref-13">^</a> For an experiment that shows such a characteristic for a common discharge tube, see <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation audio-visual cs1">Bharathwaj Muthuswamy (2013-10-03). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=hDfJoXrCSxk">A physical memristor Lissajous figure</a> – via YouTube.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+physical+memristor+Lissajous+figure&rft.date=2013-10-03&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DhDfJoXrCSxk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"> The video also illustrates how to understand deviations in the pinched hysteresis characteristics of physical memristors. </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=43" title="Edit section: References">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-chua71-1">^ <a href="#cite_ref-chua71_1-0">a</a> <a href="#cite_ref-chua71_1-1">b</a> <a href="#cite_ref-chua71_1-2">c</a> <a href="#cite_ref-chua71_1-3">d</a> <a href="#cite_ref-chua71_1-4">e</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChua1971" class="citation journal cs1">Chua, L. (1971). "Memristor-The missing circuit element". IEEE Transactions on Circuit Theory. 18 (5): 507–519. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.189.3614">10.1.1.189.3614</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTCT.1971.1083337">10.1109/TCT.1971.1083337</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Circuit+Theory&rft.atitle=Memristor-The+missing+circuit+element&rft.volume=18&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E507-%3C%2Fspan%3E519&rft.date=1971&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.189.3614%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1109%2FTCT.1971.1083337&rft.aulast=Chua&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"> </li> <li id="cite_note-chua76-2">^ <a href="#cite_ref-chua76_2-0">a</a> <a href="#cite_ref-chua76_2-1">b</a> <a href="#cite_ref-chua76_2-2">c</a> <a href="#cite_ref-chua76_2-3">d</a> <a href="#cite_ref-chua76_2-4">e</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChuaKang1976" class="citation cs2">Chua, L. O.; Kang, S. M. 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Science. 381 (6663): 1205–1211. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2023Sci...381.1205Z">2023Sci...381.1205Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.ade3483">10.1126/science.ade3483</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/37708281">37708281</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:261736380">261736380</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Edge+learning+using+a+fully+integrated+neuro-inspired+memristor+chip&rft.volume=381&rft.issue=6663&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1205-%3C%2Fspan%3E1211&rft.date=2023-09-14&rft_id=info%3Adoi%2F10.1126%2Fscience.ade3483&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A261736380%23id-name%3DS2CID&rft_id=info%3Apmid%2F37708281&rft_id=info%3Abibcode%2F2023Sci...381.1205Z&rft.aulast=Zhang&rft.aufirst=Wenbin&rft_id=https%3A%2F%2Fwww.science.org%2Fdoi%2F10.1126%2Fscience.ade3483&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=44" title="Edit section: Further reading">edit</a>]</div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChenChuaHwangWang2011" class="citation journal cs1">Chen, Dongmin; Chua, Leon O.; Hwang, Cheol Seong; Wang, Shih-Yuan; Waser, Rainer; Williams, R. Stanley; Yang, Jianhua, eds. (March 2011). "Special Issue: Memristive and Resistive Devices and Systems". <a href="/wiki/Applied_Physics_A" title="Applied Physics A">Applied Physics A</a>. 102 (4).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Physics+A&rft.atitle=Special+Issue%3A+Memristive+and+Resistive+Devices+and+Systems&rft.volume=102&rft.issue=4&rft.date=2011-03&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMazumderKangWaser2012" class="citation journal cs1">Mazumder, P.; Kang, S. M.; Waser, R., eds. (June 2012). "Special Issue: MEMRISTORS: DEVICES, MODELS, AND APPLICATIONS". <a href="/wiki/Proceedings_of_the_IEEE" title="Proceedings of the IEEE">Proceedings of the IEEE</a>. 100 (6): 1905–2092. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FJPROC.2012.2197452">10.1109/JPROC.2012.2197452</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+IEEE&rft.atitle=Special+Issue%3A+MEMRISTORS%3A+DEVICES%2C+MODELS%2C+AND+APPLICATIONS&rft.volume=100&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1905-%3C%2Fspan%3E2092&rft.date=2012-06&rft_id=info%3Adoi%2F10.1109%2FJPROC.2012.2197452&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTetzlaff2013" class="citation book cs1">Tetzlaff, Ronald, ed. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=OOW5BAAAQBAJ">Memristors and Memristive Systems</a>. <a href="/wiki/Springer_Science_%26_Business_Media" class="mw-redirect" title="Springer Science & Business Media">Springer Science & Business Media</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4614-9068-5">10.1007/978-1-4614-9068-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4614-9068-5" title="Special:BookSources/978-1-4614-9068-5"><bdi>978-1-4614-9068-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Memristors+and+Memristive+Systems&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2F978-1-4614-9068-5&rft.isbn=978-1-4614-9068-5&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DOOW5BAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdamatzkyChua2013" class="citation book cs1">Adamatzky, Andrew; Chua, Leon, eds. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Mxu4BAAAQBAJ">Memristor Networks</a>. <a href="/wiki/Springer_Science_%26_Business_Media" class="mw-redirect" title="Springer Science & Business Media">Springer Science & Business Media</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-02630-5">10.1007/978-3-319-02630-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-02630-5" title="Special:BookSources/978-3-319-02630-5"><bdi>978-3-319-02630-5</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:39739718">39739718</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Memristor+Networks&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A39739718%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-3-319-02630-5&rft.isbn=978-3-319-02630-5&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMxu4BAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtkin2013" class="citation journal cs1">Atkin, Keith (May 2013). "An introduction to the memristor". Physics Education. 48 (3): 317–321. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PhyEd..48..317A">2013PhyEd..48..317A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0031-9120%2F48%2F3%2F317">10.1088/0031-9120/48/3/317</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121268844">121268844</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Education&rft.atitle=An+introduction+to+the+memristor&rft.volume=48&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E317-%3C%2Fspan%3E321&rft.date=2013-05&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121268844%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0031-9120%2F48%2F3%2F317&rft_id=info%3Abibcode%2F2013PhyEd..48..317A&rft.aulast=Atkin&rft.aufirst=Keith&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGale2014" class="citation journal cs1">Gale, Ella (2014-10-01). "TiO2-based memristors and ReRAM: materials, mechanisms and models (a review)". Semiconductor Science and Technology. 29 (10): 104004. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1611.04456">1611.04456</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014SeScT..29j4004G">2014SeScT..29j4004G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0268-1242%2F29%2F10%2F104004">10.1088/0268-1242/29/10/104004</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:5686212">5686212</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Semiconductor+Science+and+Technology&rft.atitle=TiO%3Csub%3E2%3C%2Fsub%3E-based+memristors+and+ReRAM%3A+materials%2C+mechanisms+and+models+%28a+review%29&rft.volume=29&rft.issue=10&rft.pages=104004&rft.date=2014-10-01&rft_id=info%3Aarxiv%2F1611.04456&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A5686212%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0268-1242%2F29%2F10%2F104004&rft_id=info%3Abibcode%2F2014SeScT..29j4004G&rft.aulast=Gale&rft.aufirst=Ella&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTraversaDi_Ventra2015" class="citation journal cs1">Traversa, Fabio Lorenzo; Di Ventra, Massimiliano (November 2015). "Universal Memcomputing Machines". IEEE Transactions on Neural Networks and Learning Systems. 26 (11): 2702–2715. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1405.0931">1405.0931</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.5690">10.1.1.747.5690</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTNNLS.2015.2391182">10.1109/TNNLS.2015.2391182</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/25667360">25667360</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1406042">1406042</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Neural+Networks+and+Learning+Systems&rft.atitle=Universal+Memcomputing+Machines&rft.volume=26&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2702-%3C%2Fspan%3E2715&rft.date=2015-11&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1406042%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FTNNLS.2015.2391182&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.747.5690%23id-name%3DCiteSeerX&rft_id=info%3Apmid%2F25667360&rft_id=info%3Aarxiv%2F1405.0931&rft.aulast=Traversa&rft.aufirst=Fabio+Lorenzo&rft.au=Di+Ventra%2C+Massimiliano&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCaravelliCarbajal2019" class="citation journal cs1">Caravelli, Francesco; Carbajal, Juan Pablo (January 2019). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Ftechnologies6040118">"Memristors for the curious outsiders"</a>. Technologies. 6 (4): 118. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1812.03389">1812.03389</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Ftechnologies6040118">10.3390/technologies6040118</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:54464654">54464654</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Technologies&rft.atitle=Memristors+for+the+curious+outsiders&rft.volume=6&rft.issue=4&rft.pages=118&rft.date=2019-01&rft_id=info%3Aarxiv%2F1812.03389&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A54464654%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.3390%2Ftechnologies6040118&rft.aulast=Caravelli&rft.aufirst=Francesco&rft.au=Carbajal%2C+Juan+Pablo&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Ftechnologies6040118&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaanJayadeviJames2017" class="citation journal cs1">Maan, Akshay Kumar; Jayadevi, Deepthi Anirudhan; James, Alex Pappachen (August 2017). "A Survey of Memristive Threshold Logic Circuits". IEEE Transactions on Neural Networks and Learning Systems. 28 (8): 1734–1746. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1604.07121">1604.07121</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTNNLS.2016.2547842">10.1109/TNNLS.2016.2547842</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27164608">27164608</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1798273">1798273</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Neural+Networks+and+Learning+Systems&rft.atitle=A+Survey+of+Memristive+Threshold+Logic+Circuits&rft.volume=28&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1734-%3C%2Fspan%3E1746&rft.date=2017-08&rft_id=info%3Aarxiv%2F1604.07121&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1798273%23id-name%3DS2CID&rft_id=info%3Apmid%2F27164608&rft_id=info%3Adoi%2F10.1109%2FTNNLS.2016.2547842&rft.aulast=Maan&rft.aufirst=Akshay+Kumar&rft.au=Jayadevi%2C+Deepthi+Anirudhan&rft.au=James%2C+Alex+Pappachen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGhosh,_M.Singh,_A.Borah,_S._S.Vista,_J.2022" class="citation journal cs1">Ghosh, M., Singh, A., Borah, S. S., Vista, J., Ranjan, A., Kumar, S. (2022). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1109/ted.2022.3160940">"MOSFET-based memristor for high-frequency signal processing"</a>. IEEE Transactions on Electron Devices. 69 (5): 2248–2255. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022ITED...69.2248G">2022ITED...69.2248G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Fted.2022.3160940">10.1109/ted.2022.3160940</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0018-9383">0018-9383</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:247889089">247889089</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Electron+Devices&rft.atitle=MOSFET-based+memristor+for+high-frequency+signal+processing&rft.volume=69&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2248-%3C%2Fspan%3E2255&rft.date=2022&rft_id=info%3Adoi%2F10.1109%2Fted.2022.3160940&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A247889089%23id-name%3DS2CID&rft.issn=0018-9383&rft_id=info%3Abibcode%2F2022ITED...69.2248G&rft.au=Ghosh%2C+M.&rft.au=Singh%2C+A.&rft.au=Borah%2C+S.+S.&rft.au=Vista%2C+J.&rft.au=Ranjan%2C+A.&rft.au=Kumar%2C+S.&rft_id=http%3A%2F%2Fdx.doi.org%2F10.1109%2Fted.2022.3160940&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSingh,_A.Borah,_S._S.Ghosh,_M.2021" class="citation cs2">Singh, A., Borah, S. S., Ghosh, M. (2021), Simple grounded meminductor emulator using transconductance amplifier, IEEE</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Simple+grounded+meminductor+emulator+using+transconductance+amplifier&rft.pub=IEEE&rft.date=2021&rft.au=Singh%2C+A.&rft.au=Borah%2C+S.+S.&rft.au=Ghosh%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Memristor&action=edit&section=45" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Category:Memristors" class="extiw" title="commons:Category:Memristors">Memristors</a>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=n3XzuBt54ig">Finding the missing memristor</a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></li> <li><a rel="nofollow" class="external text" href="http://memlinks.eu">Interactive database of memristor papers (2013)</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSimonite2015" class="citation news cs1">Simonite, Tom (2015-04-21). <a rel="nofollow" class="external text" href="http://www.technologyreview.com/featuredstory/536786/machine-dreams">"Machine Dreams"</a>. Technology Review. Retrieved 2017-12-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Machine+Dreams&rft.date=2015-04-21&rft.aulast=Simonite&rft.aufirst=Tom&rft_id=http%3A%2F%2Fwww.technologyreview.com%2Ffeaturedstory%2F536786%2Fmachine-dreams&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMemristor" class="Z3988"></li> <li><a rel="nofollow" class="external text" href="https://www.sztucznainteligencja.org.pl/leon-chua-a-bulb-versus-google-go-player/">"Leon Chua: A bulb versus Google go player"</a> - (in Polish) an interview with Leon Chua, the creator of memristor</li> <li><a rel="nofollow" class="external text" href="https://www.sztucznainteligencja.org.pl/en/leon-chua-a-bulb-versus-google-go-player/">"Leon Chua: A bulb versus Google go player"</a> - (in English) an interview with Leon Chua, the creator of memristor</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" 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href="/wiki/Future-oriented_technology_analysis" title="Future-oriented technology analysis">Future-oriented technology analysis</a></li> <li><a href="/wiki/Horizon_scanning" title="Horizon scanning">Horizon scanning</a></li> <li><a href="/wiki/Moore%27s_law" title="Moore's law">Moore's law</a></li> <li><a href="/wiki/Technological_singularity" title="Technological singularity">Technological singularity</a></li> <li><a href="/wiki/Technology_scouting" title="Technology scouting">Technology scouting</a></li></ul></li> <li><a href="/wiki/Technology_in_science_fiction" title="Technology in science fiction">Technology in science fiction</a></li> <li><a href="/wiki/Technology_readiness_level" title="Technology readiness level">Technology readiness level</a></li> <li><a href="/wiki/Technology_roadmap" title="Technology roadmap">Technology roadmap</a></li> <li><a href="/wiki/Transhumanism" title="Transhumanism">Transhumanism</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/List_of_emerging_technologies" title="List of emerging technologies">List</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Electronic_components254" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electronic_components" title="Template:Electronic components"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electronic_components" title="Template talk:Electronic components"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electronic_components" title="Special:EditPage/Template:Electronic components"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Electronic_components254" style="font-size:114%;margin:0 4em"><a href="/wiki/Electronic_component" title="Electronic component">Electronic components</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Semiconductor_device" title="Semiconductor device">Semiconductor devices</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/MOSFET" title="MOSFET">MOS transistors</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Transistor" title="Transistor">Transistor</a></li> <li><a href="/wiki/NMOS_logic" title="NMOS logic">NMOS</a></li> <li><a href="/wiki/PMOS_logic" title="PMOS logic">PMOS</a></li> <li><a href="/wiki/BiCMOS" title="BiCMOS">BiCMOS</a></li> <li><a href="/wiki/Bio-FET" title="Bio-FET">BioFET</a></li> <li><a href="/wiki/Chemical_field-effect_transistor" title="Chemical field-effect transistor">Chemical field-effect transistor</a> (ChemFET)</li> <li><a href="/wiki/CMOS" title="CMOS">Complementary MOS</a> (CMOS)</li> <li><a href="/wiki/Depletion-load_NMOS_logic" title="Depletion-load NMOS logic">Depletion-load NMOS</a></li> <li><a href="/wiki/FinFET" class="mw-redirect" title="FinFET">Fin field-effect transistor</a> (FinFET)</li> <li><a href="/wiki/Floating-gate_MOSFET" title="Floating-gate MOSFET">Floating-gate MOSFET</a> (FGMOS)</li> <li><a href="/wiki/Insulated-gate_bipolar_transistor" title="Insulated-gate bipolar transistor">Insulated-gate bipolar transistor</a> (IGBT)</li> <li><a href="/wiki/ISFET" title="ISFET">ISFET</a></li> <li><a href="/wiki/LDMOS" title="LDMOS">LDMOS</a></li> <li><a href="/wiki/MOSFET" title="MOSFET">MOS field-effect transistor</a> (MOSFET)</li> <li><a href="/wiki/Multigate_device" title="Multigate device">Multi-gate field-effect transistor</a> (MuGFET)</li> <li><a href="/wiki/Power_MOSFET" title="Power MOSFET">Power MOSFET</a></li> <li><a href="/wiki/Thin-film_transistor" title="Thin-film transistor">Thin-film transistor</a> (TFT)</li> <li><a href="/wiki/VMOS" title="VMOS">VMOS</a></li> <li><a href="/wiki/Power_MOSFET#UMOS" title="Power MOSFET">UMOS</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Transistor" title="Transistor">Other transistors</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bipolar_junction_transistor" title="Bipolar junction transistor">Bipolar junction transistor</a> (BJT)</li> <li><a href="/wiki/Darlington_transistor" title="Darlington transistor">Darlington transistor</a></li> <li><a href="/wiki/Diffused_junction_transistor" title="Diffused junction transistor">Diffused junction transistor</a></li> <li><a href="/wiki/Field-effect_transistor" title="Field-effect transistor">Field-effect transistor</a> (FET) <ul><li><a href="/wiki/JFET" title="JFET">Junction Gate FET (JFET)</a></li> <li><a href="/wiki/Organic_field-effect_transistor" title="Organic field-effect transistor">Organic FET (OFET)</a></li></ul></li> <li><a href="/wiki/Light-emitting_transistor" title="Light-emitting transistor">Light-emitting transistor</a> (LET) <ul><li><a href="/wiki/Organic_light-emitting_transistor" title="Organic light-emitting transistor">Organic LET (OLET)</a></li></ul></li> <li><a href="/wiki/Pentode_transistor" title="Pentode transistor">Pentode transistor</a></li> <li><a href="/wiki/Point-contact_transistor" title="Point-contact transistor">Point-contact transistor</a></li> <li><a href="/wiki/Programmable_unijunction_transistor" title="Programmable unijunction transistor">Programmable unijunction transistor</a> (PUT)</li> <li><a href="/wiki/Static_induction_transistor" title="Static induction transistor">Static induction transistor</a> (SIT)</li> <li><a href="/wiki/Tetrode_transistor" title="Tetrode transistor">Tetrode transistor</a></li> <li><a href="/wiki/Unijunction_transistor" title="Unijunction transistor">Unijunction transistor</a> (UJT)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Diode" title="Diode">Diodes</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Avalanche_diode" title="Avalanche diode">Avalanche diode</a></li> <li><a href="/wiki/Constant-current_diode" title="Constant-current diode">Constant-current diode</a> (CLD, CRD)</li> <li><a href="/wiki/Gunn_diode" title="Gunn diode">Gunn diode</a></li> <li><a href="/wiki/Laser_diode" title="Laser diode">Laser diode</a> (LD)</li> <li><a href="/wiki/Light-emitting_diode" title="Light-emitting diode">Light-emitting diode</a> (LED)</li> <li><a href="/wiki/OLED" title="OLED">Organic light-emitting diode</a> (OLED)</li> <li><a href="/wiki/Photodiode" title="Photodiode">Photodiode</a></li> <li><a href="/wiki/PIN_diode" title="PIN diode">PIN diode</a></li> <li><a href="/wiki/Schottky_diode" title="Schottky diode">Schottky diode</a></li> <li><a href="/wiki/Step_recovery_diode" title="Step recovery diode">Step recovery diode</a></li> <li><a href="/wiki/Zener_diode" title="Zener diode">Zener diode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other devices</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Printed_electronics" title="Printed electronics">Printed electronics</a></li> <li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/DIAC" title="DIAC">DIAC</a></li> <li><a href="/wiki/Heterostructure_barrier_varactor" title="Heterostructure barrier varactor">Heterostructure barrier varactor</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a> (IC)</li> <li><a href="/wiki/Hybrid_integrated_circuit" title="Hybrid integrated circuit">Hybrid integrated circuit</a></li> <li><a href="/wiki/Light_emitting_capacitor" class="mw-redirect" title="Light emitting capacitor">Light emitting capacitor</a> (LEC)</li> <li><a href="/wiki/Memistor" title="Memistor">Memistor</a></li> <li><a class="mw-selflink selflink">Memristor</a></li> <li><a href="/wiki/Memtransistor" title="Memtransistor">Memtransistor</a></li> <li><a href="/wiki/Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li> <li><a href="/wiki/Metal-oxide_varistor" class="mw-redirect" title="Metal-oxide varistor">Metal-oxide varistor</a> (MOV)</li> <li><a href="/wiki/Mixed-signal_integrated_circuit" title="Mixed-signal integrated circuit">Mixed-signal integrated circuit</a></li> <li><a href="/wiki/MOS_integrated_circuit" class="mw-redirect" title="MOS integrated circuit">MOS integrated circuit</a> (MOS IC)</li> <li><a href="/wiki/Organic_semiconductor" title="Organic semiconductor">Organic semiconductor</a></li> <li><a href="/wiki/Photodetector" title="Photodetector">Photodetector</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/RF_CMOS" title="RF CMOS">RF CMOS</a></li> <li><a href="/wiki/Silicon_controlled_rectifier" title="Silicon controlled rectifier">Silicon controlled rectifier</a> (SCR)</li> <li><a href="/wiki/Solaristor" title="Solaristor">Solaristor</a></li> <li><a href="/wiki/Static_induction_thyristor" title="Static induction thyristor">Static induction thyristor</a> (SITh)</li> <li><a href="/wiki/Three-dimensional_integrated_circuit" title="Three-dimensional integrated circuit">Three-dimensional integrated circuit</a> (3D IC)</li> <li><a href="/wiki/Thyristor" title="Thyristor">Thyristor</a></li> <li><a href="/wiki/Trancitor" title="Trancitor">Trancitor</a></li> <li><a href="/wiki/TRIAC" title="TRIAC">TRIAC</a></li> <li><a href="/wiki/Varicap" title="Varicap">Varicap</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Voltage_regulator" title="Voltage regulator">Voltage regulators</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Linear_regulator" title="Linear regulator">Linear regulator</a></li> <li><a href="/wiki/Low-dropout_regulator" title="Low-dropout regulator">Low-dropout regulator</a></li> <li><a href="/wiki/Switching_regulator" class="mw-redirect" title="Switching regulator">Switching regulator</a></li> <li><a href="/wiki/Buck_converter" title="Buck converter">Buck</a></li> <li><a href="/wiki/Boost_converter" title="Boost converter">Boost</a></li> <li><a href="/wiki/Buck%E2%80%93boost_converter" title="Buck–boost converter">Buck–boost</a></li> <li><a href="/wiki/Split-pi_topology" title="Split-pi topology">Split-pi</a></li> <li><a href="/wiki/%C4%86uk_converter" title="Ćuk converter">Ćuk</a></li> <li><a href="/wiki/Single-ended_primary-inductor_converter" title="Single-ended primary-inductor converter">SEPIC</a></li> <li><a href="/wiki/Charge_pump" title="Charge pump">Charge pump</a></li> <li><a href="/wiki/Switched_capacitor" title="Switched capacitor">Switched capacitor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Vacuum_tube" title="Vacuum tube">Vacuum tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acorn_tube" title="Acorn tube">Acorn tube</a></li> <li><a href="/wiki/Audion" title="Audion">Audion</a></li> <li><a href="/wiki/Beam_tetrode" title="Beam tetrode">Beam tetrode</a></li> <li><a href="/wiki/Hot-wire_barretter" title="Hot-wire barretter">Barretter</a></li> <li><a href="/wiki/Compactron" title="Compactron">Compactron</a></li> <li><a href="/wiki/Vacuum_diode" class="mw-redirect" title="Vacuum diode">Diode</a></li> <li><a href="/wiki/Fleming_valve" title="Fleming valve">Fleming valve</a></li> <li><a href="/wiki/Neutron_generator" title="Neutron generator">Neutron tube</a></li> <li><a href="/wiki/Nonode" title="Nonode">Nonode</a></li> <li><a href="/wiki/Nuvistor" title="Nuvistor">Nuvistor</a></li> <li><a href="/wiki/Pentagrid_converter" title="Pentagrid converter">Pentagrid</a> (Hexode, Heptode, Octode)</li> <li><a href="/wiki/Pentode" title="Pentode">Pentode</a></li> <li><a href="/wiki/Photomultiplier_tube" title="Photomultiplier tube">Photomultiplier</a></li> <li><a href="/wiki/Phototube" title="Phototube">Phototube</a></li> <li><a href="/wiki/Tetrode" title="Tetrode">Tetrode</a></li> <li><a href="/wiki/Triode" title="Triode">Triode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Vacuum_tube" title="Vacuum tube">Vacuum tubes</a> (<a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">RF</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Backward-wave_oscillator" title="Backward-wave oscillator">Backward-wave oscillator</a> (BWO)</li> <li><a href="/wiki/Cavity_magnetron" title="Cavity magnetron">Cavity magnetron</a></li> <li><a href="/wiki/Crossed-field_amplifier" title="Crossed-field amplifier">Crossed-field amplifier</a> (CFA)</li> <li><a href="/wiki/Gyrotron" title="Gyrotron">Gyrotron</a></li> <li><a href="/wiki/Inductive_output_tube" title="Inductive output tube">Inductive output tube</a> (IOT)</li> <li><a href="/wiki/Klystron" title="Klystron">Klystron</a></li> <li><a href="/wiki/Maser" title="Maser">Maser</a></li> <li><a href="/wiki/Sutton_tube" title="Sutton tube">Sutton tube</a></li> <li><a href="/wiki/Traveling-wave_tube" title="Traveling-wave tube">Traveling-wave tube</a> (TWT)</li> <li><a href="/wiki/X-ray_tube" title="X-ray tube">X-ray tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Cathode-ray_tube" title="Cathode-ray tube">Cathode-ray tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Beam_deflection_tube" title="Beam deflection tube">Beam deflection tube</a></li> <li><a href="/wiki/Charactron" title="Charactron">Charactron</a></li> <li><a href="/wiki/Iconoscope" title="Iconoscope">Iconoscope</a></li> <li><a href="/wiki/Magic_eye_tube" title="Magic eye tube">Magic eye tube</a></li> <li><a href="/wiki/Monoscope" title="Monoscope">Monoscope</a></li> <li><a href="/wiki/Selectron_tube" title="Selectron tube">Selectron tube</a></li> <li><a href="/wiki/Storage_tube" title="Storage tube">Storage tube</a></li> <li><a href="/wiki/Trochotron" class="mw-redirect" title="Trochotron">Trochotron</a></li> <li><a href="/wiki/Video_camera_tube" title="Video camera tube">Video camera tube</a></li> <li><a href="/wiki/Williams_tube" title="Williams tube">Williams tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Gas-filled_tube" title="Gas-filled tube">Gas-filled tubes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cold_cathode" title="Cold cathode">Cold cathode</a></li> <li><a href="/wiki/Crossatron" title="Crossatron">Crossatron</a></li> <li><a href="/wiki/Dekatron" title="Dekatron">Dekatron</a></li> <li><a href="/wiki/Ignitron" title="Ignitron">Ignitron</a></li> <li><a href="/wiki/Krytron" title="Krytron">Krytron</a></li> <li><a href="/wiki/Mercury-arc_valve" title="Mercury-arc valve">Mercury-arc valve</a></li> <li><a href="/wiki/Neon_lamp" title="Neon lamp">Neon lamp</a></li> <li><a href="/wiki/Nixie_tube" title="Nixie tube">Nixie tube</a></li> <li><a href="/wiki/Thyratron" title="Thyratron">Thyratron</a></li> <li><a href="/wiki/Trigatron" title="Trigatron">Trigatron</a></li> <li><a href="/wiki/Voltage-regulator_tube" title="Voltage-regulator tube">Voltage-regulator tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Adjustable</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Potentiometer" title="Potentiometer">Potentiometer</a> <ul><li><a href="/wiki/Digital_potentiometer" title="Digital potentiometer">digital</a></li></ul></li> <li><a href="/wiki/Variable_capacitor" title="Variable capacitor">Variable capacitor</a></li> <li><a href="/wiki/Varicap" title="Varicap">Varicap</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Passive</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Connector <ul><li><a href="/wiki/Audio_and_video_interfaces_and_connectors" title="Audio and video interfaces and connectors">audio and video</a></li> <li><a href="/wiki/AC_power_plugs_and_sockets" title="AC power plugs and sockets">electrical power</a></li> <li><a href="/wiki/RF_connector" title="RF connector">RF</a></li></ul></li> <li><a href="/wiki/Electrolytic_detector" title="Electrolytic detector">Electrolytic detector</a></li> <li><a href="/wiki/Ferrite_core" title="Ferrite core">Ferrite</a></li> <li><a href="/wiki/Antifuse" title="Antifuse">Antifuse</a></li> <li><a href="/wiki/Fuse_(electrical)" title="Fuse (electrical)">Fuse</a> <ul><li><a href="/wiki/Resettable_fuse" title="Resettable fuse">resettable</a></li> <li><a href="/wiki/EFUSE" class="mw-redirect" title="EFUSE">eFUSE</a></li></ul></li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/Switch" title="Switch">Switch</a></li> <li><a href="/wiki/Thermistor" title="Thermistor">Thermistor</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li> <li><a href="/wiki/Varistor" title="Varistor">Varistor</a></li> <li><a href="/wiki/Wire" title="Wire">Wire</a> <ul><li><a href="/wiki/Wollaston_wire" title="Wollaston wire">Wollaston wire</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electrical_reactance" title="Electrical reactance">Reactive</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Capacitor" title="Capacitor">Capacitor</a> <ul><li><a href="/wiki/Capacitor_types" title="Capacitor types">types</a></li></ul></li> <li><a href="/wiki/Ceramic_resonator" title="Ceramic resonator">Ceramic resonator</a></li> <li><a href="/wiki/Crystal_oscillator" title="Crystal oscillator">Crystal oscillator</a></li> <li><a href="/wiki/Inductor" title="Inductor">Inductor</a></li> <li><a href="/wiki/Parametron" title="Parametron">Parametron</a></li> <li><a href="/wiki/Relay" title="Relay">Relay</a> <ul><li><a href="/wiki/Reed_relay" title="Reed relay">reed relay</a></li> <li><a href="/wiki/Mercury_relay" title="Mercury relay">mercury relay</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Differentiable_computing254" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Differentiable_computing" title="Template:Differentiable computing"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Differentiable_computing" title="Template talk:Differentiable computing"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Differentiable_computing" title="Special:EditPage/Template:Differentiable computing"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Differentiable_computing254" style="font-size:114%;margin:0 4em">Differentiable computing</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Differentiable_function" title="Differentiable function">General</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Differentiable_programming" title="Differentiable programming">Differentiable programming</a></li> <li><a href="/wiki/Information_geometry" title="Information geometry">Information geometry</a></li> <li><a href="/wiki/Statistical_manifold" title="Statistical manifold">Statistical manifold</a></li> <li><a href="/wiki/Automatic_differentiation" title="Automatic differentiation">Automatic differentiation</a></li> <li><a href="/wiki/Neuromorphic_computing" title="Neuromorphic computing">Neuromorphic computing</a></li> <li><a href="/wiki/Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li> <li><a href="/wiki/Ricci_calculus" title="Ricci calculus">Ricci calculus</a></li> <li><a href="/wiki/Computational_learning_theory" title="Computational learning theory">Computational learning theory</a></li> <li><a href="/wiki/Inductive_bias" title="Inductive bias">Inductive bias</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hardware</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Graphcore" title="Graphcore">IPU</a></li> <li><a href="/wiki/Tensor_Processing_Unit" title="Tensor Processing Unit">TPU</a></li> <li><a href="/wiki/Vision_processing_unit" title="Vision processing unit">VPU</a></li> <li><a class="mw-selflink selflink">Memristor</a></li> <li><a href="/wiki/SpiNNaker" title="SpiNNaker">SpiNNaker</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" 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