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href="#Photovoltaic_cells"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Photovoltaic cells</span> </div> </a> <ul id="toc-Photovoltaic_cells-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-List_of_band_gaps" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#List_of_band_gaps"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>List of band gaps</span> </div> </a> <ul id="toc-List_of_band_gaps-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Optical_versus_electronic_bandgap" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Optical_versus_electronic_bandgap"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Optical versus electronic bandgap</span> </div> </a> <ul id="toc-Optical_versus_electronic_bandgap-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Band_gaps_for_other_quasi-particles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Band_gaps_for_other_quasi-particles"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Band gaps for other quasi-particles</span> </div> </a> <ul id="toc-Band_gaps_for_other_quasi-particles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Materials" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Materials</span> </div> </a> <button aria-controls="toc-Materials-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Materials subsection</span> </button> <ul id="toc-Materials-sublist" class="vector-toc-list"> <li id="toc-List_of_electronics_topics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#List_of_electronics_topics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>List of electronics topics</span> </div> </a> <ul id="toc-List_of_electronics_topics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </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" 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href="https://ar.wikipedia.org/wiki/%D9%81%D8%AC%D9%88%D8%A9_%D8%A7%D9%84%D9%86%D8%B7%D8%A7%D9%82" title="فجوة النطاق – Arabic" lang="ar" hreflang="ar" data-title="فجوة النطاق" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Banda_prohibida" title="Banda prohibida – Catalan" lang="ca" hreflang="ca" data-title="Banda prohibida" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Bandl%C3%BCcke" title="Bandlücke – German" lang="de" hreflang="de" data-title="Bandlücke" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Keelutsoon_(f%C3%BC%C3%BCsika)" title="Keelutsoon (füüsika) – Estonian" lang="et" hreflang="et" data-title="Keelutsoon (füüsika)" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Banda_prohibida" title="Banda prohibida – Spanish" lang="es" hreflang="es" data-title="Banda prohibida" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Bendbre%C4%89o" title="Bendbreĉo – Esperanto" lang="eo" hreflang="eo" data-title="Bendbreĉo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D9%88%D8%A7%D8%B1_%D9%85%D9%85%D9%86%D9%88%D8%B9%D9%87" title="نوار ممنوعه – Persian" lang="fa" hreflang="fa" data-title="نوار ممنوعه" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Bande_interdite" title="Bande interdite – French" lang="fr" hreflang="fr" data-title="Bande interdite" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9D%A0%ED%8B%88" title="띠틈 – Korean" lang="ko" hreflang="ko" data-title="띠틈" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%88%E0%A4%A3%E0%A5%8D%E0%A4%A1_%E0%A4%85%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A4%B0%E0%A4%BE%E0%A4%B2" title="बैण्ड अन्तराल – Hindi" lang="hi" hreflang="hi" data-title="बैण्ड अन्तराल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Banda_proibita" title="Banda proibita – Italian" lang="it" hreflang="it" data-title="Banda proibita" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%A2%D7%A8_%D7%90%D7%A1%D7%95%D7%A8" title="פער אסור – Hebrew" lang="he" hreflang="he" data-title="פער אסור" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Tiltott_s%C3%A1v" title="Tiltott sáv – Hungarian" lang="hu" hreflang="hu" data-title="Tiltott sáv" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%B1%E0%B5%8D_%E0%B4%97%E0%B5%8D%E0%B4%AF%E0%B4%BE%E0%B4%AA%E0%B5%8D" title="ബാന്റ് ഗ്യാപ് – Malayalam" lang="ml" hreflang="ml" data-title="ബാന്റ് ഗ്യാപ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Verboden_zone" title="Verboden zone – Dutch" lang="nl" hreflang="nl" data-title="Verboden zone" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%90%E3%83%B3%E3%83%89%E3%82%AE%E3%83%A3%E3%83%83%E3%83%97" title="バンドギャップ – Japanese" lang="ja" hreflang="ja" data-title="バンドギャップ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Taqiqlangan_zona" title="Taqiqlangan zona – Uzbek" lang="uz" hreflang="uz" data-title="Taqiqlangan zona" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przerwa_energetyczna" title="Przerwa energetyczna – Polish" lang="pl" hreflang="pl" data-title="Przerwa energetyczna" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Banda_proibida" title="Banda proibida – Portuguese" lang="pt" hreflang="pt" data-title="Banda proibida" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BF%D1%80%D0%B5%D1%89%D1%91%D0%BD%D0%BD%D0%B0%D1%8F_%D0%B7%D0%BE%D0%BD%D0%B0" title="Запрещённая зона – Russian" lang="ru" hreflang="ru" data-title="Запрещённая зона" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Band_gap" title="Band gap – Simple English" lang="en-simple" hreflang="en-simple" data-title="Band gap" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Prepovedani_pas" title="Prepovedani pas – Slovenian" lang="sl" hreflang="sl" data-title="Prepovedani pas" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bandgap" title="Bandgap – Swedish" lang="sv" hreflang="sv" data-title="Bandgap" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%8A%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%A7%E0%B9%88%E0%B8%B2%E0%B8%87%E0%B8%9E%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%87%E0%B8%B2%E0%B8%99" title="ช่องว่างพลังงาน – Thai" lang="th" hreflang="th" data-title="ช่องว่างพลังงาน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Bant_aral%C4%B1%C4%9F%C4%B1" title="Bant aralığı – Turkish" lang="tr" hreflang="tr" data-title="Bant aralığı" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B0%D0%B1%D0%BE%D1%80%D0%BE%D0%BD%D0%B5%D0%BD%D0%B0_%D0%B7%D0%BE%D0%BD%D0%B0" title="Заборонена зона – Ukrainian" lang="uk" hreflang="uk" data-title="Заборонена зона" 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Bandgap&redirect=no" class="mw-redirect" title="Bandgap">Bandgap</a>)</span></div></div> <div id="mw-content-text" 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">Energy range in a solid where no electron states exist</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">This article is about solid state physics. For voltage control circuitry in electronics, see <a href="/wiki/Bandgap_voltage_reference" title="Bandgap voltage reference">Bandgap voltage reference</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">This article is about the electronic bandgap found in semiconductors. For the photonic band gap, see <a href="/wiki/Photonic_crystal" title="Photonic crystal">Photonic crystal</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Solid_state_electronic_band_structure.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Solid_state_electronic_band_structure.svg/440px-Solid_state_electronic_band_structure.svg.png" decoding="async" width="440" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Solid_state_electronic_band_structure.svg/660px-Solid_state_electronic_band_structure.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Solid_state_electronic_band_structure.svg/880px-Solid_state_electronic_band_structure.svg.png 2x" data-file-width="388" data-file-height="177" /></a><figcaption>Graph of carbon atoms being brought together to form a diamond crystal, demonstrating formation of the electronic band structure and band gap. The right graph shows the energy levels as a function of the spacing between atoms. When far apart <i>(right side of graph)</i> all the atoms have discrete valence orbitals <i>p</i> and <i>s</i> with the same energies. However, when the atoms come closer <i>(left side)</i>, their electron orbitals begin to spatially overlap and hybridize into <i>N</i> molecular orbitals each with a different energy, where <i>N</i> is the number of atoms in the crystal. Since <i>N</i> is such a large number, adjacent orbitals are extremely close together in energy so the orbitals can be considered a continuous energy band. At the actual diamond crystal cell size (denoted by <i>a</i>), two bands are formed, called the valence and conduction bands, separated by a 5.5 eV band gap. The <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> limits the number of electrons in a single orbital to two, and the bands are filled beginning with the lowest energy.</figcaption></figure> <p>In <a href="/wiki/Solid-state_physics" title="Solid-state physics">solid-state physics</a> and <a href="/wiki/Solid-state_chemistry" title="Solid-state chemistry">solid-state chemistry</a>, a <b>band gap</b>, also called a <b>bandgap</b> or <b>energy gap</b>, is an energy range in a solid where no <a href="/wiki/Electronic_state" class="mw-redirect" title="Electronic state">electronic states</a> exist. In graphs of the <a href="/wiki/Electronic_band_structure" title="Electronic band structure">electronic band structure</a> of solids, the band gap refers to the energy difference (often expressed in <a href="/wiki/Electronvolt" title="Electronvolt">electronvolts</a>) between the top of the <a href="/wiki/Valence_band" class="mw-redirect" title="Valence band">valence band</a> and the bottom of the <a href="/wiki/Conduction_band" class="mw-redirect" title="Conduction band">conduction band</a> in <a href="/wiki/Electrical_insulation" class="mw-redirect" title="Electrical insulation">insulators</a> and <a href="/wiki/Semiconductor" title="Semiconductor">semiconductors</a>. It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron (and the <a href="/wiki/Electron_hole" title="Electron hole">electron hole</a> in the valence band) are free to move within the crystal lattice and serve as charge carriers to conduct <a href="/wiki/Electric_current" title="Electric current">electric current</a>. It is closely related to the <a href="/wiki/HOMO/LUMO" class="mw-redirect" title="HOMO/LUMO">HOMO/LUMO gap</a> in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band (mostly full) to the conduction band (mostly empty), then current <i>can</i> flow (see <a href="/wiki/Carrier_generation_and_recombination" title="Carrier generation and recombination">carrier generation and recombination</a>). Therefore, the band gap is a major factor determining the <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a> of a solid. Substances having large band gaps (also called "wide" band gaps) are generally <a href="/wiki/Insulator_(electrical)" class="mw-redirect" title="Insulator (electrical)">insulators</a>, those with small band gaps (also called "narrow" band gaps) are <a href="/wiki/Semiconductors" class="mw-redirect" title="Semiconductors">semiconductors</a>, and <a href="/wiki/Electrical_conductor" title="Electrical conductor">conductors</a> either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band. </p><p>It is possible to produce laser induced insulator-metal transitions which have already been experimentally observed in some condensed matter systems, like thin films of <style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">C<sub class="template-chem2-sub">60</sub></span>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> doped manganites,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> or in vanadium sesquioxide <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410" /><span class="chemf nowrap">V<sub class="template-chem2-sub">2</sub>O<sub class="template-chem2-sub">3</sub></span>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> These are special cases of the more general metal-to-nonmetal transitions phenomena which were intensively studied in the last decades.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> A one-dimensional analytic model of laser induced distortion of band structure was presented for a spatially periodic (cosine) potential. This problem is periodic both in space and time and can be solved analytically using the Kramers-Henneberger <a href="/wiki/Co-moving_frame" class="mw-redirect" title="Co-moving frame">co-moving frame</a>. The solutions can be given with the help of the <a href="/wiki/Mathieu_function" title="Mathieu function">Mathieu functions.</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="In_semiconductor_physics">In semiconductor physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=1" title="Edit section: In semiconductor physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Bandgap_in_semiconductor.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bandgap_in_semiconductor.svg/220px-Bandgap_in_semiconductor.svg.png" decoding="async" width="220" height="374" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bandgap_in_semiconductor.svg/330px-Bandgap_in_semiconductor.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Bandgap_in_semiconductor.svg/440px-Bandgap_in_semiconductor.svg.png 2x" data-file-width="300" data-file-height="510" /></a><figcaption>Semiconductor <a href="/wiki/Electronic_band_structure" title="Electronic band structure">band structure</a>.</figcaption></figure> <p>Every solid has its own characteristic <a href="/wiki/Electronic_band_structure" title="Electronic band structure">energy-band structure</a>. This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials. Depending on the dimension, the band structure and spectroscopy can vary. The different types of dimensions are as listed: one dimension, two dimensions, and three dimensions.<sup id="cite_ref-:0_6-0" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In semiconductors and insulators, <a href="/wiki/Electron" title="Electron">electrons</a> are confined to a number of <a href="/wiki/Electronic_band_structure" title="Electronic band structure">bands</a> of energy, and forbidden from other regions because there are no allowable electronic states for them to occupy. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band. Electrons are able to jump from one band to another. However, in order for a valence band electron to be promoted to the conduction band, it requires a specific minimum amount of energy for the transition. This required energy is an <a href="/wiki/Intrinsic_and_extrinsic_properties" title="Intrinsic and extrinsic properties">intrinsic</a> characteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either a <a href="/wiki/Phonon" title="Phonon">phonon</a> (heat) or a <a href="/wiki/Photon" title="Photon">photon</a> (light). </p><p>A <a href="/wiki/Semiconductor" title="Semiconductor">semiconductor</a> is a material with an intermediate-sized, non-zero band gap that behaves as an insulator at T=0K, but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point. In contrast, a material with a large band gap is an <a href="/wiki/Electrical_insulator" class="mw-redirect" title="Electrical insulator">insulator</a>. In <a href="/wiki/Electrical_conductor" title="Electrical conductor">conductors</a>, the valence and conduction bands may overlap, so there is no longer a bandgap with forbidden regions of electronic states. </p><p>The <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">conductivity</a> of <a href="/wiki/Intrinsic_semiconductor" title="Intrinsic semiconductor">intrinsic semiconductors</a> is strongly dependent on the band gap. The only available charge carriers for conduction are the electrons that have enough thermal energy to be excited across the band gap and the <a href="/wiki/Electron_hole" title="Electron hole">electron holes</a> that are left off when such an excitation occurs. </p><p>Band-gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor <a href="/wiki/Alloy" title="Alloy">alloys</a>, such as <a href="/wiki/Aluminium_gallium_arsenide" title="Aluminium gallium arsenide">GaAlAs</a>, <a href="/wiki/Indium_gallium_arsenide" title="Indium gallium arsenide">InGaAs</a>, and <a href="/wiki/Aluminium_indium_arsenide" title="Aluminium indium arsenide">InAlAs</a>. It is also possible to construct layered materials with alternating compositions by techniques like <a href="/wiki/Molecular-beam_epitaxy" title="Molecular-beam epitaxy">molecular-beam epitaxy</a>. These methods are exploited in the design of <a href="/wiki/Heterojunction_bipolar_transistor" title="Heterojunction bipolar transistor">heterojunction bipolar transistors</a> (HBTs), <a href="/wiki/Laser_diode" title="Laser diode">laser diodes</a> and <a href="/wiki/Solar_cell" title="Solar cell">solar cells</a>. </p><p>The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as a type of insulator with a narrow band gap. Insulators with a larger band gap, usually greater than 4 eV,<sup id="cite_ref-Solid_State_Devices_and_Technology_7-0" class="reference"><a href="#cite_note-Solid_State_Devices_and_Technology-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. <a href="/wiki/Electron_mobility" title="Electron mobility">Electron mobility</a> also plays a role in determining a material's informal classification. </p><p>The band-gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increase, leading to larger interatomic spacing. The interaction between the lattice <a href="/wiki/Phonon" title="Phonon">phonons</a> and the free electrons and holes will also affect the band gap to a smaller extent.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The relationship between band gap energy and temperature can be described by <a href="/wiki/Y._P._Varshni" title="Y. P. Varshni">Varshni</a>'s empirical expression (named after <a href="/wiki/Y._P._Varshni" title="Y. P. Varshni">Y. P. Varshni</a>), </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{g}(T)=E_{g}(0)-{\frac {\alpha T^{2}}{T+\beta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>T</mi> <mo>+</mo> <mi>β</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{g}(T)=E_{g}(0)-{\frac {\alpha T^{2}}{T+\beta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/640a2018b284aaaa072256b71ca208ae08314876" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.474ex; height:6.176ex;" alt="{\displaystyle E_{g}(T)=E_{g}(0)-{\frac {\alpha T^{2}}{T+\beta }}}" /></span>, where <i>E<sub>g</sub></i>(0), α and β are material constants.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Furthermore, lattice vibrations increase with temperature, which increases the effect of electron scattering. Additionally, the number of charge carriers within a semiconductor will increase, as more carriers have the energy required to cross the band-gap threshold and so conductivity of semiconductors also increases with increasing temperature.<sup id="cite_ref-:03_10-0" class="reference"><a href="#cite_note-:03-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The external pressure also influences the electronic structure of semiconductors and, therefore, their optical band gaps.<sup id="cite_ref-Pankove_11-0" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states. In a <a href="/wiki/Quantum_dot" title="Quantum dot">quantum dot</a> crystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> It is also known as <a href="/wiki/Quantum_confinement_effect" class="mw-redirect" title="Quantum confinement effect">quantum confinement effect</a>. </p><p>Band gaps can be either <a href="/wiki/Direct_and_indirect_bandgaps" class="mw-redirect" title="Direct and indirect bandgaps">direct or indirect</a>, depending on the <a href="/wiki/Electronic_band_structure" title="Electronic band structure">electronic band structure</a> of the material.<sup id="cite_ref-Pankove_11-1" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Yu&Cardona_13-0" class="reference"><a href="#cite_note-Yu&Cardona-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fox_14-0" class="reference"><a href="#cite_note-Fox-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>It was mentioned earlier that the dimensions have different band structure and spectroscopy. For non-metallic solids, which are one dimensional, have optical properties that are dependent on the electronic transitions between valence and conduction bands. In addition, the spectroscopic transition probability is between the initial and final orbital and it depends on the integral.<sup id="cite_ref-:0_6-1" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> φ<sub>i</sub> is the initial orbital, φ<sub>f</sub> is the final orbital, ʃ φ<sub>f</sub><sup>*</sup>ûεφ<sub>i</sub> is the integral, ε is the electric vector, and u is the dipole moment.<sup id="cite_ref-:0_6-2" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Two-dimensional structures of solids behave because of the overlap of atomic orbitals.<sup id="cite_ref-:0_6-3" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The simplest two-dimensional crystal contains identical atoms arranged on a square lattice.<sup id="cite_ref-:0_6-4" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Energy splitting occurs at the Brillouin zone edge for one-dimensional situations because of a weak periodic potential, which produces a gap between bands. The behavior of the one-dimensional situations does not occur for two-dimensional cases because there are extra freedoms of motion. Furthermore, a bandgap can be produced with strong periodic potential for two-dimensional and three-dimensional cases.<sup id="cite_ref-:0_6-5" class="reference"><a href="#cite_note-:0-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Direct_and_indirect_band_gap">Direct and indirect band gap</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=2" title="Edit section: Direct and indirect band gap"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Direct_and_indirect_bandgaps" class="mw-redirect" title="Direct and indirect bandgaps">Direct and indirect bandgaps</a></div> <p>Based on their band structure, materials are characterised with a direct band gap or indirect band gap. In the free-electron model, k is the momentum of a free electron and assumes unique values within the Brillouin zone that outlines the periodicity of the crystal lattice. If the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band of a material have the same value, then the material has a direct bandgap. If they are not the same, then the material has an indirect band gap and the electronic transition must undergo momentum transfer to satisfy conservation. Such indirect "forbidden" transitions still occur, however at very low probabilities and weaker energy.<sup id="cite_ref-Pankove_11-2" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Yu&Cardona_13-1" class="reference"><a href="#cite_note-Yu&Cardona-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fox_14-1" class="reference"><a href="#cite_note-Fox-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In contrast, for materials with an indirect band gap, a photon and <a href="/wiki/Phonon" title="Phonon">phonon</a> must both be involved in a transition from the valence band top to the conduction band bottom, involving a <a href="/wiki/Direct_and_indirect_band_gaps" title="Direct and indirect band gaps">momentum change</a>. Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited for <a href="/wiki/Photovoltaics" title="Photovoltaics">photovoltaics</a> (PVs), <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">light-emitting diodes</a> (LEDs), and <a href="/wiki/Laser_diode" title="Laser diode">laser diodes</a>;<sup id="cite_ref-Sze_16-0" class="reference"><a href="#cite_note-Sze-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties. </p> <div class="mw-heading mw-heading3"><h3 id="Light-emitting_diodes_and_laser_diodes">Light-emitting diodes and laser diodes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=3" title="Edit section: Light-emitting diodes and laser diodes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">Light-emitting diode</a></div> <p>LEDs and <a href="/wiki/Laser_diode" title="Laser diode">laser diodes</a> usually emit photons with energy close to and slightly larger than the band gap of the semiconductor material from which they are made. Therefore, as the band gap energy increases, the LED or laser color changes from infrared to red, through the rainbow to violet, then to UV.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Photovoltaic_cells">Photovoltaic cells</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=4" title="Edit section: Photovoltaic cells"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Solar_cell" title="Solar cell">Solar cell</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:ShockleyQueisserFullCurve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/ShockleyQueisserFullCurve.svg/220px-ShockleyQueisserFullCurve.svg.png" decoding="async" width="220" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/ShockleyQueisserFullCurve.svg/330px-ShockleyQueisserFullCurve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/ShockleyQueisserFullCurve.svg/440px-ShockleyQueisserFullCurve.svg.png 2x" data-file-width="969" data-file-height="720" /></a><figcaption>The <a href="/wiki/Shockley%E2%80%93Queisser_limit" title="Shockley–Queisser limit">Shockley–Queisser limit</a> gives the maximum possible efficiency of a single-junction solar cell under un-concentrated sunlight, as a function of the semiconductor band gap. If the band gap is too high, most daylight photons cannot be absorbed; if it is too low, then most photons have much more energy than necessary to excite electrons across the band gap, and the rest is wasted.<sup id="cite_ref-Goetzberger_18-0" class="reference"><a href="#cite_note-Goetzberger-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The semiconductors commonly used in commercial solar cells have band gaps near the peak of this curve, as it occurs in silicon-based cells. The Shockley–Queisser limit has been exceeded experimentally by combining materials with different band gap energies to make, for example, <a href="/wiki/Tandem_solar_cell" class="mw-redirect" title="Tandem solar cell">tandem solar cells</a>.</figcaption></figure> <p>The optical band gap (see below) determines what portion of the solar spectrum a <a href="/wiki/Photovoltaics" title="Photovoltaics">photovoltaic cell</a> absorbs.<sup id="cite_ref-Goetzberger_18-1" class="reference"><a href="#cite_note-Goetzberger-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Strictly, a semiconductor will not absorb photons of energy less than the band gap; whereas most of the photons with energies exceeding the band gap will generate heat. Neither of them contribute to the efficiency of a solar cell. One way to circumvent this problem is based on the so-called photon management concept, in which case the solar spectrum is modified to match the absorption profile of the solar cell.<sup id="cite_ref-Zanatta1_19-0" class="reference"><a href="#cite_note-Zanatta1-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="List_of_band_gaps">List of band gaps</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=5" title="Edit section: List of band gaps"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Below are band gap values for some selected materials.<sup id="cite_ref-Tropf_20-0" class="reference"><a href="#cite_note-Tropf-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> For a comprehensive list of band gaps in semiconductors, see <a href="/wiki/List_of_semiconductor_materials" title="List of semiconductor materials">List of semiconductor materials</a>. </p> <table class="wikitable sortable"> <tbody><tr> <th><a href="/wiki/Group_(periodic_table)#CAS_and_old_IUPAC" title="Group (periodic table)">Group</a></th> <th>Material</th> <th>Symbol</th> <th>Band gap (<a href="/wiki/Electron_volt" class="mw-redirect" title="Electron volt">eV</a>) @ 302<a href="/wiki/Kelvin" title="Kelvin">K</a></th> <th>Reference </th></tr> <tr> <td>III–V </td> <td><a href="/wiki/Aluminium_nitride" title="Aluminium nitride">Aluminium nitride</a> </td> <td>AlN </td> <td>6.0 </td> <td><sup id="cite_ref-FenebergLeute2010_21-0" class="reference"><a href="#cite_note-FenebergLeute2010-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>IV </td> <td><a href="/wiki/Diamond" title="Diamond">Diamond</a> </td> <td><a href="/wiki/Carbon" title="Carbon">C</a> </td> <td>5.5 </td> <td><sup id="cite_ref-Kittel7_22-0" class="reference"><a href="#cite_note-Kittel7-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>IV </td> <td><a href="/wiki/Silicon" title="Silicon">Silicon</a> </td> <td>Si </td> <td>1.14 </td> <td><sup id="cite_ref-Streetman_23-0" class="reference"><a href="#cite_note-Streetman-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pankove_11-3" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zanatta2_24-0" class="reference"><a href="#cite_note-Zanatta2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>IV </td> <td><a href="/wiki/Germanium" title="Germanium">Germanium</a> </td> <td>Ge </td> <td>0.67 </td> <td><sup id="cite_ref-Streetman_23-1" class="reference"><a href="#cite_note-Streetman-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pankove_11-4" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zanatta2_24-1" class="reference"><a href="#cite_note-Zanatta2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>III–V </td> <td><a href="/wiki/Gallium_nitride" title="Gallium nitride">Gallium nitride</a> </td> <td>GaN </td> <td>3.4 </td> <td><sup id="cite_ref-Streetman_23-2" class="reference"><a href="#cite_note-Streetman-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pankove_11-5" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zanatta2_24-2" class="reference"><a href="#cite_note-Zanatta2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>III–V </td> <td><a href="/wiki/Gallium_phosphide" title="Gallium phosphide">Gallium phosphide</a> </td> <td>GaP </td> <td>2.26 </td> <td><sup id="cite_ref-Streetman_23-3" class="reference"><a href="#cite_note-Streetman-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pankove_11-6" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zanatta2_24-3" class="reference"><a href="#cite_note-Zanatta2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>III–V </td> <td><a href="/wiki/Gallium_arsenide" title="Gallium arsenide">Gallium arsenide</a> </td> <td>GaAs </td> <td>1.43 </td> <td><sup id="cite_ref-Streetman_23-4" class="reference"><a href="#cite_note-Streetman-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pankove_11-7" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zanatta2_24-4" class="reference"><a href="#cite_note-Zanatta2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>IV–V </td> <td><a href="/wiki/Silicon_nitride" title="Silicon nitride">Silicon nitride</a> </td> <td>Si<sub>3</sub>N<sub>4</sub> </td> <td>5 </td> <td><sup id="cite_ref-Bauer1977_25-0" class="reference"><a href="#cite_note-Bauer1977-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>IV–VI </td> <td><a href="/wiki/Lead(II)_sulfide" title="Lead(II) sulfide">Lead(II) sulfide</a> </td> <td>PbS </td> <td>0.37 </td> <td><sup id="cite_ref-Streetman_23-5" class="reference"><a href="#cite_note-Streetman-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pankove_11-8" class="reference"><a href="#cite_note-Pankove-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>IV–VI </td> <td><a href="/wiki/Silicon_dioxide" title="Silicon dioxide">Silicon dioxide</a> </td> <td>SiO<sub>2</sub> </td> <td>9 </td> <td><sup id="cite_ref-Vella_26-0" class="reference"><a href="#cite_note-Vella-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td> </td> <td><a href="/wiki/Copper(I)_oxide" title="Copper(I) oxide">Copper(I) oxide</a> </td> <td>Cu<sub>2</sub>O </td> <td>2.1 </td> <td><sup id="cite_ref-Baumeister_27-0" class="reference"><a href="#cite_note-Baumeister-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Optical_versus_electronic_bandgap">Optical versus electronic bandgap</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=6" title="Edit section: Optical versus electronic bandgap"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In materials with a large <a href="/wiki/Exciton" title="Exciton">exciton</a> binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In this situation, there is a distinction between "optical band gap" and "electronic band gap" (or "transport gap"). The optical bandgap is the threshold for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole pair that is <i>not</i> bound together. The optical bandgap is at lower energy than the transport gap. </p><p>In almost all inorganic semiconductors, such as silicon, gallium arsenide, etc., there is very little interaction between electrons and holes (very small exciton binding energy), and therefore the optical and electronic bandgap are essentially identical, and the distinction between them is ignored. However, in some systems, including <a href="/wiki/Organic_semiconductors" class="mw-redirect" title="Organic semiconductors">organic semiconductors</a> and <a href="/wiki/Carbon_nanotube" title="Carbon nanotube">single-walled carbon nanotubes</a>, the distinction may be significant. </p> <div class="mw-heading mw-heading2"><h2 id="Band_gaps_for_other_quasi-particles">Band gaps for other quasi-particles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=7" title="Edit section: Band gaps for other quasi-particles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Photonics" title="Photonics">photonics</a>, band gaps or stop bands are ranges of photon frequencies where, if tunneling effects are neglected, no photons can be transmitted through a material. A material exhibiting this behaviour is known as a <a href="/wiki/Photonic_crystal" title="Photonic crystal">photonic crystal</a>. The concept of <a href="/wiki/Hyperuniformity" title="Hyperuniformity">hyperuniformity</a><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> has broadened the range of photonic band gap materials, beyond photonic crystals. By applying the technique in <a href="/wiki/Supersymmetric_quantum_mechanics" title="Supersymmetric quantum mechanics">supersymmetric quantum mechanics</a>, a new class of optical disordered materials has been suggested,<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> which support band gaps perfectly equivalent to those of <a href="/wiki/Crystal" title="Crystal">crystals</a> or <a href="/wiki/Quasicrystal" title="Quasicrystal">quasicrystals</a>. </p><p>Similar physics applies to <a href="/wiki/Phonon" title="Phonon">phonons</a> in a <a href="/wiki/Phononic_crystal" class="mw-redirect" title="Phononic crystal">phononic crystal</a>.<sup id="cite_ref-EichenfieldChan2009_30-0" class="reference"><a href="#cite_note-EichenfieldChan2009-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Materials">Materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=8" title="Edit section: Materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Aluminium_gallium_arsenide" title="Aluminium gallium arsenide">Aluminium gallium arsenide</a></li> <li><a href="/wiki/Boron_nitride" title="Boron nitride">Boron nitride</a></li> <li><a href="/wiki/Indium_gallium_arsenide" title="Indium gallium arsenide">Indium gallium arsenide</a></li> <li><a href="/wiki/Indium_arsenide" title="Indium arsenide">Indium arsenide</a></li> <li><a href="/wiki/Gallium_arsenide" title="Gallium arsenide">Gallium arsenide</a></li> <li><a href="/wiki/Gallium_nitride" title="Gallium nitride">Gallium nitride</a></li> <li><a href="/wiki/Germanium" title="Germanium">Germanium</a></li> <li><a href="/wiki/Metallic_hydrogen" title="Metallic hydrogen">Metallic hydrogen</a></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="List_of_electronics_topics">List of electronics topics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=9" title="Edit section: List of electronics topics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115" /><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Electronics" title="Electronics">Electronics</a></li> <li><a href="/wiki/Bandgap_voltage_reference" title="Bandgap voltage reference">Bandgap voltage reference</a></li> <li><a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">Condensed matter physics</a></li> <li><a href="/wiki/Direct_and_indirect_bandgaps" class="mw-redirect" title="Direct and indirect bandgaps">Direct and indirect bandgaps</a></li> <li><a href="/wiki/Electrical_conduction" class="mw-redirect" title="Electrical conduction">Electrical conduction</a></li> <li><a href="/wiki/Electron_hole" title="Electron hole">Electron hole</a></li> <li><a href="/wiki/Field-effect_transistor" title="Field-effect transistor">Field-effect transistor</a></li> <li><a href="/wiki/Light-emitting_diode" title="Light-emitting diode">Light-emitting diode</a></li> <li><a href="/wiki/Photodiode" title="Photodiode">Photodiode</a></li> <li><a href="/wiki/Photoresistor" title="Photoresistor">Photoresistor</a></li> <li><a href="/wiki/Photovoltaics" title="Photovoltaics">Photovoltaics</a></li> <li><a href="/wiki/Solar_cell" title="Solar cell">Solar cell</a></li> <li><a href="/wiki/Solid_state_physics" class="mw-redirect" title="Solid state physics">Solid state physics</a></li> <li><a href="/wiki/Semiconductor" title="Semiconductor">Semiconductor</a></li> <li><a href="/wiki/Semiconductor_device" title="Semiconductor device">Semiconductor devices</a></li> <li><a href="/wiki/Strongly_correlated_material" title="Strongly correlated material">Strongly correlated material</a></li> <li><a href="/wiki/Valence_band" class="mw-redirect" title="Valence band">Valence band</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Wide-bandgap_semiconductor" title="Wide-bandgap semiconductor">Wide-bandgap semiconductors</a></li> <li><a href="/wiki/Band_bending" title="Band bending">Band bending</a></li> <li><a href="/wiki/Spectral_density" title="Spectral density">Spectral density</a></li> <li><a href="/wiki/Pseudogap" title="Pseudogap">Pseudogap</a></li> <li><a href="/wiki/Tauc_plot" title="Tauc plot">Tauc plot</a></li> <li><a href="/wiki/Moss%E2%80%93Burstein_effect" title="Moss–Burstein effect">Moss–Burstein effect</a></li> <li><a href="/wiki/Urbach_energy" title="Urbach energy">Urbach energy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Band_gap&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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-columns references-column-width" style="column-width: 35em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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 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