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mw-portlet-user-menu-anon-editor" lang="zh-Hant" dir="ltr"> <div class="vector-menu-heading"> 用於已登出編輯者的頁面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%96%80" aria-label="了解更多有關編輯"><span>了解更多</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="由此 IP 位址編輯的清單[y]" accesskey="y"><span>貢獻</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="有關來自此 IP 位址編輯的討論[n]" accesskey="n"><span>討論</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站台"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目次" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至側邊欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隱藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-相關議題" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#相關議題"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>相關議題</span> </div> </a> <ul id="toc-相關議題-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="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="zh-Hant" dir="ltr"> <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="切換目次" > <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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">切換目次</span> </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" lang="zh-Hant" dir="ltr"><span class="mw-page-title-main">能隙</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="zh-Hant" dir="ltr"> <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 mw-interlanguage-selector" aria-label="前往別種語言的條目。有 28 種語言可用" > <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-28" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">28 種語言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Bandgaping" title="Bandgaping – 南非荷蘭文" lang="af" hreflang="af" data-title="Bandgaping" data-language-autonym="Afrikaans" data-language-local-name="南非荷蘭文" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a 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 – 阿拉伯文" lang="ar" hreflang="ar" data-title="فجوة النطاق" data-language-autonym="العربية" data-language-local-name="阿拉伯文" 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 – 加泰蘭文" lang="ca" hreflang="ca" data-title="Banda prohibida" data-language-autonym="Català" data-language-local-name="加泰蘭文" 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 – 德文" lang="de" hreflang="de" data-title="Bandlücke" data-language-autonym="Deutsch" data-language-local-name="德文" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Band_gap" title="Band gap – 英文" lang="en" hreflang="en" data-title="Band gap" data-language-autonym="English" data-language-local-name="英文" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Bendbre%C4%89o" title="Bendbreĉo – 世界文" lang="eo" hreflang="eo" data-title="Bendbreĉo" data-language-autonym="Esperanto" data-language-local-name="世界文" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Banda_prohibida" title="Banda prohibida – 西班牙文" lang="es" hreflang="es" data-title="Banda prohibida" data-language-autonym="Español" data-language-local-name="西班牙文" class="interlanguage-link-target"><span>Español</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) – 愛沙尼亞文" lang="et" hreflang="et" data-title="Keelutsoon (füüsika)" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" class="interlanguage-link-target"><span>Eesti</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 – 波斯文" lang="fa" hreflang="fa" data-title="نوار ممنوعه" data-language-autonym="فارسی" data-language-local-name="波斯文" 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 – 法文" lang="fr" hreflang="fr" data-title="Bande interdite" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</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 – 希伯來文" lang="he" hreflang="he" data-title="פער אסור" data-language-autonym="עברית" data-language-local-name="希伯來文" class="interlanguage-link-target"><span>עברית</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 – 印地文" lang="hi" hreflang="hi" data-title="बैण्ड अन्तराल" data-language-autonym="हिन्दी" data-language-local-name="印地文" class="interlanguage-link-target"><span>हिन्दी</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 – 匈牙利文" lang="hu" hreflang="hu" data-title="Tiltott sáv" data-language-autonym="Magyar" data-language-local-name="匈牙利文" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Banda_proibita" title="Banda proibita – 義大利文" lang="it" hreflang="it" data-title="Banda proibita" data-language-autonym="Italiano" data-language-local-name="義大利文" class="interlanguage-link-target"><span>Italiano</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 – 日文" lang="ja" hreflang="ja" data-title="バンドギャップ" data-language-autonym="日本語" data-language-local-name="日文" class="interlanguage-link-target"><span>日本語</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 – 韓文" lang="ko" hreflang="ko" data-title="띠틈" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</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 – 馬來亞拉姆文" lang="ml" hreflang="ml" data-title="ബാന്റ് ഗ്യാപ്" data-language-autonym="മലയാളം" data-language-local-name="馬來亞拉姆文" 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 – 荷蘭文" lang="nl" hreflang="nl" data-title="Verboden zone" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przerwa_energetyczna" title="Przerwa energetyczna – 波蘭文" lang="pl" hreflang="pl" data-title="Przerwa energetyczna" data-language-autonym="Polski" data-language-local-name="波蘭文" 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 – 葡萄牙文" lang="pt" hreflang="pt" data-title="Banda proibida" data-language-autonym="Português" data-language-local-name="葡萄牙文" 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 – 俄文" lang="ru" hreflang="ru" data-title="Запрещённая зона" data-language-autonym="Русский" data-language-local-name="俄文" 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 – 斯洛維尼亞文" lang="sl" hreflang="sl" data-title="Prepovedani pas" data-language-autonym="Slovenščina" data-language-local-name="斯洛維尼亞文" 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 – 瑞典文" lang="sv" hreflang="sv" data-title="Bandgap" data-language-autonym="Svenska" data-language-local-name="瑞典文" 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 – 泰文" lang="th" hreflang="th" data-title="ช่องว่างพลังงาน" data-language-autonym="ไทย" data-language-local-name="泰文" 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 – 土耳其文" lang="tr" hreflang="tr" data-title="Bant aralığı" data-language-autonym="Türkçe" data-language-local-name="土耳其文" 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 – 烏克蘭文" lang="uk" hreflang="uk" data-title="Заборонена зона" data-language-autonym="Українська" data-language-local-name="烏克蘭文" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Taqiqlangan_zona" title="Taqiqlangan zona – 烏茲別克文" lang="uz" hreflang="uz" data-title="Taqiqlangan zona" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="烏茲別克文" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q806352#sitelinks-wikipedia" title="編輯跨語言連結" class="wbc-editpage">編輯連結</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空間"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" lang="zh-Hant" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E8%83%BD%E9%9A%99" title="瀏覽條目正文[c]" accesskey="c"><span>條目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E8%83%BD%E9%9A%99" rel="discussion" title="有關頁面內容的討論[t]" accesskey="t"><span>討論</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " lang="zh-Hant" dir="ltr"> <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="變更語言變體" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span 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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">維基百科，自由的百科全書</div> </div> <div id="contentSub" lang="zh-Hant" dir="ltr"><div id="mw-content-subtitle" lang="zh-Hant" dir="ltr"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh-Hant" dir="ltr"><div id="noteTA-313d33b8" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Electronics"></div><div data-noteta-group-source="module" data-noteta-group="Physics"></div></div><div class="noteTA-local"><div data-noteta-code="zh-cn:本征半导体;zh-hk:本徵半導體;zh-tw:本質半導體"></div><div data-noteta-code="zh-hans:激光二极管;zh-hk:激光二極管;zh-tw:雷射二極體"></div></div></div> <p><b>帶隙</b>（band gap）、<b>帶溝</b>，或稱<b>能隙</b>（energy gap）、<b>能帶隙</b>（energy band gap）、<b>禁帶寬度</b>（width of forbidden band），在<a href="/wiki/%E5%9B%BA%E6%85%8B%E7%89%A9%E7%90%86%E5%AD%B8" class="mw-redirect" title="固態物理學">固態物理學</a>中泛指<a href="/wiki/%E5%8D%8A%E5%B0%8E%E9%AB%94" class="mw-redirect" title="半導體">半導體</a>或<a href="/wiki/%E7%B5%95%E7%B7%A3%E9%AB%94" title="絕緣體">絕緣體</a>的<a href="/wiki/%E5%83%B9%E5%B8%B6" title="價帶">價帶</a>頂端至<a href="/wiki/%E5%82%B3%E5%B0%8E%E5%B8%B6" class="mw-redirect" title="傳導帶">傳導帶</a>底端的能量差距。 </p><p>對一個<a href="/wiki/%E6%9C%AC%E5%BE%81%E5%8D%8A%E5%AF%BC%E4%BD%93" title="本徵半導體">本質半導體</a>而言，其<a href="/wiki/%E5%AF%BC%E7%94%B5%E6%80%A7" class="mw-redirect" title="導電性">導電性</a>與能隙的大小有關，只有獲得足夠能量的電子才能從<a href="/wiki/%E5%83%B9%E5%B8%B6" title="價帶">價帶</a>被激發，跨過能隙並<a href="/wiki/%E8%BA%8D%E9%81%B7" class="mw-redirect mw-disambig" title="躍遷">躍遷</a>至<a href="/wiki/%E5%82%B3%E5%B0%8E%E5%B8%B6" class="mw-redirect" title="傳導帶">傳導帶</a>。利用<a href="/wiki/%E8%B2%BB%E7%B1%B3-%E7%8B%84%E6%8B%89%E5%85%8B%E7%B5%B1%E8%A8%88" class="mw-redirect" title="費米-狄拉克統計">費米-狄拉克統計</a>可以得到電子佔據某個<a href="/wiki/%E8%83%BD%E9%9A%8E" class="mw-redirect" title="能階">能階</a><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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span>的機率。又假設<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_{0}>>E_{F}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>>></mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}>>E_{F}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a8ecc0a14a9ac40e74acbb72f8f1f495cb4a3a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.854ex; height:2.509ex;" alt="{\displaystyle E_{0}>>E_{F}}"></span>，<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_{F}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{F}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c11f54775db7f6468779534bdcc4ce0f9054905f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.178ex; height:2.509ex;" alt="{\displaystyle E_{F}}"></span>是所謂的<a href="/wiki/%E8%B2%BB%E7%B1%B3%E8%83%BD%E9%9A%8E" title="費米能階">費米能階</a>，電子佔據<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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span>的機率可以利用波茲曼近似簡化為： </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^{\left({\frac {-E_{g}}{kT}}\right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mrow> <mrow> <mi>k</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{\left({\frac {-E_{g}}{kT}}\right)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c17c39176feef38664a7296b996ad6da0e23cab0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.368ex; height:4.843ex;" alt="{\displaystyle e^{\left({\frac {-E_{g}}{kT}}\right)}}"></span></dd></dl> <p>在上式中，<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}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e16fa5287303e19370026edc85a044dd74cbc78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.737ex; height:2.843ex;" alt="{\displaystyle E_{g}}"></span>是能隙的寬度、<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 k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span>是<a href="/wiki/%E6%B3%A2%E8%8C%B2%E6%9B%BC%E5%B8%B8%E6%95%B8" title="波茲曼常數">波茲曼常數</a>，而<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 T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>則是溫度。 </p><p>半導體材料的能隙可以利用一些工程手法加以調整，特別是在<a href="/wiki/%E5%8C%96%E5%90%88%E7%89%A9%E5%8D%8A%E5%AF%BC%E4%BD%93" title="化合物半導體">化合物半導體</a>中，例如控制砷化鎵鋁（AlGaAs）或砷化鎵銦（InGaAs）各種元素間的比例，或是利用如<a href="/wiki/%E5%88%86%E5%AD%90%E6%9D%9F%E5%A4%96%E5%BB%B6" title="分子束外延">分子束磊晶</a>（Molecular Beam Epitaxy, MBE）成長出多層的磊晶材料。這類半導體材料在高速半導體元件或是光電元件，如<a href="/wiki/%E5%BC%82%E8%B4%A8%E7%BB%93%E5%8F%8C%E6%9E%81%E6%80%A7%E6%99%B6%E4%BD%93%E7%AE%A1" title="異質結雙極性晶體管">異質接面雙載子電晶體</a>（Heterojunction Bipolar Transistor, HBT）、<a href="/wiki/%E6%BF%80%E5%85%89%E4%BA%8C%E6%A5%B5%E7%AE%A1" title="激光二極管">雷射二極體</a>，或是太陽能電池上已經成為主流。 </p> <div class="mw-heading mw-heading2"><h2 id="相關議題"><span id=".E7.9B.B8.E9.97.9C.E8.AD.B0.E9.A1.8C"></span>相關議題</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%83%BD%E9%9A%99&action=edit&section=1" title="編輯章節：相關議題"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a 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title="半導體">半導體物理學</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">原理</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%9C%AC%E5%BE%81%E5%8D%8A%E5%AF%BC%E4%BD%93" title="本徵半導體">本徵半導體</a></li> <li><a href="/wiki/%E6%9D%82%E8%B4%A8%E5%8D%8A%E5%AF%BC%E4%BD%93" title="雜質半導體">雜質半導體</a></li> <li><a href="/wiki/%E8%83%BD%E5%B8%A6%E7%BB%93%E6%9E%84" title="能帶結構">能帶結構</a></li> <li><a href="/wiki/%E5%AF%BC%E5%B8%A6" title="導帶">導帶</a></li> <li><a href="/wiki/%E5%83%B9%E5%B8%B6" title="價帶">價帶</a></li> <li><a class="mw-selflink selflink">能隙</a></li> <li><a href="/wiki/%E8%BD%BD%E6%B5%81%E5%AD%90" title="載流子">載流子</a> <ul><li><a href="/wiki/%E7%94%B5%E5%AD%90" title="電子">電子</a></li> <li><a href="/wiki/%E7%A9%BA%E7%A9%B4" title="空穴">空穴</a></li></ul></li> <li><a href="/wiki/%E6%96%BD%E4%B8%BB_(%E5%8D%8A%E5%AF%BC%E4%BD%93)" title="施主 (半導體)">施主</a></li> <li><a href="/wiki/%E5%8F%97%E4%BD%93_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="受體 (物理學)">受主</a></li> <li><a href="/wiki/%E5%85%89%E7%94%9F%E4%BC%8F%E6%89%93%E6%95%88%E5%BA%94" title="光生伏打效應">光生伏打效應</a></li> <li><a href="/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93%E6%BF%80%E5%85%89" title="半導體激光">半導體激光</a></li> <li><a href="/wiki/%E9%9C%8D%E7%88%BE%E6%95%88%E6%87%89" title="霍爾效應">霍爾效應</a></li> <li><a href="/wiki/%E8%82%96%E7%89%B9%E5%9F%BA%E5%8A%BF%E5%9E%92" title="肖特基勢壘">肖特基勢壘</a></li> <li><a href="/wiki/%E6%AD%90%E5%A7%86%E6%8E%A5%E8%A7%B8" title="歐姆接觸">歐姆接觸</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93%E5%99%A8%E4%BB%B6%E5%88%B6%E9%80%A0" title="半導體器件製造">工藝</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%85%89%E5%88%BB" title="光刻">光刻</a></li> <li><a href="/wiki/%E5%88%BB%E8%9A%80" title="刻蝕">刻蝕</a></li> <li><a href="/wiki/%E6%8E%BA%E6%9D%82_(%E5%8D%8A%E5%AF%BC%E4%BD%93)" title="摻雜 (半導體)">摻雜</a> <ul><li><a href="/wiki/%E7%AE%80%E5%B9%B6%E5%8D%8A%E5%AF%BC%E4%BD%93" title="簡併半導體">簡併</a></li></ul></li> <li><a href="/wiki/%E7%A6%BB%E5%AD%90%E6%B3%A8%E5%85%A5" title="離子注入">離子注入</a></li> <li><a href="/wiki/%E5%88%86%E5%AD%90%E6%9D%9F%E5%A4%96%E5%BB%B6" title="分子束外延">分子束外延</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E6%B0%94%E7%9B%B8%E6%B2%89%E7%A7%AF" title="物理氣相沉積">物理氣相沉積</a></li> <li><a href="/wiki/%E5%8C%96%E5%AD%A6%E6%B0%94%E7%9B%B8%E6%B2%89%E7%A7%AF" title="化學氣相沉積">化學氣相沉積</a></li> <li><a href="/wiki/%E5%8C%96%E5%AD%A6%E6%9C%BA%E6%A2%B0%E5%B9%B3%E5%9D%A6%E5%8C%96" title="化學機械平坦化">化學機械平坦化</a></li> <li><a href="/wiki/SOI" title="SOI">SOI</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93%E5%99%A8%E4%BB%B6" title="半導體器件">器件</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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