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費米能階

費米能階(英語:Fermi level),通常標示為「µ」或「EF[1]。也稱為「電化學電位英语Electrochemical potential[2]

能帶理論中,費米能階可視為熱力學平衡時,電子有50%機率佔據的假想能階。費米能階不需要對應到真正存在的能階(比如絕緣體的費米能階在能隙上),不過費米能階仍是精確定義過的熱力學物理量。[1]

費米能階與費米能在定義上有所差異,費米能定義於絕對零度[3],費米能階在任何溫度皆有定義。

能帶結構

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费米–狄拉克统计 F() vs. 能量 , 费米能级μ = 0.55 eV 温度范围为50K ≤ T ≤ 375K.

在熱力學平衡下,能量為ϵ被電子占據的機率可以用費米-狄拉克分布表示:[4]

上式中,T是溫度(單位:K),k是波茲曼常數

f越接近1,表示該能量的態被電子佔據的概率越大,f越接近0,表示該能量的態被電子佔據的概率越小。如果態的能量剛好位於費米能階(即ϵ=µ),電子占據的機率剛好會是50%。

費米能階(µ)在能帶結構中的位置可用來決定物質的導電性。

  • 絕緣體中,µ位於能隙上,與傳導帶和價帶相距甚遠。
  • 金屬、半金屬退化半導體中,µ位於傳導帶上。
  • 無雜質半導體或少量摻雜的半導體中,µ雖位於能隙上,但與傳導帶和價帶較近。

半金屬與半導體可以透過摻雜或gating改變能帶與費米能階的相對位置,進而改變其導電性。

參考資料

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  1. ^ 1.0 1.1 Kittel, Charles. Introduction to Solid State Physics, 7th Edition. Wiley. ISBN 047-111-181-3. 
  2. ^ The use of the term "Fermi energy" as synonymous with Fermi level (a.k.a. electrochemical potential) is widespread in semiconductor physics. For example: Electronics (fundamentals And Applications)页面存档备份,存于互联网档案馆) by D. Chattopadhyay, Semiconductor Physics and Applications页面存档备份,存于互联网档案馆) by Balkanski and Wallis.
  3. ^ Charles Kittle. Introduction to Solid State Physics Global Edition. : 137-138. 
  4. ^ Kittel, Charles; Herbert Kroemer. Thermal Physics (2nd Edition). W. H. Freeman. 1980-01-15: 357 [2014-03-26]. ISBN 978-0-7167-1088-2. (原始内容存档于2020-10-17). 
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費米能階
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