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This lecture discusses the Fermi distribution function and how it applies to energy levels in solid state electronic devices. Topics covered include the Fermi level, the distribution function at different temperatures, available states vs. energy levels, and the approximation/limits on the distribution function.
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ECE 874:Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu
Lecture 21, 12 Nov 12 VM Ayres, ECE874, F12
f(E) = probability = Fermi distribution function Streetman and Banerjee, Solid State Electronic Devices (Pierret Section 4.2 and Pr. 4.8) VM Ayres, ECE874, F12
The Fermi (energy) level EF: 50% VM Ayres, ECE874, F12
At T = 0K: VM Ayres, ECE874, F12
f(E) at T above 0K: VM Ayres, ECE874, F12
f(E) at T above 0K: VM Ayres, ECE874, F12
DOS available statesVersus f(E) and EF VM Ayres, ECE874, F12
Approximation/limits on f(E): Recall: Two conditions: Temperature T E – EF > 0 E – EF < 0 VM Ayres, ECE874, F12
E Restricting E to values for which there are available states this is: Two conditions: Temperature T E – EF > 0, where E > EC E – EF < 0, where E < EV EC Ei EV VM Ayres, ECE874, F12
E Two conditions => Four conditions: Temperature T Degeneracy E – EF > 0 => EF < EC < E versus EC < E < EF 1. Non-degenerate n-type doping 2. Degenerate n-type doping EF EC EC EF Ei Ei EV EV VM Ayres, ECE874, F12
E Four conditions: Temperature T Degeneracy EF – E > 0 => E < EC < EV versus E < EV < EF 3. Non-degenerate p-type doping 4. Degenerate p-type doping EC EC Ei Ei EF EV EV EF VM Ayres, ECE874, F12
Approximation/limits on f(E): VM Ayres, ECE874, F12
Approximation/limits on f(E): VM Ayres, ECE874, F12
Approximation/limits on f(E): Use the “hot” limit in ECE 874. VM Ayres, ECE874, F12
