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 states Versus f(E) and EF VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

Approximation/limits on f(E): Recall: Two conditions: Temperature T E – EF > 0 E – EF < 0 VM Ayres, ECE874, F12

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 E EC Ei EV VM Ayres, ECE874, F12

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 E EC EC EF Ei Ei EV EV VM Ayres, ECE874, F12

Four conditions: E 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 E 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

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12