ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 22, 13 Nov 12 VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

- Approximation/limits on f(E): Use the “hot” limit in ECE 874. VM Ayres, ECE874, F12

Let’s deal with it. VM Ayres, ECE874, F12

Deal with E – EF versus E – EC: VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

Always do the easy one first: VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

Done! This part is sometimes called NC: the effective density of states at the conduction band edge E = EC. VM Ayres, ECE874, F12

Some commonly used gamma functions: Reference: http://en.wikipedia.org/wiki/Gamma_function#Integration_problems Some commonly used gamma functions: n is always a positive whole number VM Ayres, ECE874, F12

Would get a similar result for holes: This part is sometimes called NV: the effective density of states at the valence band edge E = EV. VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

With these expressions for n and p, can get several familiar results: VM Ayres, ECE874, F12

Familiar results: for EF =Ei: VM Ayres, ECE874, F12

Familiar results: doped n and p in terms of intrinsic ni and Ei: VM Ayres, ECE874, F12