ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu
Lecture 23, 15 Nov 12 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: pi = VM Ayres, ECE874, F12
Familiar results: doped n and p in terms of intrinsic ni and Ei: VM Ayres, ECE874, F12
New result: Exact position of Ei: Step 1. Step 2. VM Ayres, ECE874, F12
New result: Exact position of Ei: VM Ayres, ECE874, F12
New result: effect of degenerate doping (Pr. 4.12): VM Ayres, ECE874, F12
New result: effect of degenerate doping (Pr. 4.12): “At the degenerate limit”: EC – EF = 3kT (EF – EC = -3kT) EF – EV = 3 kT (EV – EF = -3kT) VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Return to simple energy band diagrams: VM Ayres, ECE874, F12
Also: KE goes up as PE goes down, and vice versa PE: same shape as Ec. Also: KE goes up as PE goes down, and vice versa V: upside down from PE/Ec Plot of (-) slope of V n or p: check EF – Ei or Ei - EF VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Exponential donor doping L to R leading to uniform built-in electric field Schottky barrier between a p-type semiconductor and a metal having a smaller work function p-n-p transitor VM Ayres, ECE874, F12
(b) E : Plot of (-) slope of V PE: Same shape as Ec (a) V: Upside down from PE/Ec (b) E : Plot of (-) slope of V x E VM Ayres, ECE874, F12
(d) KE: PE goes down, KE goes up (c) PE: Same shape as Ec (d) KE: PE goes down, KE goes up (e) n or p: check EF – Ei or Ei - EF 0 n n n (log) Concentration (cm-3) x VM Ayres, ECE874, F12
(d) KE: PE goes down, KE goes up (c) PE: Same shape as Ec (d) KE: PE goes down, KE goes up (e) n or p: check EF – Ei or Ei - EF 0 n n n (log) Concentration (cm-3) p x VM Ayres, ECE874, F12
(b) E : Plot of (-) slope of V PE: Same shape as Ec (a) V: Upside down from PE/Ec (b) E : Plot of (-) slope of V E x VM Ayres, ECE874, F12
(d) KE: PE goes down, KE goes up PE: Same shape as Ec (d) KE: PE goes down, KE goes up (e) n or p: check EF – Ei or Ei - EF n n p pmax (log) Concentration (cm-3) x VM Ayres, ECE874, F12
(d) KE: PE goes down, KE goes up PE: Same shape as Ec (d) KE: PE goes down, KE goes up (e) n or p: check EF – Ei or Ei - EF n n p pmax (log) Concentration (cm-3) x VM Ayres, ECE874, F12
Chp. 05: Recombination-Generation Processes Skipping: space charge neutrality dopant ionization as a function of temperature Chp. 05: Recombination-Generation Processes VM Ayres, ECE874, F12