ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Net transition rate U for: Chp. 01: find a time t: a lifetime Lecture 13, 07 Feb 14 Chp. 01 – Chp. 02 Net transition rate U for: Chp. 01: find a time t: a lifetime Chp. 02: find an extra current due to generation or recombination VM Ayres, ECE875, S14

Definition and uses of U: U = net transition rate = # of band-to-band transitions / Vol s. The corresponding current is: IR-G = q U length Area Definition of band-to band transitions: from EV to EC and from EC back to EV Electrons in EC and holes in EV  to usable current I (Amps) Band-to band transitions can happen via direct band-to-band generation and recombination OR Band-to band transitions can happen via intermediate trap-based generation and recombination “Injection” refers to operation of a pn junction

Low level injection in a trap-dominated material: U  Eq (92) (indirect bandgap material like Si): Eq’s 95 assume: Et = Ei in Eq (92):

Review: Low level injection: normal forward bias operation of a pn junction: pp0 ≈ NA- nn0 ≈ ND+ Minority carrier pn0 < Dp < majority carrier nn0 Minority carrier np0 < Dn < majority carrier pp0 pn0 ≈ ni2/n=ND+ Lp np0 ≈ ni2/p=NA- Ln excess holes: Dp electrons: Dn VM Ayres, ECE875, S14

Example: What are n and p under conditions of low level injection: (a) on the n-side? (b) on the p-side?

Answer: (a) (b)

Example: What is (np – ni2) under conditions of low level injection: (a) on the n-side? (b) on the p-side?

Answer: (a)

(a) Example: moderately doped Si @ 300K

Also: for fully ionized: exact

Either way: Answer: (a)

Answer: (b)

Low level injection in a trap-dominated material: U  Eq (92) (indirect bandgap material like Si): Pr. 1.25: Et = Ei in Eq (95): what happens when it is not? Pr. 1.25: sp = sn = s0 tp = tn = tr0

VM Ayres, ECE875, S14

Find U in usual way Note that s0 can be written in terms of tr0 Set U that you found = U as given to solve for tr Set tr = 2t0 Solve for Et - Ei Importance of Pr. 1.25: that you can deal with Et a little above or a little below Ei since this is what you will really be working with.

Net transition rate U for: Chp. 01: find a time t: a lifetime Lecture 13, 07 Feb 14 Chp. 01 – Chp. 02 Net transition rate U for: Chp. 01: find a time t: a lifetime Chp. 02: find an extra current due to generation or recombination VM Ayres, ECE875, S14

Igen = ? OR Irec = ? Which: are you in forward or reverse bias? What happens to the depletion region WD?

Igen = ? OR Irec = ? Which: are you in forward or reverse bias? What happens to the depletion region WD?

= everything that’s left in U In Pr. 2.07: tg is given.

Igen = ? OR Irec = ? Which: are you in forward or reverse bias? What happens to the depletion region WD?