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

VM Ayres, ECE875, S14 Chp. 01 – Chp. 02 Net transition rate U for: Indirect band-to-band transitions Direct band-to-band transitions Effect on I diode : examples Chp. 01: find a time  a lifetime Chp. 02: find an extra current due to generation or recombination Lecture 12, 05 Feb 14

Definition of U: U = net transition rate = # of band-to-band transitions / Vol s Definition of band-to band transitions: from E V to E C and from E C back to E V 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 an indirect bandgap material: Assume: E t = E i. Then: Proportional to trap concentration because most carriers pass through trap

COMPARE: Low level injection in a direct bandgap material: Proportional to carrier concentration from host material doping

Note: in ECE 474,  p and  n are given as values and used to calculate, e.g. a diffusion length. ECE 875 shows where these values come from

High level injection (with laser light) in an indirect bandgap material: Proportional to trap concentration because most carriers pass through trap

COMPARE: High level injection (with laser light) in a direct bandgap material: Proportional to light-generated carrier concentration

VM Ayres, ECE875, S14 Chp. 01 – Chp. 02 Net transition rate U for: Direct bandgap materials Indirect bandgap materials Deep level dopants/traps Effect on I diode : examples Chp. 01: find a time  Chp. 02: find an extra current due to generation or recombination Lecture 12, 05 Feb 14

VM Ayres, ECE875, S14

Find: Lec 11, slide 16:

VM Ayres, ECE875, S14

The time = the generation time  g

^R-G centers (Pierret) Given: Complete depletion of carriers: n = 0 p = 0 Therefore: (pn – n i 2 ) => (0 – n i 2 ) ≠ 0. Generation (-) of EHP is triggered by depletion of carriers. The time =  g not  r VM Ayres, ECE875, S14 Wording is a bit tricky:

VM Ayres, ECE875, S14

Find expression for average generation time  g Evaluate  g for given situation NOT given: E t = E i, so don’t assume this

VM Ayres, ECE875, S14 Keep the exponentials

VM Ayres, ECE875, S14 Suggestive re-writing:

VM Ayres, ECE875, S14

= sec

VM Ayres, ECE875, S14 HW03

VM Ayres, ECE875, S14 Eq 95

Slide 04: Low level injection in an indirect bandgap material: Assume: E t = E i. Then: Proportional to trap concentration because most carriers pass through trap

VM Ayres, ECE875, S14

Find U in usual way Note that  0 can be written in terms of  r0 Set U that you found = U as given to solve for  r Set  r = 2  0 Solve for E t - E i