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: Direct bandgap materials Indirect bandgap materials Deep level dopants/traps Effect on I diode : Review of low and high level injection: Low level injection: pn junction without light High level injection pn junction with light Effect on I diode : examples Lecture 11, 04 Feb 14

VM Ayres, ECE875, S14 ECEC EVEV Recombination rate R e Generation rate G th Definition of net transition rate U: U = R e – G th Averaged over a long time: U = R e – G th = 0 However: over short time(s)  : U = R e – G th > 0 OR U = R e – G th < 0 (photon or other) Direct bandgap material: band-to-band transitions in GaAs:

VM Ayres, ECE875, S14 Looking at the Recombination rate Re: R e = R ec np = if mass actions holds: R ec n i 2 - Concentration n of electrons in E C, - Concentration p of holes in E V to take the e- - Probability of spontaneous recombination R e Looking at the Generation rate G th : R ec n i 2 – G th = 0 => G th = R ec n i 2 Therefore: net transition rate U can be written: U = R ec (pn – n i 2 ) = R e – G th Expect: U = 0 but over short time(s) t, it can be > OR < 0 U < 0 drives recombination U > 0 drives generation When this matters: in transient situations when you try to turn a device ON of OFF. We will consider this in the context of turning a diode (pn junction ON, then OFF.

VM Ayres, ECE875, S14 ECEC EVEV Recombination rate R e Generation rate G th The net transition rate U (# transitions / Vol s) is: U = R ec (pn – n i 2 ) = R e – G th R ec ≈ cm 3 /s (photon or other) Direct bandgap material: band-to-band transitions in GaAs:

Indirect bandgap material: band-to-band transitions in Si: VM Ayres, ECE875, S14 ECEC EVEV E t (E D or E A ) or Note: Recombining e- must have a momentum value that matches the crystal momentum of the hole it is dropping into. Indirect bandgap = can’t get a match with the valence band

Indirect bandgap material: band-to-band transitions in Si: Two step process via an impurity energy level E t : VM Ayres, ECE875, S14 ECEC EVEV Recombination rate 01 R e01 Generation rate 02 G th02 (other or photon) E t (E D or E A ) or Recombination rate 02 R e02 Generation rate 01 G th01 (other or photon)

Lecture 09: Neutral N D Electron occupies a local energy level E D Note: e- must be in local neighborhood. Likelihood of “capture” described by a capture cross section  n : cm 2 Ionized N A - Electron occupies a local energy level E A Note: e- must be in local neighborhood. Likelihood of “capture” described by a capture cross section  n : cm 2 VM Ayres, ECE875, S14

Lecture 09: Ionized N D + Local energy level E D is empty and available “capture” of a hole described by a capture cross section  p : cm 2 Neutral N A Local energy level E A is empty and available “capture” of a hole described by a capture cross section  p : cm 2 VM Ayres, ECE875, S14

An e- drops into an acceptor impurity at E t creating an A- level. Then a hole migrates into one of the nearby trap bonds. e- and hole interact and annihilate. ECEC EVEV EtEt nn pp OR: A hole migrates into a bond at E t creating an acceptor level. Then an e- drops into the acceptor level at E t and annihilates the hole  n and  p are electron and hole capture cross sections, roughly how good is the trap at attracting e- or holes into the E t level. Non-radiative transitions Recombination via a trap:

VM Ayres, ECE875, S14 The net transition rate U (#transition/s) is: U = R ec (pn – n i 2 ) = R e – G th SLOWER: R ec ≈ cm 3 /s MORE COMPLICATED: R ec Net transition rate U in Indirect bandgap material: band-to-band transitions in Si: ECEC EVEV Recombination rate 01 R e01 Generation rate 02 G th02 (other or photon) E t (E D or E A ) or Recombination rate 02 R e02 Generation rate 01 G th01 (other or photon)

VM Ayres, ECE875, S14 What temperature is it and what does the crystal E-k environment look like: v th = ✔ 3kT/m* What’s the likelihood of an available e- in E C /hole in E V What’s the likelihood that E t already has an e- /a hole in it What’s the concentration of traps N t U R ec

VM Ayres, ECE875, S14 Sign of (pn – n i 2 ) determine whether there is net recombination or net generation going on: pn < n i 2 -generation increases p and n pn > n i 2 +recombination decreases p and n U

VM Ayres, ECE875, S14 Net transition rate U is highest when denominator is smallest: E t = E i U

VM Ayres, ECE875, S14 Net transition rate U is highest when denominator is smallest: E t = E i The E t = 0.54 eV level in Au is an efficient trap in Si that can be used for recombination and generation that creates and maintain n i at a given temperature. P and B are not. kT

Useful trick from Units: VM Ayres, ECE875, S14 U Therefore: time = N t |U|

VM Ayres, ECE875, S14 1. Chp. 01. No E-field  electrons and holes do random motion. Note that  p and  n in our discussions are in the neutral regions of the pn junction device. Role of efficient mid-gap traps like Au in Si: maintain n i at a given kT. One question to ask (Prs ): how much time is needed to achieve this goal. 2. Chp 02: E-field in depletion region W. Deep level traps are a reservoir of electrons and holes. When the number of carriers decreases in W during change to OFF  reverse bias, traps release carriers, so get opposing generation current. When number of carriers increases in W during change to ON  forward bias, traps recombine out the attempt to re-establish the diode current, so get opposing recombination current. How deep level traps in Si influence applications:

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 : Review of low and high level injection: Low level injection: pn junction without light High level injection pn junction with light Effect on I diode : examples Lecture 11, 04 Feb 14

VM Ayres, ECE875, S14 n n0 ≈ N D + p n0 ≈ n i 2 /n=N D + excess holes:  p LpLp p p0 ≈ N A - n p0 ≈ n i 2 /p=N A - electrons:  n LnLn Review: a pn junction operating in forward bias: Assume: nondegenerate doping with T such that saturation range operation is occurring:

VM Ayres, ECE875, S14 n n0 ≈ N D + p n0 ≈ n i 2 /n=N D + excess holes:  p LpLp p p0 ≈ N A - n p0 ≈ n i 2 /p=N A - electrons:  n LnLn Review: Low level injection: Minority carrier p n0 <  p < majority carrier n n0 Minority carrier n p0 <  n < majority carrier p p0

VM Ayres, ECE875, S14 n n0 ≈ N D + p n0 ≈ n i 2 /n=N D + excess holes:  p LpLp p p0 ≈ N A - n p0 ≈ n i 2 /p=N A - electrons:  n LnLn Review: High level injection: requires external energy: e.g., laser light in W:  p > majority carrier n n0  n > majority carrier p p0  n =  p

VM Ayres, ECE875, S14 Evaluate U: within 1 diffusion length of the junction. Example: on the n-side of a pn junction:

Evaluate U: within 1 diffusion length of the junction. Example: on the n-side 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

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