ECE 875: Electronic Devices

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

2. Lecture 11, 04 Feb 14 • Chp. 01 – Chp. 02 • Net transition rate U for: • Direct bandgap materials • Indirect bandgap materials • Deep level dopants/traps • Effect on Idiode: Review of low and high level injection: • Low level injection: pn junction without light • High level injection pn junction with light • Effect on Idiode: examples VM Ayres, ECE875, S14

3. Direct bandgap material: band-to-band transitions in GaAs: Recombination rate Re EC (photon or other) EV Generation rate Gth Definition of net transition rate U: U = Re – Gth Averaged over a long time: U = Re – Gth = 0 However: over short time(s) t: U = Re – Gth > 0 OR U = Re – Gth < 0 VM Ayres, ECE875, S14

4. Looking at the Recombination rate Re: Re = Rec np = if mass actions holds: Rec ni2 - Concentration n of electrons in EC, - Concentration p of holes in EV to take the e- - Probability of spontaneous recombination Re Looking at the Generation rate Gth: Rec ni2 – Gth = 0 => Gth = Rec ni2 Therefore: net transition rate U can be written: U = Rec(pn – ni2) = Re – Gth 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

5. Direct bandgap material: band-to-band transitions in GaAs: Recombination rate Re EC (photon or other) EV Generation rate Gth The net transition rate U (# transitions / Vol s) is: U = Rec(pn – ni2) = Re – Gth Rec ≈ 10-10 cm3/s VM Ayres, ECE875, S14

6. Indirect bandgap material: band-to-band transitions in Si: EC 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 or Et (ED or EA) EV VM Ayres, ECE875, S14

7. Indirect bandgap material: band-to-band transitions in Si:Two step process via an impurity energy level Et : Recombination rate 01 Re01 EC (other or photon) Generation rate 01 Gth01 or Et (ED or EA) Recombination rate 02 Re02 Generation rate 02 Gth02 (other or photon) EV VM Ayres, ECE875, S14

8. Lecture 09: Neutral ND Electron occupies a local energy level ED Note: e- must be in local neighborhood. Likelihood of “capture” described by a capture cross section sn: cm2 Ionized NA- Electron occupies a local energy level EA Note: e- must be in local neighborhood. Likelihood of “capture” described by a capture cross section sn: cm2 VM Ayres, ECE875, S14

9. Lecture 09: Ionized ND+ Local energy level ED is empty and available “capture” of a hole described by a capture cross section sp: cm2 Neutral NA Local energy level EA is empty and available “capture” of a hole described by a capture cross section sp: cm2 VM Ayres, ECE875, S14

10. Recombination via a trap: An e- drops into an acceptor impurity at Et creating an A- level. Then a hole migrates into one of the nearby trap bonds. e- and hole interact and annihilate. EC sn Non-radiative transitions Et sp EV OR: A hole migrates into a bond at Et creating an acceptor level. Then an e- drops into the acceptor level at Et and annihilates the hole sn and sp are electron and hole capture cross sections, roughly how good is the trap at attracting e- or holes into the Et level. VM Ayres, ECE875, S14

11. Net transition rate U in Indirect bandgap material:band-to-band transitions in Si: Recombination rate 01 Re01 EC (other or photon) Generation rate 01 Gth01 or Et (ED or EA) Recombination rate 02 Re02 Generation rate 02 Gth02 (other or photon) EV The net transition rate U (#transition/s) is: U = Rec(pn – ni2) = Re – Gth SLOWER: Rec ≈ 10-15 cm3/s MORE COMPLICATED: Rec VM Ayres, ECE875, S14

12. Rec What temperature is it and what does the crystal E-k environment look like: vth = ✔3kT/m* What’s the concentration of traps Nt U What’s the likelihood of an available e- in EC/hole in EV What’s the likelihood that Et already has an e- /a hole in it VM Ayres, ECE875, S14

13. U Sign of (pn – ni2) determine whether there is net recombination or net generation going on: pn < ni2 - generation increases p and n pn > ni2 + recombination decreases p and n VM Ayres, ECE875, S14

14. U Net transition rate U is highest when denominator is smallest: Et = Ei VM Ayres, ECE875, S14

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

16. Useful trick from Units: U Therefore: time = Nt |U| VM Ayres, ECE875, S14

17. How deep level traps in Si influence applications: 1. Chp. 01. No E-field  electrons and holes do random motion. Note that Dp and Dn in our discussions are in the neutral regions of the pn junction device. Role of efficient mid-gap traps like Au in Si: maintain ni at a given kT. One question to ask (Prs. 1.25-28): 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. VM Ayres, ECE875, S14

18. Lecture 11, 04 Feb 14 • Chp. 01 – Chp. 02 • Net transition rate U for: • Direct bandgap materials • Indirect bandgap materials • Deep level dopants/traps • Effect on Idiode: Review of low and high level injection: • Low level injection: pn junction without light • High level injection pn junction with light • Effect on Idiode: examples VM Ayres, ECE875, S14

19. Review:a pn junction operating in forward bias: Assume: nondegenerate doping with T such that saturation range operation is occurring: pp0 ≈ NA- nn0 ≈ ND+ pn0 ≈ ni2/n=ND+ Lp np0 ≈ ni2/p=NA- Ln excess holes: Dp electrons: Dn VM Ayres, ECE875, S14

20. Review:Low level injection: 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

21. Review:High level injection: requires external energy: e.g., laser light in W: Dn = Dp Dn > majority carrier pp0 Dp > majority carrier nn0 pp0 ≈ NA- nn0 ≈ ND+ pn0 ≈ ni2/n=ND+ Lp np0 ≈ ni2/p=NA- Ln excess holes: Dp electrons: Dn VM Ayres, ECE875, S14

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

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

24. Low level injection in an indirect bandgap material: Assume: Et = Ei. Then: Proportional to trap concentration because most carriers pass through trap

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

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

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