ECE 802-604: Nanoelectronics

1. ECE 802-604:Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

2. Lecture 03, 05 Sep 13 In Chapter 01 in Datta: Two dimensional electron gas (2-DEG) DEG goes down, mobility goes up Define mobility (and momentum relaxation) One dimensional electron gas (1-DEG) Special Schrödinger eqn (Con E) that accommodates: Electronic confinement: band bending due to space charge Useful external B-field Experimental measure for mobility VM Ayres, ECE802-604, F13

3. n = 0 for 1st m = meff for conduction band e- in GaAs. At 300K this is 0.067 m0 a = ? U(z) = a z z Expected Units of a = ? VM Ayres, ECE802-604, F13

4. n = 0 for 1st m = meff for conduction band e- in GaAs. At 300K this is 0.067 m0 a = ? U(z) = a z z Expected Units of a = eV/m or eV/nm VM Ayres, ECE802-604, F13

5. Another way to ballpark an answer: Equate the first triangular well energy level to the first energy level of a 10 nm GaAs infinite square well (familiar problem) and then solve for asymmetry a: Set; Triangular well Ec1 = infinite square well Ec1 VM Ayres, ECE802-604, F13

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8. Space Charge: HEMT VM Ayres, ECE802-604, F13

9. Space Charge: start finish ECE 875: Sze: Classification of heterojunctions into types I, II, and III. Look at the opportunities for e- and o movement as EF is established. VM Ayres, ECE802-604, F13

10. Refer everything to Evac. When separated (starting condition) you have: Evac Evac Evac Type-I: Material 01 (identified by its smaller energy bandgap) has lower EC1 and higher EV1 Type-II: Material 01 has lower EC1 and lower EV1 Type-III: Material 01 has EC1 that is close to (“overlaps”) EV2 VM Ayres, ECE802-604, F13

11. When Materials 01 and 02 come together: what e-’s and o’s are most likely to do first: Evac Evac Evac e- e- e- o o Type-I: e-’s are collected at lower EC1 and o’s are collected at higher EV1 Type-II: e-’s collected at lower EC1 and o’s collected at higher EV2. Therefore e-s and o’s are confined in different spaces Type-III: e-’s can be collected at lower EC1but can also recombine in the nearby “overlapping” EV2 levels VM Ayres, ECE802-604, F13

12. Space Charge: Compare: Datta and class examples were both Type I: Evac e- o Type-I: e-’s are collected at lower EC1 and o’s are collected at higher EV1 VM Ayres, ECE802-604, F13

13. Space Charge: Compare: Datta and class examples were both Type I: Evac e- e-’s go into a triangular quantum well region. In HEMT, o’s go into EV1 : changed by DEV but no quantum well o Type-I: e-’s are collected at lower EC1 and o’s are collected at higher EV1 VM Ayres, ECE802-604, F13

14. Space Charge: Contrast o’s for HEMT and for familiar infinite potential well: Do also have quantized energy levels for o’s in infinite square potential well. But not for HEMT VM Ayres, ECE802-604, F13

15. Expected transitions between EC and EV for, e.g. light emission J DEC DEV VM Ayres, ECE802-604, F13

16. Back to current, not light: J DEC DEV Note: e-’s likely to be stuck in 1st energy level because of the amount DE it takes to physically move on to further location VM Ayres, ECE802-604, F13

17. Space Charge: J DEC ND+ Lots of e-’s come here and stay here. They came from an n-type side. They left behind ND+ Space charge region on both sides of junction DEV VM Ayres, ECE802-604, F13

18. Space Charge: J DEC ND+ DEV Band bending  due to space charge Have a local E-field and potential U(z) here that are different from periodic lattice potential of GaAs and AlGaAs VM Ayres, ECE802-604, F13

19. Space Charge: J DEC ND+ DEV This is why we will use Eqn 1.2.1 where U(r ) is the potential energy due to space charge not the Bloch lattice potential. VM Ayres, ECE802-604, F13

20. How will you wire this up? HEMT VM Ayres, ECE802-604, F13

21. How will you wire this up? Wire it up to use the triangular quantum well region in GaAs VM Ayres, ECE802-604, F13

22. Please! assign a consistent coordinate system; Wire it up to use the triangular quantum well region in GaAs -z y x y z VM Ayres, ECE802-604, F13

23. Please! assign a consistent coordinate system; Wire it up to use the triangular quantum well region in GaAs -z y n- Ey x = (-|e |)(-|Ey|) y z Seems correct for e-’s with Drain = + Note: current I is IDS VM Ayres, ECE802-604, F13

24. Why do this: increase in Mobility 931C: 3D Scattering Sweet spot at 300K mobility T = cold: Impurity = ND+, NA- scattering T = hot: Phonon lattice scattering VM Ayres, ECE802-604, F13

25. Why do this: increase in Mobility Compare 3-DEG (dotted lines) and 2-DEG (shaded area). 2-DEG is better especially at low T. VM Ayres, ECE802-604, F13

26. Datta explanation: When tm is long, m is high VM Ayres, ECE802-604, F13

27. Streetman explanation brings out scattering and group aspects better: Drain Source VM Ayres, ECE802-604, F13

28. Streetman explanation: VM Ayres, ECE802-604, F13

29. Streetman explanation: VM Ayres, ECE802-604, F13

30. Streetman explanation: VM Ayres, ECE802-604, F13

31. Streetman explanation: VM Ayres, ECE802-604, F13

32. Streetman explanation: 1) Direction of electron drift velocity is opposite to direction of E-field. 2) Could stop here with <vx> = vd = mE. Mind the vectors/directions. 3) Next slide relates mobility to current, which can be measured not <vx> which can’t. VM Ayres, ECE802-604, F13

33. Streetman explanation: VM Ayres, ECE802-604, F13

34. Streetman explanation: Key: 1) When number of e’s that have not scattered N(t) goes up => t must go up 2) Then m goes up 3) Scattering involves energy and momentum conserving interactions. Putting quantum restrictions on these interactions means that fewer can occur. VM Ayres, ECE802-604, F13