1 / 34

ECE 802-604: Nanoelectronics

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

dixie
Download Presentation

ECE 802-604: Nanoelectronics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

  6. VM Ayres, ECE802-604, F13

  7. VM Ayres, ECE802-604, F13

  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

More Related