ECE 802-604: Nanoelectronics

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

2. Lecture 14, 15 Oct 13 In Chapters 02 and 03 in Datta: How to correctly measure I = GV Brief discussion: Roukes article Two typo correction HW02 Pr. 2.3 Add scattering to Landauer-Buttiker Caveat: when Landauer-Buttiker doesn’t work When it does: Sections 2.5 and 2.6: motivation: why: 2.5: Probes as scatterers especially at high bias/temps Buttiker approach for dealing with incoherent scatterers 2.6 occupied states as scatterers 3.1 scattering/S matrix VM Ayres, ECE802-604, F13

3. Roukes article: VM Ayres, ECE802-604, F13

4. Roukes article: VM Ayres, ECE802-604, F13

5. Roukes article: TR possibilities: rebound direct rebound direct B X + seems to be F = q(v x B) = -|e| (v X B) VM Ayres, ECE802-604, F13

6. Roukes article: TL possibilities: direct direct rebound rebound F = q(v x B) = -|e| (v X B) VM Ayres, ECE802-604, F13

7. Roukes article: HW01 VA Pr.01: x = 0.4, here it is x = 0.3 HW01 Datta E1.2 Find n and m HW01 Datta E1.1 Find lf VM Ayres, ECE802-604, F13

8. Two typos Pr. 2.3: Roukes article: TL Roukes article: TR direct rebound direct rebound VM Ayres, ECE802-604, F13

9. T2 1 Two typos Pr. 2.3, marked in magenta: Datta Pr. 2.3, p. 113: TL Datta Pr. 2.3, p. 113: TR B X VM Ayres, ECE802-604, F13

10. Lecture 14, 15 Oct 13 In Chapters 02 and 03 in Datta: How to correctly measure I = GV Brief discussion: Roukes article: HW02 Pr. 2.3: Add scattering to Landauer-Buttiker Caveat: when Landauer-Buttiker doesn’t work When it does: Sections 2.5 and 2.6: motivation: why: 2.5: Probes as scatterers especially at high bias/temps Buttiker approach for dealing with incoherent scatterers 3.1 scattering/S matrix VM Ayres, ECE802-604, F13

11. Lec13: In Section 2.5: 2-t example: with broadened Fermi f0 Practical example: Roukes VM Ayres, ECE802-604, F13

12. Lec13: i as a function of how much energy E/what channel M the e- is in If T = T’, can get to Landauer-Buttiker but no reason why T should = T’. Especially if energies from probes took e- far from equilibrium. VM Ayres, ECE802-604, F13

13. Lec13: Can expect T = T’ at equilibrium. Consider: if energies from probes don’t take e- far from equilibrium: VM Ayres, ECE802-604, F13

14. Lec13: New useful G: VM Ayres, ECE802-604, F13

15. Lec13: Basically I = G^V = G^ (m1-m2) e that works when probes hotted things up but not too far from equilibrium VM Ayres, ECE802-604, F13

16. Lec13: Example: does the figure shown appear to meet the linear (I = G^ V) regime criteria? Criteria is: m1-m2 << kBT FWHM shown is kBT Answer: No, they appear to be about the same (red and blue). However, part of FT(E) is low value. Comparing an ‘effective’ m1-m2 (green)maybe it’s OK. VM Ayres, ECE802-604, F13

17. Lec13: If T(E) changes rapidly with energy, the “correlation energy” ec is said to be small. 0.85 T(E) 0.09 E 5 eV 5.001 eV A very minimal change in e- energy and you are getting a different and much worse transmission probability. VM Ayres, ECE802-604, F13

18. 2-DEG VM Ayres, ECE802-604, F13

19. Example: in HW01 Pr. 1.1 you solved for tf for a 2-DEG in GaAs @ 1 K using the graph shown in Figure 1.3.2 . Estimate the corresponding correlation energy ec VM Ayres, ECE802-604, F13

20. Estimate the corresponding correlation energy ec Answer: VM Ayres, ECE802-604, F13

21. Lecture 14, 15 Oct 13 In Chapters 02 and 03 in Datta: How to correctly measure I = GV Brief discussion: Roukes article Two typo correction HW02 Pr. 2.3 Add scattering to Landauer-Buttiker Caveat: when Landauer-Buttiker doesn’t work When it does: Sections 2.5 and 2.6: motivation: why: 2.5: Probes as scatterers especially at high bias/temps Buttiker approach for dealing with incoherent scatterers 3.1 scattering/S matrix VM Ayres, ECE802-604, F13

22. Lec10: Scattering: Landauer formula for R for 1 coherent scatterer X: Reflection = resistance VM Ayres, ECE802-604, F13

23. Lec 10: Coherent scattering means that phases of both transmitted and reflected e- waves are related to the incoming e- wave in a known manner E > barrier height V0 E < barrier height V0 VM Ayres, ECE802-604, F13

24. Lec 10: Transmission probability for 2 scatterers: T => T12: That’s interesting. That Ratio is additive: Assuming that the scatterers are identical: VM Ayres, ECE802-604, F13

25. Therefore: Resistance for two coherent scatterers is: VM Ayres, ECE802-604, F13

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30. Resistance is due to partially coherent /partially incoherent transmission VM Ayres, ECE802-604, F13

31. 1 Deg, M = 1 mR mL X O X Example: probe m VM Ayres, ECE802-604, F13

32. 1 Deg, M = 1 mR mL X O X probe m m VM Ayres, ECE802-604, F13

33. Model the phase destroying impurity as two channels attached to an energy reservoir m VM Ayres, ECE802-604, F13

34. Influence of the incoherent impurity can be described using a Landauer approach as: VM Ayres, ECE802-604, F13

35. mL mR m VM Ayres, ECE802-604, F13

36. mL mR m VM Ayres, ECE802-604, F13

37. mL mR m VM Ayres, ECE802-604, F13

38. mL mR m VM Ayres, ECE802-604, F13

39. Landauer-Buttiker treats all “probes” equally: what is going into “probe” 3: mL mR m VM Ayres, ECE802-604, F13

40. Landauer-Buttiker treats all “probes” equally: what is going into “probe” 4: mL mR m VM Ayres, ECE802-604, F13

41. Outline of the solution: Goal: V = IR, solve for R What is V: mA – mB What is I: I = I1 = I2 VM Ayres, ECE802-604, F13

42. 1 Deg, M = 1 mR mL X O X probe m mA mB m VM Ayres, ECE802-604, F13

43. VM Ayres, ECE802-604, F13

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46. Condition: net current I3 + I4 = 0 VM Ayres, ECE802-604, F13

47. VM Ayres, ECE802-604, F13

48. Condition: net current I3 + I4 = 0 VM Ayres, ECE802-604, F13

49. Condition: net current I3 + I4 = 0 VM Ayres, ECE802-604, F13

50. VM Ayres, ECE802-604, F13