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

2. VM Ayres, ECE802-604, F13 Lectures 09 and 10, 26 Sep and 01 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M  M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability How to correctly measure I = GV Landauer-Buttiker: all things equal 4-point probe experiments: set-up and read out

3. VM Ayres, ECE802-604, F13 Lecture 09 and 10, 26 Sep and 01 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M  M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability How to correctly measure I = GV Landauer-Buttiker: all things equal 4-point probe experiments: set-up and read out

4. VM Ayres, ECE802-604, F13 M N Varies by edition:

5. VM Ayres, ECE802-604, F13

13. Point 01: What are  1 and  2 :  1 and  2 are being used as quasi Fermi levels A quasi Fermi level is a Fermi energy level that exists as long as an external energy is supplied, e.g, E-field, light, etc. In what follows,  1  F + and  2  F -  1 and  2 are also chemical potentials (2)

14. VM Ayres, ECE802-604, F13 Point 02: normal current versus unconventional e- current Battery picture

15. VM Ayres, ECE802-604, F13 Lecture 09 and 10, 26 Sep and 01 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M  M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability How to correctly measure I = GV Landauer-Buttiker: all things equal 4-point probe experiments: set-up and read out

16. VM Ayres, ECE802-604, F13 Point 02: normal current versus unconventional e- current Note + terminal of battery versus electron I 1 +

17. VM Ayres, ECE802-604, F13 Point 03: energy levels below E f are filled in these diagrams: No current left to right

18. VM Ayres, ECE802-604, F13 Point 03: energy levels below E f are filled in these diagrams: Even random motion back and forth requires holes below and e-s above E f in both +k x and -k x : fluctuations in the e- and hole populations

19. VM Ayres, ECE802-604, F13 Point 04: (a) scattering in non-ideal quasi-1-DEG versus (b) transport in ideal 1-DEG h bar  0 + X W t 1 : e- t 2 : e-

20. VM Ayres, ECE802-604, F13 Point 04: (a) scattering in non-ideal quasi-1-DEG versus (b) transport in ideal 1-DEG h bar  0 + W t 1 : e- t 2 : e-

21. VM Ayres, ECE802-604, F13 Ideal: no scattering: totally wavelike-transport: ballistic Point 04: (b) transport in ideal 1-DEG

22. VM Ayres, ECE802-604, F13 Lecture 09 and 10, 26 Sep and 01 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M  M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability How to correctly measure I = GV Landauer-Buttiker: all things equal 4-point probe experiments: set-up and read out

23. VM Ayres, ECE802-604, F13 Contact Conductance/Resistance V DS How do you step down:

24. VM Ayres, ECE802-604, F13 Contact Conductance/Resistance V DS How do you step down: Have  1 -  2 : What drives transport

25. VM Ayres, ECE802-604, F13 Lecture 09 and 10, 26 Sep and 01 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M  M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability How to correctly measure I = GV Landauer-Buttiker: all things equal 4-point probe experiments: set-up and read out

26. VM Ayres, ECE802-604, F13 Have assumed: Reflectionless: R C comes from stepping down. V DS

27. VM Ayres, ECE802-604, F13 With reflections:

28. VM Ayres, ECE802-604, F13 Within 1-DEG:

29. VM Ayres, ECE802-604, F13 Example: where does I 1 - come from?

30. VM Ayres, ECE802-604, F13 Answer: Scattering If T = 1, recover the previous reflectionless discussion.

31. VM Ayres, ECE802-604, F13 Answer: Scattering

32. VM Ayres, ECE802-604, F13 Landauer formula:

33. VM Ayres, ECE802-604, F13 Transmission probability example (Anderson, Quantum Mechanics) Example: describe what this could be a model of. Barrier height V 0 is an energy in eV

34. VM Ayres, ECE802-604, F13 Transmission probability example (Anderson, Quantum Mechanics) Answer:Modelling the scatterer X as a finite step potential in a certain region. Modelling the e- as having energy E > V 0

35. VM Ayres, ECE802-604, F13 Transmission probability example (Anderson, Quantum Mechanics)

36. VM Ayres, ECE802-604, F13

37. Modelling the e- as having energy E > V 0

38. VM Ayres, ECE802-604, F13

39. E > barrier height V 0 E < barrier height V 0

40. VM Ayres, ECE802-604, F13 2