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ECE 802-604: Nanoelectronics

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

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ECE 802-604: Nanoelectronics

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

  2. 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 = GC 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 VM Ayres, ECE802-604, F13

  3. 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 = GC 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 VM Ayres, ECE802-604, F13

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

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  13. Point 01: What are m1 and m2: m1 and m2 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, m1 F+ and m2 F- m1 and m2 are also chemical potentials (2) VM Ayres, ECE802-604, F13

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

  15. 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 = GC 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 VM Ayres, ECE802-604, F13

  16. Point 02: normal current versus unconventional e- current Note + terminal of battery versus electron I1+ VM Ayres, ECE802-604, F13

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

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

  19. Point 04:(a) scattering in non-ideal quasi-1-DEGversus(b) transport in ideal 1-DEG W t1: e- X t2: e- hbarw0 + hbarw0 + VM Ayres, ECE802-604, F13

  20. Point 04:(a) scattering in non-ideal quasi-1-DEGversus(b) transport in ideal 1-DEG W t1: e- t2: e- hbarw0 + hbarw0 + VM Ayres, ECE802-604, F13

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

  22. 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 = GC 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 VM Ayres, ECE802-604, F13

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

  24. Contact Conductance/Resistance VDS How do you step down: Have m1-m2: What drives transport VM Ayres, ECE802-604, F13

  25. 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 = GC 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 VM Ayres, ECE802-604, F13

  26. Have assumed: Reflectionless: RC comes from stepping down. VDS VM Ayres, ECE802-604, F13

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

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

  29. Example:where does I1- come from? VM Ayres, ECE802-604, F13

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

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

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

  33. Transmission probability example(Anderson, Quantum Mechanics) Example: describe what this could be a model of. Barrier height V0 is an energy in eV VM Ayres, ECE802-604, F13

  34. 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 > V0 VM Ayres, ECE802-604, F13

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

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  37. VM Ayres, ECE802-604, F13 Modelling the e- as having energy E > V0

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  39. E > barrier height V0 E < barrier height V0 VM Ayres, ECE802-604, F13

  40. 2 VM Ayres, ECE802-604, F13

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