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

2. Lecture 15, 17 Oct 13 In Chapters 02 and 03 in Datta:
How to correctly measure I = GV
Add scattering to Landauer-Buttiker
Buttiker approach for dealing with incoherent scatterers
2.6 occupied states as scatterers
3.1 scattering/S matrix
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3. 1 Deg, M = 1 mR mL X O X
probe m m
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4. Outline of the solution:
Goal: V = IR, solve for R
What is V: mA – mB
What is I: I = I1 = I2
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6. Lec 14:
where
Ielectron
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7. Lec 14: Further benefit: from I3 + I4 = 0 with Unitarity and symmetry, found m:
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8. Lec 14: Used 3 conditions: 1/ I3 + I4 = 0 2/ 3/
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9. Datta Sec. 2.6
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10. 1 Deg, M = 1 mR mL X O X
probe m mA mB m
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12. NT(E)
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13. Where from:
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14. Where from:
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15. Where from:
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21. above mB
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32. Datta Sec. 3.1
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33. What is a scattering S matrix?:
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34. Introduce an S-matrix to describe both probe and occupied state scattering while maintaining Landuaer-Buttiker approach of treating all terminals alike:
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36. Datta, Sec. 3.1:
Two propagating modes into one propagating mode:
expect scattering due to occupied states
Game plan: for each Si j element: determine: is it a reflection or a transmission?
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37. Start with a more familiar example from a paper by Engquist:
The single in/out channel for the incoherent scatterer gives an experimentally wrong resistance. The Buttiker two-channel probe description turned out to be correct.
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38. Example: find the S-matrix for the diagram shown.
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39. Example: find the S-matrix for the diagram shown.
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40. Example: find the S-matrix for the diagram shown.
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41. Example: find the scattering matrix S for the Engquist diagram:
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42. Example: find the scattering matrix S for the Engquist diagram:
aout
bin
gin
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46. Datta Sec. 3.1
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47. Example: find the S-matrix for the diagram shown.
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