Lecture 3: Resistance-Ballistic to Diffusive

By Mark Lundstrom

Electrical and Computer Engineering, Purdue University, West Lafayette, IN

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Abstract

The resistance of a ballistic conductor and concepts such as the quantum contact resistance are introduced and discussed. The results are then generalized to treat transport all the way from the ballistic to diffusive regimes. We will show how to treat bulk conductors (electrons free to move in 3D) and will also discuss 2D conductors (electrons free to move in a plane) and 1D conductors (electrons free to move along a wire).

Outline:

  1. Review
  2. 2D ballistic resistors
  3. 2D diffusive resistors
  4. Discussion
  5. Summary

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“Electronics from the Bottom Up” is an educational initiative designed to bring a new perspective to the field of nano device engineering. It is co-sponsored by the Intel Foundation and the Network for Computational Nanotechnology.

Cite this work

Researchers should cite this work as follows:

  • Mark Lundstrom (2011), "Lecture 3: Resistance-Ballistic to Diffusive," https://nanohub.org/resources/11746.

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Location

Burton Morgan 121, Purdue University, West Lafayette, IN

Tags

  1. ballistic
  2. ballistic transport
  3. bottom up approach
  4. diffusion
  5. diffusive transport
  6. nanoelectronics
  7. Summer School
Lecture 3: Resistance-Ballistic to Diffusive
  • NCN Summer School: July 2011 Near-equilibrium Transport: Fundamentals and Applications Lecture 3: Resistance - ballistic to diffusive Mark Lundstrom 1. NCN Summer School: July 2011 … 0
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  • copyright 2011 2. copyright 2011 23.066666666666666
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  • resistors 3. resistors 25.566666666666666
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  • Landauer picture 4. Landauer picture 86.6
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  • driving “forces” for transport 5. driving “forces” for trans… 165.1
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  • transport regimes 6. transport regimes 282.36666666666667
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  • outline 7. outline 344.03333333333336
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  • an isothermal 2D resistor 8. an isothermal 2D resistor 359.06666666666666
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  • the ballistic conductance 9. the ballistic conductance 391.53333333333336
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  • T = 0K ballistic conductance 10. T = 0K ballistic conductance 489.03333333333336
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  • quantized conductance 11. quantized conductance 537.33333333333337
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  • for wider resistors, M(E) ~ W 12. for wider resistors, M(E) ~ W 811.86666666666667
    00:00/00:00
  • conductance in 2D (T > 0K) 13. conductance in 2D (T > 0K) 995.66666666666663
    00:00/00:00
  • conductance in 2D (T > 0K) 14. conductance in 2D (T > 0K) 1088.8333333333333
    00:00/00:00
  • conductance in 2D (T > 0K) 15. conductance in 2D (T > 0K) 1147.9
    00:00/00:00
  • conductance in 2D (T > 0K) 16. conductance in 2D (T > 0K) 1253.3333333333333
    00:00/00:00
  • Fermi-Dirac integrals 17. Fermi-Dirac integrals 1366.8
    00:00/00:00
  • conductance and carrier density 18. conductance and carrier densit… 1575.7666666666667
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  • conductance in 2D 19. conductance in 2D 1617.4333333333334
    00:00/00:00
  • example: nanoscale MOSFETs 20. example: nanoscale MOSFETs 1696.3333333333333
    00:00/00:00
  • example: nanoscale MOSFETs 21. example: nanoscale MOSFETs 1799.9333333333334
    00:00/00:00
  • exercise: nanoscale MOSFETs 22. exercise: nanoscale MOSFETs 1886.8
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  • 40 nm channel length III-V FETs 23. 40 nm channel length III-V FET… 1905.7
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  • outline 24. outline 2051.5666666666666
    00:00/00:00
  • an isothermal 2D resistor 25. an isothermal 2D resistor 2068.4666666666667
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  • the TL = 0 diffusive conductance 26. the TL = 0 diffusive conductan… 2079.3333333333335
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  • ballistic to diffusive 27. ballistic to diffusive 2114.5
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  • example: nanoscale MOSFETs 28. example: nanoscale MOSFETs 2176.2666666666669
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  • outline 29. outline 2215.8
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  • i) about mobility 30. i) about mobility 2242.9
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  • in the diffusive limit 31. in the diffusive limit 2357.1666666666665
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  • ballistic to diffusive… 32. ballistic to diffusive… 2396.5666666666666
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  • TL = 0K apparent mobility 33. TL = 0K apparent mobility 2489.2666666666669
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  • Example: “ballistic mobility” in 2D at TL = 0K 34. Example: “ballistic mobilit… 2576.2666666666669
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  • physical interpretation 35. physical interpretation 2717.6333333333332
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  • ii) ways to write the 2D conductivity 36. ii) ways to write the 2D condu… 2810.1666666666665
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  • other ways to write the 2D conductivity 37. other ways to write the 2D con… 2840.5
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  • one more way… 38. one more way… 2935.3333333333335
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  • general expression for 2D conductivity… 39. general expression for 2D cond… 3030.5333333333333
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  • example: nanoscale FETs 40. example: nanoscale FETs 3078.5666666666666
    00:00/00:00
  • iii) power dissipation in a ballistic resistor 41. iii) power dissipation in a ba… 3147
    00:00/00:00
  • power dissipation in a ballistic resistor 42. power dissipation in a ballist… 3181.9333333333334
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  • iv) where is the voltage drop? 43. iv) where is the voltage drop? 3300.0333333333333
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  • v) 1D and 3D resistors 44. v) 1D and 3D resistors 3450
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  • quantum confinement 45. quantum confinement 3466.4333333333334
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  • modes or channels 46. modes or channels 3559.1333333333332
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  • 1D 47. 1D 3588.9666666666667
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  • 3D 48. 3D 3606.6666666666665
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  • 1D, 2D, and 3D resistors 49. 1D, 2D, and 3D resistors 3635.9333333333334
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  • 1D, 2D, and 3D resistors 50. 1D, 2D, and 3D resistors 3649.6666666666665
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  • 1D resistors 51. 1D resistors 3713.1
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  • 2D resistors 52. 2D resistors 3733.1
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  • 3D resistors 53. 3D resistors 3748.9666666666667
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  • vi) 1D: example: low-field transport in metallic CNTs 54. vi) 1D: example: low-field t… 3784.9
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  • outline 55. outline 3915.0666666666666
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  • near-equilibrium ballistic transport 56. near-equilibrium ballistic tra… 3916.5
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  • the key point 57. the key point 3977.7
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  • questions 58. questions 3991.2333333333331
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