Lecture 5: Thermoelectric Effects - Mathematics

By Mark Lundstrom

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

Published on

Abstract

Beginning with the general model for transport, we mathematically derive expressions for the four thermoelectric transport coefficients:

(i) Electrical conductivity,
(ii) Seebeck coefficient (or "thermopower"),
(iii) Peltier coefficient,
(iv) Electronic heat conductivity.
The relationship between the coefficients (e.g. the Kelvin relation and the Weidemann-Franz Law).

Outline:
  1. Introduction
  2. Driving forces for current flow
  3. Charge current
  4. Heatcurrent
  5. Discussion
  6. Summary

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Cite this work

Researchers should cite this work as follows:

  • Mark Lundstrom (2011), "Lecture 5: Thermoelectric Effects - Mathematics," http://nanohub.org/resources/11851.

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Time

Location

Burton Morgan 121, Purdue University, West Lafayette, IN

Tags

Lecture 5: Thermoelectric Effects - Mathematics
  •   NCN Summer School:  July 2011  Near-equilibrium Transport: Fundamentals and Applications  Lecture 5: Thermoelectric Effects:   Mathematics   Mark Lundstrom 1. NCN Summer School: July 201… 0
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  • copyright 2011 2. copyright 2011 6.2666666666666666
    00:00/00:00
  • Landauer picture 3. Landauer picture 7.2666666666666666
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  • driving “forces” for transport 4. driving “forces” for trans… 50
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  • review:  constant temperature 5. review: constant temperature 90.3
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  • questions 6. questions 269.66666666666669
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  • outline 7. outline 309.1
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  • when ΔT = 0, the driving force is:  ΔEF 8. when ΔT = 0, the driving forc… 310.8
    00:00/00:00
  • driving force:  differences in temperature 9. driving force: differences in… 382.86666666666667
    00:00/00:00
  • n-type vs. p-type… 10. n-type vs. p-type… 531.8
    00:00/00:00
  • n-type vs. p-type (ii)… 11. n-type vs. p-type (ii)… 585.43333333333328
    00:00/00:00
  • finally:  differences in both EF and T 12. finally: differences in both … 603.26666666666665
    00:00/00:00
  • outline 13. outline 652.56666666666672
    00:00/00:00
  • the math… 14. the math… 658.4
    00:00/00:00
  • the math… 15. the math… 748.83333333333337
    00:00/00:00
  • re-cap 16. re-cap 836.63333333333333
    00:00/00:00
  • exercise 17. exercise 885.8
    00:00/00:00
  • hot point probe 18. hot point probe 1069.2
    00:00/00:00
  • outline 19. outline 1141.3333333333333
    00:00/00:00
  • electric current 20. electric current 1146.5333333333333
    00:00/00:00
  • heat current 21. heat current 1268.0333333333333
    00:00/00:00
  • the math 22. the math 1308.2666666666667
    00:00/00:00
  • the result 23. the result 1391.4333333333334
    00:00/00:00
  • outline 24. outline 1443.7666666666667
    00:00/00:00
  • re-cap 25. re-cap 1448.5
    00:00/00:00
  • exercise 26. exercise 1497.9
    00:00/00:00
  • inverting the equations 27. inverting the equations 1557.2
    00:00/00:00
  • Seebeck coefficient 28. Seebeck coefficient 1643.5333333333333
    00:00/00:00
  • Seebeck coefficient of bulk semiconductors 29. Seebeck coefficient of bulk se… 1715.0333333333333
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  • “full band” Seebeck coefficient 30. “full band” Seebeck coeffi… 1811.8333333333333
    00:00/00:00
  • inverting the equations (ii) 31. inverting the equations (ii) 1961.8666666666666
    00:00/00:00
  • Peltier coefficient 32. Peltier coefficient 2034.7666666666667
    00:00/00:00
  • summary 33. summary 2056.3
    00:00/00:00
  • for bulk 3D semiconductors 34. for bulk 3D semiconductors 2111.3666666666668
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  • transport parameters 35. transport parameters 2213.3
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  • Wiedemann-Franz “Law” 36. Wiedemann-Franz “Law” 2289.2
    00:00/00:00
  • what about the valence band? 37. what about the valence band? 2505.8
    00:00/00:00
  • treating both bands:  conductivity 38. treating both bands: conducti… 2601.6
    00:00/00:00
  • treating both bands:  S 39. treating both bands: S 2674.7333333333331
    00:00/00:00
  • outline 40. outline 2866.1
    00:00/00:00
  • physics of Peltier cooling 41. physics of Peltier cooling 2869.2666666666669
    00:00/00:00
  • summary 42. summary 2995.6666666666665
    00:00/00:00
  • questions 43. questions 3042.6666666666665
    00:00/00:00
  • when ΔT = 0, the driving force is:  ΔEF 44. when ΔT = 0, the driving forc… 3181.9666666666667
    00:00/00:00
  • driving force:  differences in temperature 45. driving force: differences in… 3189.2333333333331
    00:00/00:00
  • re-cap 46. re-cap 3454.5333333333333
    00:00/00:00
  • the result 47. the result 3571.7333333333331
    00:00/00:00