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ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 12: Semiconductors

ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 12: Semiconductors. Dr. Li Shi Department of Mechanical Engineering The University of Texas at Austin Austin, TX 78712 www.me.utexas.edu/~lishi lishi@mail.utexas.edu. Semiconductors. X (real space).

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ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 12: Semiconductors

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  1. ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 12: Semiconductors Dr. Li Shi Department of Mechanical Engineering The University of Texas at Austin Austin, TX 78712 www.me.utexas.edu/~lishi lishi@mail.utexas.edu

  2. Semiconductors X (real space)

  3. K Space Semiconductor Forbidden gap Metal E k k

  4. Band Gap Energy: Eg

  5. How is the Band Gap formed? • For free electron in metals: U 0 because of high electron density • and short electrostatic screening length • Electron wavefunction scattered by periodic potentialstanding • wave when K= np/a (think about interference of light)

  6. Bandgap Formation

  7. Multiple Bands

  8. Bandstructure of Si and Ge

  9. Electrons and Holes

  10. Charge Carrier Density Parabolic approx (free electron): Electron: Hole: m*: effective mass

  11. f(E) and D(E) Intrinsic Semiconductor Doped Semiconductor

  12. Law of mass action:

  13. Intrinsic Semiconductors

  14. Doped Semiconductors

  15. Dopant Energy Level

  16. Carrier Densities in Doped Semiconductors “Law of Mass Action” for semiconductors Charge accounting:

  17. Charge Density in Doped Semiconductors From now on: pure n-type semiconductor (pure p-type is similar) Approximation = 0 (Only one type of dopant at a time) Charge neutrality (accounting): Occupation of donors by electrons: Occupation of acceptors by holes:

  18. where

  19. Temperature Dependance of Carrier Concentration I) Low temperature limit Carrier freeze-out II) Higher temperature limit Saturation III) Muy caliente limit: n ~ ni intrinsic region

  20. Carrier Density vs. Temperature HOT COLD

  21. Carrier Transport in Semiconductors • Current Density: • Mobility: • Electrical Conductivity: • Drift Velocity:

  22. Carrier Scattering • Carrier Scattering Mechanisms • Defect Scattering • Phonon Scattering • Boundary Scattering (Film Thickness, • Grain Boundary)

  23. CarrierScattering • Intra-valley • Inter-valley • Inter-band

  24. Defect Scattering (i) Ionized defects Perturb potential periodicity Charged defect (ii) Neutral defects

  25. Scattering from Ionized Defects (“Rutherford Scattering”) • Average Carrier Velocity in Semiconductors • (not the drift velocity): • Mean Free Time: 1/  <v>-3  T-3/2 • Mobility:

  26. Carrier-Phonon Scattering • Phonon modulates the periodic potential Carrier scattered by moving potential 1/tph~

  27. Mobility

  28. Electrical Conductivity

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