1. 1 ME 381R Lecture 13: 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. 2 Free Electron Bands Origin of Energy Bands Free electron band Na: 1s 2 2s 2 2p 6 3s 1 Pauli ’ s Exclusion Principle

3. 3 Semiconductors X (real space)

4. 4 K Space E k k Metal Semiconductor Forbidden gap

5. 5 Band Gap Energy: E g

6. 6 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= n  /a (think about interference of light)

7. 7 Multiple Bands

8. 8 Bandgap Formation

9. 9 Bandstructure of Si and GaAs

10. 10 Electrons and Holes

11. 11 Charge Carrier Density Parabolic approx (free electron): m*: effective mass Electron: Hole:

12. 12 f(E) and D(E) Intrinsic Semiconductor Doped Semiconductor

13. 13 Law of mass action:

14. 14 Intrinsic Semiconductors

15. 15 Doped Semiconductors

16. 16 Dopant Energy Level

17. 17 Carrier Densities in Doped Semiconductors “Law of Mass Action” for semiconductors Charge accounting:

18. 18 Charge neutrality (accounting): Occupation of donors by electrons: Occupation of acceptors by holes: From now on: pure n-type semiconductor (pure p-type is similar) = 0 Approximation (Only one type of dopant at a time) Charge Density in Doped Semiconductors

19. 19 where

20. 20 I) Low temperature limit Carrier freeze-out II) Higher temperature limit Saturation III) Muy caliente limit: n ~ n i  intrinsic region Temperature Dependance of Carrier Concentration

21. 21 HOT COLD Carrier Density vs. Temperature

22. 22 Carrier Transport in Semiconductors Current Density: Mobility: Electrical Conductivity: Drift Velocity:

23. 23 Carrier Scattering Mechanisms Defect Scattering Phonon Scattering Boundary Scattering (Film Thickness, Grain Boundary) Carrier Scattering

24. 24 Carrier Scattering Intra-valley Inter-valley Inter-band

25. 25 Defect Scattering Charged defect Perturb potential periodicity (i) Ionized defects (ii) Neutral defects

26. 26 Scattering from Ionized Defects (“Rutherford Scattering”) 1/   -3  T -3/2 Average Carrier Velocity in Semiconductors (not the drift velocity): Mean Free Time: Mobility:

27. 27 Carrier-Phonon Scattering Phonon modulates the periodic potential  Carrier scattered by moving potential 1/  ph ~

28. 28 Mobility

29. 29 Electrical Conductivity