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Slide 1: 

1 Semiconductors

Slide 2: 

2 Free Electron Bands Origin of Energy Bands Na: 1s22s22p63s1 Pauli’s Exclusion Principle

Semiconductors : 

3 Semiconductors X (real space)

Slide 4: 

4 K Space E k k Metal Semiconductor Forbidden gap

Slide 5: 

5 Band Gap Energy: Eg

How is the Band Gap formed? : 

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= np/a (think about interference of light)

Multiple Bands : 

7 Multiple Bands

Bandgap Formation : 

8 Bandgap Formation

Bandstructure of Si and GaAs : 

9 Bandstructure of Si and GaAs

Electrons and Holes : 

10 Electrons and Holes

Slide 11: 

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

Slide 12: 

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

Slide 13: 

13 Law of mass action:

Slide 14: 

14 Intrinsic Semiconductors

Slide 15: 

15 Doped Semiconductors

Slide 16: 

16 Dopant Energy Level

Slide 17: 

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

Slide 18: 

18 Charge neutrality (accounting): Occupation of donors by electrons: Occupation of acceptors by holes: Charge Density in Doped Semiconductors

Slide 19: 

19 where

Slide 20: 

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

Slide 21: 

21 HOT COLD Carrier Density vs. Temperature

Carrier Transport in Semiconductors : 

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

Slide 23: 

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

CarrierScattering : 

24 CarrierScattering Intra-valley Inter-valley Inter-band

Defect Scattering : 

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

Slide 26: 

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

Carrier-Phonon Scattering : 

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

Slide 28: 

28 Mobility

Slide 29: 

29 Electrical Conductivity