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Transcript 
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
[email protected]
Semiconductors
X (real space)
K Space
Semiconductor
Forbidden
gap
Metal
E
k
k
Band Gap Energy: Eg
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)
Bandgap Formation
Multiple Bands
Bandstructure of Si and Ge
Electrons and Holes
Charge Carrier Density
Parabolic approx (free electron):
Electron:
Hole:
m*: effective mass
f(E) and D(E)
Intrinsic Semiconductor
Doped Semiconductor
Law of mass action:
Intrinsic Semiconductors
Doped Semiconductors
Dopant Energy Level
Carrier Densities in Doped Semiconductors
“Law of Mass Action” for semiconductors
Charge accounting:
Charge Density in Doped Semiconductors
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)
Approximation
= 0 (Only one type of dopant at a time)
where
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
Carrier Density
vs. Temperature
HOT
COLD
Carrier Transport in Semiconductors
• Current Density:
• Mobility:
• Electrical Conductivity:
• Drift Velocity:
Carrier Scattering
Carrier Scattering Mechanisms
• Defect Scattering
• Phonon Scattering
• Boundary Scattering (Film Thickness,
Grain Boundary)
Grain
Grain Boundary
Carrier
Scattering
•Intra-valley
•Inter-valley
•Inter-band
Defect Scattering
(i) Ionized defects
Perturb potential
periodicity
Charged defect
(ii) Neutral defects
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:
Carrier-Phonon Scattering
• Phonon modulates the periodic potential
1/ph~
Carrier scattered by moving potential
Mobility
Electrical Conductivity
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