ME 381R Fall 2003

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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_at_mail.utexas.
edu
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Semiconductors
X (real space)
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K Space
Semiconductor
Forbidden gap
Metal
E
k
k
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Band Gap Energy Eg
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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)

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Bandgap Formation
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Multiple Bands
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Bandstructure of Si and Ge
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Electrons and Holes
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Charge Carrier Density
Parabolic approx (free electron)
Electron
Hole
m effective mass
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f(E) and D(E)
Intrinsic Semiconductor
Doped Semiconductor
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Law of mass action
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Intrinsic Semiconductors
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Doped Semiconductors
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Dopant Energy Level
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Carrier Densities in Doped Semiconductors
Law of Mass Action for semiconductors
Charge accounting
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Charge Density in Doped Semiconductors
Charge neutrality (accounting)
Occupation of donors by electrons
Occupation of acceptors by holes
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where
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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
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Carrier Density vs. Temperature
HOT
COLD
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Carrier Transport in Semiconductors

• Current Density
• Mobility
• Electrical Conductivity
• Drift Velocity

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Carrier Scattering

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

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CarrierScattering

• Intra-valley
• Inter-valley
• Inter-band

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Defect Scattering
(i) Ionized defects
Perturb potential periodicity
Charged defect
(ii) Neutral defects
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Scattering from Ionized Defects (Rutherford
Scattering)

• Average Carrier Velocity in Semiconductors
• (not the drift velocity)

• Mean Free Time

1/? ? ltvgt-3 ? T-3/2

• Mobility

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Carrier-Phonon Scattering

• Phonon modulates the periodic potential?
• Carrier scattered by moving potential

1/tph
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Mobility
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Electrical Conductivity