Semiconductors: Effective density of states

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Semiconductors Effective density of states
Most of the electrons are close to the C.B.
minimum Most of the holes are close to the V.B.
maximum
Calculate the total electron density Assuming
non-degenerate semiconductor
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Intrinsic Semiconductor
For any material, including intrinsic
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Carrier concentrations at equilibrium
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Doping
Donor
Acceptor

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Ionization Energy
Occuied donors
Ionization Energy
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Populating a donor level
Or add an electron spin down to Ed
Add an electron spin up to Ed
Strong repulsion
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Complete Ionization
Complete ionization
if
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Freeze out
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Equilibrium carrier concentration
Assume complete ionization
intrinsic
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Fermi Level Position
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Conductivity in a semiconductor
Averaging over all energies
In a metal
Averaging over the Fermi surface
Isotropic parabolic band
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Mobility
Drift velocity
Tensor of inverse effective mass
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Thermo-electric effect in a semiconductor
Consider isotropic medium
Parabolic band
Energies are relative to Eg
In a weakly doped n-type
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Generation and Recombination
Assume n-type semiconductor
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Diffusion
Einstein Relations
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In 3-D
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Continuity
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pn(x)pn(0) JD(-ls)0
New boundary condition
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for xgt0
diffusion length
boundary conditions
solution
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