Lec06 DOS _ Fermi Statistics

Lec06 DOS _ Fermi Statistics - EECS 320 Density Of States...

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EECS 320 Density Of States
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Electronic states Start with a piece of semiconductor material How would you define the number of electron states?
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Electronic states Electron states distributed in energy Semiconductor Valence band filled with electrons Core electrons valence electrons Conduction band E vac Energy Bandgap Electron states are not uniformly distributed in energy We are primarily concerned with states near E C and E V
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States In Conduction/Valence Band Recall Conduction and Valence Band Define electron states in conduction band E E C No states in the bandgap E V Define “hole” states in valence band Number of states Unit volume x Unit energy Density Of States = (Note we have 4-D, 3-D in space + energy)
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Density Of States Density of states may be determined if bandstructure is known Conduction Band E G p=0 Valence Band p Near bandedge (E C and E V ), approximate using effective mass m n * and m p * E E C E V
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Density Of States (Insert quantum mechanics + E-k + geometry) (You will see this in detail in 420, or in office hours)
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Density Of States 3 2 2 / 1 2 / 3 * ) ( 2 ) ( h π C n c E E m E g = 3 2 2 / 1 2 / 3 * ) ( 2 ) ( h E E m E g V p v = E g(E) E V E C Valence band Conduction band Density Of States Number of electrons per unit volume per unit energy (cm -3 eV -1 ) Density of states determined by effective mass, square root dependence on energy relative to E C , E V
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Calculating Density Of States Tricky units, be careful!
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This note was uploaded on 01/31/2011 for the course EECS 320 taught by Professor Philips during the Spring '06 term at University of Michigan.

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Lec06 DOS _ Fermi Statistics - EECS 320 Density Of States...

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