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Unformatted text preview: Previous Lectures Density Of States FermiDirac Statistics f(E) 1 E E f 0.5 E g(E) E V E C Valence band Conduction band E g(E) E V E C Valence band Conduction band 3 2 ) ( 2 ) ( h c n n c E E m m E g = 3 2 ) ( 2 ) ( h E E m m E g v p p v = kT E E f e E f ) ( 1 1 ) ( + = Note that the f(E) is the probability of occupation regardless of whether or not a state exists! EECS 320 Carrier Statistics Determining Carrier Density ( ) ( ) ( ) E f E g E n C = E g(E) E V E C Valence band Conduction band E g(E) E V E C Valence band Conduction band T=300K 1 f(E) E f 0.5 E ( ) ( ) ( ) [ ] E f E g E p V = 1 f(E) 1 E f E g(E) E V E C E g(E) E V E C Determining Carrier Density Density of states x Occupation probability ( ) ( ) ( ) E f E g E n C = ( ) ( ) dE E f E g n C E C = ( ) ( ) ( ) [ ] E f E g E p V = 1 ( ) ( ) [ ] dE E f E g p V E V = 1 Carrier Density (Quantitative) Density of states x Occupation probability ( ) ( ) ( ) E f E g E n C = ( ) ( ) dE E f E g n C E C = ( ) ( ) >> kT E E E f kT E E f f exp , for ( ) ( ) ( ) [ ] E f E g E p V = 1 ( ) ( ) [ ] dE E f E g p V E V = 1 (Boltzmann approximation) = kT E E kT m p f V p exp 2 2 2 / 3 2 * h...
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 Spring '06
 Philips

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