07 - Carrier Statistics

07 - Carrier Statistics - EECS 320 Carrier Statistics...

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EECS 320 Carrier Statistics Review g(E) and f(E) Density Of States Fermi-Dirac Statistics 1 f(E) E E f 0.5 E g(E) E V E C Valence band Conduction band 3 2 ) ( 2 ) ( h π 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 ) ( + =
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Review g(E) and f(E) ( ) ()() E f E g E n C = E g(E) E V E C Valence band Conduction band 1 f(E) E E f 0.5 ( ) ( ) ( ) [ ] E f E g E p V = 1 T=300K f(E) 1 E f E g(E) E V E C J. Phillips EECS 320 Determining Carrier Density Density of states x Occupation probability () ()() E f E S E n = ()() dE E f E g n C E C = () () () [] E f E S E p = 1 () () dE E f E g p V E V = 1
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J. Phillips EECS 320 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 = kT E E kT m n C f n exp 2 2 2 / 3 2 * h π = kT E E kT m p f V p exp 2 2 2 / 3 2 * h (Boltzmann approximation) J. Phillips EECS 320 N C , N V – Effective Density of States
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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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07 - Carrier Statistics - EECS 320 Carrier Statistics...

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