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Equations_07Dec07

Equations_07Dec07 - EECE 480 Equations 07Dec07 Chapter 2 m0...

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EECE 480 Equations: 07Dec07 1 Chapter 2: m 0 v = h λ ¯ hk d 2 ψ dx 2 + 2 m 0 ¯ h 2 [ E U ] ψ ( x ) = 0 d 2 ψ dx 2 + g 2 ψ ( x ) = 0 Gen. solutions ( U =constant): ψ ( x ) = A sin( gx ) + B cos( gx ) or: ψ ( x ) = A exp( igx ) + B exp( igx ) Bloch’s Theorem: ψ ( x + a ) = e ika ψ ( x ) k = 2 π n Na , ( n = 0 , ± 1 , ± 2 , ... ± N/ 2) Chapter 3: v = 1 ¯ h dE dk m = ± 1 ¯ h 2 d 2 E dk 2 = 1 n J = 1 ² fi lled states q n v k Chapter 4: n i = p i n 0 p 0 = n 2 i g C ( E ) = 8 2 π h 3 m 3 / 2 e ( E E C ) 1 / 2 f ( E ) = 1 1+exp[( E E F ) /kT ] N C = 2 p 2 π m e kT h 2 Q 3 / 2 n 0 = N C exp p E F E C kT Q p 0 = N V exp p E V E F kT Q f MB ( E ) = e ( E E F ) kT n i = N C exp p E F i E C kT Q p i = N V exp p E V E F i kT Q $ device q ( p ( x ) n ( x ) + N D ( x ) N A ( x )) dx = 0 n 0 = n i exp p E F E F i kT Q p 0 = n i exp p E F i E F kT Q Chapter 5: v R = ³ kT 2 π m 1 /v d = 1 E + 1 /v sat μ q ¯ τ coll m n J e, drift = qn n v d = qnμ e ( n E ) n J h, drift = qp n v d = qpμ e n E σ = 1 / ρ = q ( e + h ) n J h, di ff = qD h n dp dx n J e, di ff = qD e n dn dx D e = kT q μ e
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