J n n t thermal r g n t other p t 1 q j p p t thermal

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J n + ∂n ∂t thermal R-G + ∂n ∂t other ∂p ∂t = - 1 q ∇ · J p + ∂p ∂t thermal R-G + ∂p ∂t other Minority Carrier Diffusion Equations: n p ∂t = D N 2 n p ∂x 2 - n p τ n + G L p n ∂t = D P 2 p n ∂x 2 - p n τ p + G L Minority Carrier Diffusion Lengths: L P = D P τ p L N = D N τ n Quasi-Fermi Levels (non-equilibrium): F N = E i + kT ln ( n n i ) F P = E i - kT ln ( p n i ) Step p-n Junction: V bi = kT q ln ( N A N D n 2 i ) N A x p = N D x n W = 2 K S ϵ 0 q ( 1 N D + 1 N A ) ( V bi - V A ) x n = 2 K S ϵ 0 q N A N D ( N A + N D ) ( V bi - V A ) x p = 2 K S ϵ 0 q N D N A ( N A + N D ) ( V bi - V A ) In the depletion region np = n 2 i e ( F N - F P ) /kT = n 2 i e qV A /kT n p ( - x p ) = n 2 i N A ( e qV A /kT - 1 ) p n ( x n ) = n 2 i N D ( e qV A /kT - 1 ) J N ( x ≤ - x p ) = q D N L N n 2 i N A ( e qV A /kT - 1 ) e ( x + x p ) /L N J P ( x x n ) = q D P L P n 2 i N D ( e qV A /kT - 1 ) e - ( x - x n ) /L P I = I 0 ( e qV A /kT - 1 ) I 0 = qA ( D N L N n 2 i N A + D P L P n 2 i N D ) 330final-formulas.tex Spring 2018
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P. R. Nelson 3 Metal-Semiconductor Structures: Φ S = χ + ( E c - E F ) FB V bi = 1 q B - ( E c - E F ) FB ] Φ B = { Φ M - χ ideal n-type E G + χ - Φ M ideal p-type [ E c - E F ] FB = E G 2 - kT ln ( N D n i ) n type E G 2 + kT ln ( N A n i ) p type n-type p-type Φ M > Φ S rectifying Ohmic Φ M < Φ S Ohmic rectifying 330final-formulas.tex Spring 2018
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