ee3161 spring10 lecture note 6

Charge neutrality qna xp nd xn we expect that a

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Unformatted text preview: xp = ND xn We expect that a (forward or reverse?) bias will increase stored charge. EE3161 Semiconductor Devices Sang-Hyun Oh 8 UNIVERSITY OF MINNESOTA Gauss’s Law: Review If S is a closed surface that bounds the volume V, ￿ −− →→ 1 E · n da = ￿0 S ￿ ρ dV V =Q Using the divergence theorem from vector calculus, ￿ ￿ ￿ −− →→ − → 1 E · n da = ∇ · E dV = ρ dV ￿0 V S Differential form of Gauss’s law: dE (x) ρ(x) ρ = ∇·E = 1-D: dx ￿0 ￿0 EE3161 Semiconductor Devices Sang-Hyun Oh 9 UNIVERSITY OF MINNESOTA Gauss’s Law: Examples R Q E ￿ −− →→ 1 E · n da = ￿0 S 4π R 2 E Q/￿0 ￿ ￿ ρ dV Q E= 4π￿0 R2 V L.H.S. R.H.S. ￿ −− →→ 1 E · n da = ￿0 S EA σ A/￿0 ρ dV σ E= ￿0 V Area: A +σ E -σ L.H.S. R.H.S. 10 EE3161 Semiconductor Devices Sang-Hyun Oh UNIVERSITY OF MINNESOTA Poisson’s Equation in 1-D Notation: E(x): electric field, V(x): electric potential K: dielectric constant (K=3.9 for SiO2, 11.7 for Si) dE (x) ρ(x) = dx K ￿0 dV (x) E (x) = − dx d2 V ρ(x) =− 2 dx K ￿0 EE3161 Semiconductor Devices Sang-Hyun Oh 11 UNIVERSITY OF MINNESOTA Depletion Approximations To proceed further, let...
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This note was uploaded on 02/24/2010 for the course EE 3161 taught by Professor Prof.sang-­hyunoh during the Spring '10 term at University of Minnesota Crookston.

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