ee3161 spring10 hw2

# Continuity of charge for holes p djp q t dx 2

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Unformatted text preview: miconductor Devices Sang-Hyun Oh 22 UNIVERSITY OF MINNESOTA Overview: Ingredients 1. Continuity of charge for holes ∂p dJp q =− ∂t dx 2. Diffusion of holes dp Jp = −qDp dx 3. Generation and recombination d(∆p) ∆p = GL − dt τp EE3161 Semiconductor Devices Sang-Hyun Oh 23 UNIVERSITY OF MINNESOTA Current Continuity: Basic Idea I1 I2 Suppose I1 = 10 charges/sec and I2 = 8 charges/sec. Then there is a net increase of 2 charges/sec x q = I1 - I2 EE3161 Semiconductor Devices Sang-Hyun Oh 24 UNIVERSITY OF MINNESOTA Current Continuity (cont.) dJ dJ = dx dx Hole current ∂ (p dV ) q = (J (x) − J (x + dx)) A ￿ ￿￿ ￿ ∂t −dJ dV = Adx Electron current ∂p dJp q =− ∂t dx 25 ∂n dJn q =+ ∂t dx EE3161 Semiconductor Devices Sang-Hyun Oh UNIVERSITY OF MINNESOTA Current Continuity (cont.) In a time dt in the region (x, x+dx), the change in the # of carriers is: (# in) - (# out) I (x) − I (x + dx) dN = · dt q 1 dJ dp · dV = − A dxdt q dx dp 1 dJ =− dt q dx Diffusion current for holes: dp Jp = −qDp dx EE3161 Semiconductor Devices Sang-Hyun Oh p = p0 + ∆ p ∂ ∆p ∂ 2 ∆p = Dp ∂t ∂ x2 (for n-type material) 26 UNIVERSITY OF MINNESOTA Current Continuity (cont.) ∂ ∆p ∂ 2 ∆p ∆p = Dp − + GL 2 ∂t ∂x τp which is the minority carrier diffusion equation where we assume (for now) that Jp,drif t ￿ Jp,dif f EE3161 Semiconductor Devices Sang-Hyun Oh 27 UNIVERSITY OF MINNESOTA Changes in density of excess carriers Change in carrier concentration = (illumination) ± (current ﬂow) - (recombination) 1 dJ ∆(conc.) = +GL ± − q dx τ d∆(conc.) J = ±q D dx EE3161 Semiconductor Devices Sang-Hyun Oh 28 UNIVERSITY OF MINNESOTA Minority Carrier Diffusion Equation For n-type material: ∂ ∆p ∂ 2 ∆p ∆p = Dp − + GL 2 ∂t ∂x τp For p-type material: ∂ ∆n ∂ 2 ∆ n ∆n = Dn − + GL 2 ∂t ∂x τn where ∆≡ excess amount above equilibrium Main Assumptions: 1-D; Low-level injection; Minority carrier analysis; Neglect drift currents (E~0 and majority excess carriers n...
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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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