Continuity of charge for holes p djp q t dx 2

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online