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121B_1_EE121B_Slide02 - PN Junction Review

# 121B_1_EE121B_Slide02 - PN Junction Review - EE 121B...

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© 2006 Marko Sokolich All Rights Reserved EE 121B – Chi On Chui Slide 2-1 EE 121B Principles of Semiconductor Device Design Review of PN Junctions Professor Chi On Chui Electrical Engineering Department University of California, Los Angeles Email: [email protected] Slide 2-2 © 2006 Marko Sokolich All Rights Reserved EE 121B – Chi On Chui Outline Review of Currents in Semiconductors Diffusion current Drift current Electric Field in a Semiconductor Einstein Relation PN Junction in Equilibrium Band Diagram Built-in potential in terms of hole or electron concentrations Current in PN Junction Forward Bias junction Reverse Bias junction

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Slide 2-3 © 2006 Marko Sokolich All Rights Reserved EE 121B – Chi On Chui Diffusion Processes Consider the one dimensional diffusion problem. We would like to know the nature of a particle flux (the number of particles per second per area) crossing a boundary in a semiconductor with a non-uniform concentration, n ( x ) . Assume that particles can only move left or right. In this example, we would expect more particles to cross from left to right than from right to left because there are more on the left to begin with. Slide 2-4 © 2006 Marko Sokolich All Rights Reserved EE 121B – Chi On Chui Diffusion Processes One dimensional diffusion problem. n ( x ) x 0 n ( -l ) l -l n ( l ) n (0) Half the particles at n ( -l ) moving at the thermal velocity will reach the x= 0 boundary in each collision time provided that l is the mean free path. (The other half are going the other way). The flux of particles from the left is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) dx dn l v dx dn l n dx dn l n v l n l n v l n v l n v th th net th net th th = + = = ←= →= ϕ ϕ ϕ ϕ ϕ 0 0 2 1 2 1 2 1 2 1 Expand this in a Taylor series keeping only the first two terms