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 0 0 2 1 2 1 2 1 2 1 Expand this in a Taylor series keeping only the first two terms
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Slide 2-5 © 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) dx dn l v th n = ϕ dx dn l qv q J n th n n = = ) ( dx dp l qv q J p th p p = = This is the diffusion current of electrons Slide 2-6 © 2006 Marko Sokolich All Rights Reserved EE 121B – Chi On Chui () ( ) ( ) ( ) ( ) () () () () () x E x qp x v x p q x J x E x qn x v x n q x J p p p n n n µ = = = = Diffusion and Drift If we combine the equations above for Drift current with the equations for Diffusion current we get the following expressions for electron and hole current density: Note: In these expressions E ( x ) is the electric field. Electrons in a solid drift under the influence of an electric field. They move at a velocity proportional to field, the proportionality constant is called the mobility, μ n for electrons and μ p for holes () ()() ( ) () () () () x J x J x J dx x dp qD x E x p q x J dx x dn qD x E x n q x J p n p p p n n n + = = + =
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Slide 2-7 © 2006 Marko Sokolich All Rights Reserved EE 121B – Chi On Chui Directions of Current Flow and Particle Flow n ( x ) p ( x ) E ( x ) Consider a semiconductor with the gradients shown and electric field pointing to the right
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This note was uploaded on 11/11/2010 for the course EE 121b taught by Professor Bjt-gamma during the Winter '08 term at UCLA.

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

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