- ECE 340 1 Homework VIII Due Friday Spring 2004 A bar of silicon has a donor doping profile of n(x = Noexpcfw-Ax2 where A is a constant Derive an

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ECE 340 Homework VIII Spring 2004 Due: Friday, February 27, 2004 1. A bar of silicon has a donor doping profile of n(x) = N o exp{-Ax 2 } where A is a constant. Derive an expressing for the built-in electric field as a function of x. If A = 5.6 x 10 7 /cm 2 , determine the position at which the electric field is 10 4 V/cm. Why is the electric field zero at x=0? Solutions: Use quasi-neutral approximation to solve this problem. Quasi-neutral means that even there is carrier redistribution due to diffusion or the induced drift, we assume the redistribution is small, therefore space charge-neutrality holds everywhere. Under quasi-neutral assumption, we can approximate the carrier profile by the doping profile. At equilibrium, J = 0; Hole diffusion current can be neglected (why?), therefore J p = 0; 0 nn n dn Jq nq D dx µ + = , therefore: n n D dn ndx Ε=− By using Einstein relation (Equation. 4-29), Dk T q = 2 2 0 0 11 0.0259 0.0259 0.0259(2 ) 0.0518 Ax Ax dN e kT dn dn A xA x qn dx n dx dx Ne =− = = If A = 5.6 x 10 7 /cm 2 , electric field is 10 4 V/cm, then 47 3 / 0.0518 10 /(0.0518 5.6 10 ) 3.45 10 x
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This note was uploaded on 01/28/2010 for the course ECE 440 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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- ECE 340 1 Homework VIII Due Friday Spring 2004 A bar of silicon has a donor doping profile of n(x = Noexpcfw-Ax2 where A is a constant Derive an

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