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ece340Spring04HW8Sol - ECE 340 1 Homework VIII Due Friday...

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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 n n n dn J q n qD dx µ = Ε + = , therefore: n n D dn n dx µ Ε = − By using Einstein relation (Equation. 4-29), D kT q µ = 2 2 0 0 1 1 0.0259 0.0259 0.0259(2 ) 0.0518 Ax Ax dN e kT dn dn Ax Ax qn dx n dx dx N e Ε = − = − = − = = If A = 5.6 x 10 7 /cm 2 , electric field is 10 4
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