hw12 - ECE 440 Homework XII Spring 2006 Due: Friday, March...

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ECE 440 Homework XII Spring 2006 Due: Friday, March 31, 2006 1. Assume that a p + -n diode with a uniform cross section area, A, is built with an n region width l smaller than a hole diffusion length ( l < L p ). This is the so-called narrow base diode. Since for this case holes are injected into a short n region under forward bias, we cannot use the assumption δ p(x n = ) = 0 in Eq. 4-35. Instead, we must use as a boundary condition the fact that δ p =0 at x n = l . (a) Solve the diffusion equation to obtain δ px pe e ee n n xL x L LL np n p pp ( ) = () ll (b) Show that the current in the diode is I = qAD p L ctnh L e pn qV kT l 1 (c ) If the n-region is relatively short compared to the diffusion length, the excess hole δ p(x n ) can be approximated as a straight line, i.e. it varies linearly from p n at x n =0 to zero at the ohmic contact (x n = l ). Find the steady-state total excess charges, Q p in the n-region and determine the percentage of error comparing the total excess holes in the n-region obtained
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