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Unformatted text preview: ECE 440 Homework XII Solutions Spring 2006 1. Assume that a p + -n diode with a uniform cross section area, A, is built with an n region width smaller than a hole diffusion length ( < 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 l l (a) Solve the diffusion equation to obtain δ p x n ( ) = Δ p n e l − x n ( ) L p − e x n − l ( ) L p ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ e l L p − e − l L p (b) Show that the current in the diode is I = qAD p p n L p ctnh l L p ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ e qV kT − 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 Δ p n at x n =0 to zero at the ohmic contact (x n = ). 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 from part (a) with that from the straight-line approximation for /L p = 0.05, 0.1, 0.5, 1 and 5. l l (d) Calculate the current due to recombination in the n region....
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- Spring '11
- Boundary value problem, Partial differential equation, Green's function, Qp