ECE 440 Homework XIISpring 2006Due: Friday, March 31, 20061. Assume that a p+-n diode with a uniform cross section area, A, is built with an n regionwidthlsmaller than a hole diffusion length (l< Lp). This is the so-called narrowbase diode. Since for this case holes are injected into a short n region under forwardbias, we cannot use the assumption δp(xn= ∞) = 0 in Eq. 4-35. Instead, we must useas a boundary condition the fact that δp =0 at xn= l.(a) Solve the diffusion equation to obtainδpxpeeeennxLxLLLnpnppp( )=−⎡⎣⎢⎤⎦⎥−−()−−∆ll(b) Show that the current in the diode isI=qAD pLctnhLepnqVkTl⎛⎝⎜⎞⎠⎟−⎛⎝⎜⎞⎠⎟1(c ) If the n-region is relatively short compared to the diffusion length, the excess hole δp(xn)can be approximated as a straight line, i.e. it varies linearly from∆pnat xn=0 to zero at theohmic contact (xn=l). Find the steady-state totalexcess charges, Qpin the n-region anddetermine the percentage of error comparing the totalexcess holes in the n-region obtained
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