1. A silicon sample of length L is uniformly doped with NA = 10¹⁶ cm-³ acceptors. We shine laser light on one end of this ample that produces ∆p = ∆n = δp, n|x=0 =10¹⁴ cm-³ electron-hole pairs only at that edge. A contact at the other end x = L extracts all excess carriers i.e. δp, n|x=L = 0. Minority carrier life time of electrons is 1 μsec, and that of holes is 0.1 μsec.
(a) Write the diffusion equation for L>x>0. Indicate the boundary conditions.
(b) Find excess carrier concentration as a function of x, δp(x) = δn(x) assuming L>> diffusion length Ln, Re call that Ln,p = sqrt(D n,p τ n,p)
(c) Find the diffusion current density J(x) for this case as a function of x, and give its value at x =0
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