Assume that a p+-- n diode is built with a quasi-neutral n-region having a width l which is smaller than the hole diffusion length (l < Lp). This is a so-called narrow base diode. Since for this case holes are injected into a short n region under forward bias, we cannot use the boundary condition &p(x' = co) = 0. Instead, our boundary condition becomes &p(x' = l) = 0 (where x' is the x-coordinate having its origin at the depletion edge xn).
Apn |e(l-x)/Lp -e-(l-x)/Ly (a) Solve the continuity equation for this case to obtain: &p(x') = el/Lp=e-l/Lp where pn = Pno(eqVa/kT -1)
(b) If l < Lp, show that this equation becomes &p(x') = pn (1 -- x'/). [i.e., hole profile is linear]