698 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



where L is the effective diffusion length in the middle region 



L = [2Dn r/ib + 1)]^'=^ (61) 



The solution of (60) may be written 



no sinh (w — z) + w„, sinh z 



n{z) 



sinh 



CO 



(62) 



where z = x/L is the position variable and w = w/L is the length of the 

 middle region in units of L. Fig. 4 shows several of these solutions for the 



In equation (60) and the solution (62) we have neglected the equi- 

 librium carrier densities Up , pp . The criterion for the validity of this 

 approximation is 



sinh Hco « (rio/P), inJP) (63) 



X/w 



Fig. 4 — Tlie carrier (l(Misi(y accordiiii;- (o ('(|ua1i(>n (iS'l) for the case 7?u 

 and several values of co. 



= n.u 



