1274 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



form as J„ had for the b = 1 case. It is therefore desirable to deal with 

 the fictitious carrier flow J p + J„/b and the ficfitious current q{Jp — 

 Jn/b) since these have the same form in terms of E and s = (w + p)/2ni 

 as J and / had for b = 1. Thus 



bj 1 + 6" L"" ™ dx 



' dx^] 



Es - £'~\ (6.2) 



where Ei and £ have the same meaning as before and the conductivit}' 

 of intrinsic material is noAv a = qniij.(l + b). As before D and fj. are re- 

 spectively the diffusion constant and mobility for holes. Equations (6.1) 

 and (6.2) reduce respecti\Tly to (2.7) for ./ and (2.6) for I = cj{Jp — /„) 

 where 6=1. 



When the flow is by pure diffusion, the holes and electrons diffuse "in 

 parallel" so the effective diffusion constant is the reciprocal of the average 

 of the reciprocal hole and electron diffusion constants. Hence the effective 

 diffusion length is given by 



Lf = Dr ^^ (6.3) 



We continue to let 2L = I/qg be the effective length of current genera- 

 tion; again it is the actual length for the no recombination case. Let x,, 

 and Xp be the coordinates of the AU and IP junctions respectively. 

 Since the problem is not symmetrical we will not take a' = in the center 

 of the intrinsic I'ogion even for the no-recombination case. 



No-Recoinbiualiun Case 



Setting r = we can immediately integrate the continuity equa+ ' 



dJp _ dJn _ 

 dx dx 



subject to the boundary conditions: 



at the iV/ junction, x = rc„ , Jp = 0, Jn = ~Uq 



at the IP junction, x = Xp , Jp = I/(j, Jn = 



The result is Jp = g(x — .r„) and J„ = g{x — Xp). This agrees with / = 

 q(Jp — J„) = "^qgL since 2L = Xp — x„ is the length of the intrinsic 

 region, which, for no-recombjnation, is also the effective length of cur- 



