127G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 l! 



term in (6.9) gives the cubic equation ' 



for the field distribution. 



In germanium, where b = 2.1, /? = 0.406, Xp = 1.35L and x„ = 

 — 0.65L. The coefficient of I/aEi therefore varies from 1.47 to 3.10, or 

 by a factor of a Httle more than 2. This will introduce some asymmetry 

 into the E versus x curve in the low field region where the fictitious car- 

 rier flow Jp + Jn/b is by diffusion. It is evident that, as the voltage in-i 

 creases, the field versus x curve becomes increasingly symmetrical about 

 the x = point; so the effect of having b 9^ 1 is simply to shift the 

 field distribution along the x axis. 



Recombination -s 



The arguments of section 4 again apply. Where recombination is im- 

 portant, n — p is small compared to n -\- p, so g — r = g(l — s^). The 

 diffusion term dominates in the fictitious particle flow Jp + Jn/b; that 

 is, E^/Ei is small compared to s, so (6.1) becomes 



•^= -2n,D^ 

 ax 



Jp +-^= -^mD"^ 



The continuity equations give 



So again we have 



(fs^^ (1 - /) 

 dx^ 2Li2 



(6.11) 



The solution joins the no recombination solution where s = A — 

 {x/2Li)". Therefore A is again related to Sq , the maximum s, by ^ = :j 

 So(l — si/Z) and the s versus x curve is given by (4.8) and is symmetrica] 

 about the point where s is a maximum. When the recombination solu- 

 tion joins onto no-recombination solutions, there will be a difi'orent 

 no-recombination solution on each side of the recombination region. 

 The junctions will be at the points Xp and .r„ on the respective no-recom- 

 bination solutions. The length of the intrinsic region will not be Xp — 

 Xn = 2L since the x = points are different on the two no-recombination 

 solutions and are separated by a region of maximimi recombination. 



