1264 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



1.0 



10 



10 



10 



-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 



x/2Li, 



0.2 0.4 0.6 0.8 1.0 



Fig. 6 — Field and carrier distributions for L = 2Lt and A = 0.665 (so = 0.95). 



unit field, 2Lj as unit length and (tEi as unit current. Then on the cubic 

 s = //£", and E^ — I IE = x — A. The current is related to L by 

 / = '\/2£L where the dimensionless £ is of the order^of 10~ for ger- 

 manium at room temperature. Substituting the exact no-recombination 

 solution E' — s = .r' — A into the solution (2.6), or (3.8), for the current 

 gives the second order differential equation 







EJ 



E{x' - A) - I 



(5.1) 



for E as a function of .t. The two boundary conditions are as follows: At 

 X = 0, clE/dx = by symmetry. At the IP junction the carrier concen- 

 tration must rise and approach that in the normal P material. For a 

 strongly extrinsic P region the normal hole concentration P is large 

 compared to both iii and the electron concentration. Thus s must in- 

 crease and approach P/2w, » 1 as we approach the P region. Clearly 

 the cubic cannot satisfy this requirement. On the cubic the maximum 

 value of .s comes at x = and is less than unity. As we approach the June- 



