1280 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



E. 

 E, 



J a' Xf J 



y' / X ' y 



^J^ti \ 



-3.0 -2.5 -2.0 -1.5 -1.0 0.5 0.5 1.0 1.5 2.0 2.5 3.0 



X/2LL 



Fig. 9 — Field Distribution in the Range of Pure Drift for a fixed charge 

 N = N{ ,ora = 1 . 



ACKNOWLEDGEMENTS 



The author wishes to thank Miss M. M. Segrich for doing the exten- 

 sive computations and plotting the curves, and Miss M. C. Gray for 

 help with the calculations leading to Fig. 7. 



APPENDIX A 



Prim's Zero-Current Approximation 



Prim's analysis is based on the assumption that the hole and electron 

 currents are negligibly small differences between their drift and diffusion 

 terms. Setting Jp = /„ = then gives n and p as functions of the po- 

 tential, which is found by substituting n and p into Poisson's equation 

 and solving subject to the boundary conditions at the junctions. These 

 conditions involve the applied bias and the majority carrier densities in 

 the extrinsic regions. Since the current is assumed to vanish, the phe- 

 nomena of carrier generation and recombination do not enter the 

 problem and the results are independent of carrier mobility. The results 

 will be exact when there is no applied voltage; the potential drop across 

 the unit is then the built-in potential. In this appendix we use an internal 

 consistency check to see for what values of applied bias the analysis 



