420 



BELL SYSTEM TECIIMCAL JOi KXAL 



for ideal volume recombination; while, for the assumptions leading to eqs. 

 (31b), etc. the relation is 



U = -EIh>, t[( - e- 2 - In (1 - e)] + const. (39b) 



Thus, in the steady state, the difference in potential between any two points 

 to the right of .v = can be obtained by finding the values of e for these 

 two points by (37), and then using these to evaluate the difference in the 

 values of (39) at the two points. To the left of .v = 0, of course, E is constant 

 and equal to /<i/cr. 



5. Diffusion' Effects 



Diffusion will obviously be very important at small values of ^ = x/EoHhT 

 when n,,i is large, because of the tremendous concentration gradients which 



0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 



Fig. 8 — Transient behavior of m, with time at position .t/£o p-kt = 0.5 and 1.0, as- 

 suming nh\ = 0.3 Mo and recombination rate = nhne/rna. 



Figs. 5 and 6 predict for such cases. Also, of course, diffusion will round ofif 

 the discontinuities in slope which appear at the front and rear of the transient 

 disturbance as in Fig. 7 and Fig. 8. At other points the importance of diffu- 

 sion effects can be roughly estimated either by comparing the diffusion cur- 

 rent with the drift current or by comparing the divergences of these two 

 contributions to the current, i.e., the last and first terms on the right of (24). 

 Referring to these terms in (lA) we have 



diffusion currentl 

 drift current J 



div. diffusion current"! _ / J' 

 div. drift current J \ / 



G J '^V^ 6] («) 



H + (1 + m/,/mo)»'][1 + 2v] 







fj'h/ 



)U.) 





_ (41) 



