FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



589 



applied field obtains for large P results from diffusion in conjunction with 

 the increase of conductivity. As may be expected, the solutions for the 

 case of constant mean lifetime also have this property, the recombination 

 law merely affecting the form of the common solution. 



In Fig. 6 are shown curves for P, Cp , and F for the case of constant mean 

 lifetime in w-type germanium, evaluated for C equal to 16.3. These curves 

 are intended to illustrate the qualitative differences between the solutions 

 for this case and those for mass-action recombination, which are manifest 



100 

 60 



40 



LD 0.6 



O 0.4 



I 



£ 0.2 

 O 



g 0-1 



0.04 

 0.02 



0.01 



2 4 6 8 10 12 14 16 18 20 22 24 



REDUCED DISTANCE VARIABLE, X 



Fig. 4. — The dependence of the reduced hole flow density on reduced distance for the 

 steady-state one-dimensional flow of holes with mass-action recombination in «-type 

 germanium. 



primarily at the larger concentrations. The dashed curves in the figure 

 give the corresponding solutions for the case of mass-action recombina- 

 tion; and the A'-origins for the two cases have been so chosen that cor- 

 responding curves, which exhibit essentially the same dependence on X 

 for small P, coincide in the limit of small P. As the figure shows, constant 

 mean lifetime gives an exponential dependence of P on X for large P, 

 while mass-action recombination gives larger concentration gradients, 

 with an increase of P to indefinitely large values in the neighborhood of a 

 vertical asymptote. 



