FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



591 



solutions, which hold for any recombination law, are obtained quite 

 simply, by integration, from G in terms of P to the first term of the Mac- 

 laurin's expansion, given in the Appendix. It might be noted that for this 

 approximation the electrostatic field is equal to the applied field, so that 

 F equals C. 



10 



8 



U- 6 



^ 2 



1.0 

 0.8 

 0.6 



0.4 



8 10 12 14 16 



REDUCED DISTANCE VARIABLE, X 



Fig. 6. — The dependence of the reduced hole concentration, hole flow density, and 

 electrostatic field on reduced distance for steady-state one-dimensional hole flow in «-type 

 germanium, for the cases of constant mean lifetime and mass-action recombination. 



Since F is small, the transport velocity of holes is equal to their differ- 

 ential transport velocity"". Writing the equation for Cp in dimensional 

 form, the transport velocity is found to equal 



(47) 



S = i[±V(M£a)2 + 4Dp/T + nEa], 



with the plus sign for field aiding and the minus sign for field opposing, 

 if the applied field, Ea , is positive. This result is consistent with the 



'^In accordance with equations (7), (8), and (10), the differential transport velocity 

 for the steady state in one dimension may be found from the general formula, 



hM^CJdP = - (P - P,)R/G. 



Its equalling the transport velocity proper for P small appears to result from the property 

 of non-composite cases that the dependent variables, for a given C, are all functions of P 

 which do not depend on any quantity determined by the boundary values, a property 

 which composite cases, with their additional degree of freedom, do not possess. 



