FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



575 



It appears that solutions neglecting recombination furnish useful ap- 

 proximations for some applications. If recombination is neglected, by 

 assuming that the mean lifetime is infinite, the definitions (8) of the di- 

 mensionless quantities no longer have meaning, but essentially the same 

 differential equations and corresponding boundary-condition equations can 

 still be used. The reduced equations become essentially homogeneous in 

 T for T large, and it suffices to suppress the recombination terms, PQ — 

 Pq , retaining formally the definitions of the dimensionless quantities in 

 which now r, and thus Lp and Eq or /o no longer have physical significance. 

 One of these unitary quantities may be chosen arbitrarily. It might be 

 noted that if Poisson's equation is retained the length unit is advantage- 

 ously chosen as La , which gives a dielectric relaxation time for the time 

 unit.-^ 



In one cartesian dimension, with total current a function of time only, 

 W may be eliminated by means of the equation for C in (12) and, upon 

 substituting for it in any of the three remaining equations in (12) and 

 (14), a differential equation for P results which depends on b, Po , andC 

 as parameters. Dropping vector notation, this equation is 



dP 

 dU 



(17) 



Similarly, from (10), 



(P - Po)R- 



(18) 



On — 



MoCP - (1 + 2P) ^ 



bM, 



1 + 



'4-^^ 



. . ^ b - idP 



F = 



dX 



l + '-±-'p 



The expressions for F and Cp possess some interesting features. That for 

 the reduced field, F, is composed of two terms, the first of which expresses 

 Ohm's law, since C is reduced total current density and the denominator 

 is proportional to the local conductivity. The second term is a contribu- 

 tion which is directed away from a hole source, since b is greater than 



