FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



593 



with those already derived: For large applied aiding fields, the differential 

 transport velocity changes from the drift velocity, for Po equal to zero 

 and Mo unity, to the diffusion velocity given in (50) as Po and Mo in- 

 crease indefinitely. 



3.32 The zero-current solutions and the behavior for large concentrations 



The solutions for the intrinsic semiconductor for the current parameter 

 equal to zero are, of course, the same as the general ones given in Section 

 3.1, since the current parameter does not occur in the differential equa- 

 tion. For the »-type semiconductor, the differential equation (27) be- 

 comes an equation of the Bernouilli type for C equal to zero, and may be 

 solved by quadratures. It is then linear in G', and gives, for field aiding or 

 field opposing, 



(51) 



G' = 2 



Jo 



P(l + P)(l + aP) 



dP, 



expressing the recombination function R according to equation (16) for a 

 combination of the two recombination mechanisms. Writing, for brevity. 



(52) 



/3^ 



b + 1 



M-l+^lip, 



and evaluating the integral in (51), the following result is obtained: 



G" = 2/3 



[r 



M 



[1 



(53) 



+ 2P. 



[/3(M2 - 1) 4- ( 1- 4/3)(M - 1) - (1 - 2/3) log M] 

 + a[f/32(M3 - 1) + 1(1 - 2/3) (M2 - 1) 



+ (1 - 6/3 + 6/3-) (M - 1) - (1 - ^)(1 - 2/3) log M] 

 For P large, this solution gives the approximations, 



'b + r 



(54) 



G = ± 



2b 



for constant mean lifetime, with a = 0, and 



(55) 



G = dz 



' a(b -f 1) 

 3b 



li 



