FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



595 



P° is proportional in the limit to C for constant mean lifetime, and to C^ 

 for mass-action recombination; and, for/^ = l/(b + 1) in the case of the 

 w-type semiconductor, P° increases as C' for constant mean lifetime, and 

 as C for mass-action recombination. 



Consider now the doubly-infinite semiconductor filament with a 

 source at the origin, and suppose that the total injected current at the 

 source is C, , in reduced form, with a fraction /« of this current carried 

 by holes. Denote by C~ and by C+ the reduced total currents for A^ < 

 and for .Y > 0, respectively. Since the injection of holes requires that Ce 

 be positive, at least one of C" and C+ must be positive, since total current 

 is conserved. Let /~ and /+ denote, respectively, the ratio of the hole 

 current at the origin to the left, Cp , to the total current C~ , and the 

 ratio of the hole current at the origin to the right, Cp , to the total current, 

 C+ . It might be noted that, for a flow of holes to the left, say, against 

 the field, C~ and C+ are positive and f~ is negative, and that, if C~ is 

 (plus) zero, /~ is (negatively) infinite, corresponding to the flow of holes 

 under zero applied field. Now, general boundary-condition equations of 

 the form of (33) or (34) hold with the sign conventions here employed, 

 as indicated in Section 2.4. One may be written for the flow to the left, 

 another for the flow to the right, making use of the condition that the 

 relative concentration P is everywhere continuous; G exhibits a discon- 

 tinuity of the first kind at the source, with a change in sign. Writing G~ 

 for the limiting value of the reduced concentration gradient as the origin 

 is approached from the left, and G+ the limiting value as the origin is 

 approached from the right, the boundary-condition equations are, for 

 the «-type semiconductor, 



b + (b -\- l)Po 



(56) 



cr = 



G+= - 



1 + 2P» 



b + {b + DP' 



[r- 



1 + 2P» 



For the intrinsic semiconductor, they are 



ib + D" " 



b-}-{b+ 1)P\ 



P° 

 6 + (6 + l)^'". 



C' 



C\ 



(57) 



G~ = 



G+ = - 



2b 



{b + 1)^ 

 2b 



r - 



r 



6 + ij 



C' 



c 



There are, in addition, an equation which expresses the conservation of hole 

 flow, and one which expresses the conservation of total current, as follows: 



+ r^+ 



(58) 



\r c 



c 



re- =f.c. 



