FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1187 



H. Solutions with (P = (P(/), N 9^ O 

 The condition 



grad (P = (47) 



yields from (21) and (22) 



f ^' + ^ (PJ div grad V =- (48) 



and 



(P div grad V = ^ UCCP) + ^ ^1 • (49) 



Two cases arise for (R 7^ 0: 

 Case 1: 



<P=-^ (50) 



and 



Case 2: 



or 



div grad V = — ^ (R((P) 



(P = - ^ (51) 



a 



«<.) + !!- = . 



^ ~ ^ — I ^^/^x (^^ arbitrary constant) (52) 



and 



div grad V = 0. (53) 



When recombination is absent, these cases reduce to: 



(P = E (E: arbitrary constant) (54) 



and (53). 



When time variation is absent, Case 2 again yields (53) and (54). 



It should be recalled that V can depend on / as well as x, y, z; so that 

 arbitrary functions of t play the role of arbitrary constants in (51) and (53), 

 whenever time variation is allowed. 



