FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 



1191 



L. Solutions with v = Vih, t), (P = (P(/r, /), grad (P t^ 0, 

 Div grad h = Oy N 9^ 



For formal reasons we shall work, not with the conditions (P = (P(A, /) 

 and V = V{h, t), but with the equivalent conditions 



^ = aL(/r, /) and 5C = JC(A, /). 



(71) 



The condition grad (? 9^ now implies — r 5*^ 0. 



dfi 



Substitution of (79) into (30) and (32) yields— after use of (70): 

 — (gradW =-_[_(R(cu)+__- + ___J 

 and 



(Vm^ 



dh\\_ ae ^ I a/i dh 



■]S+-S) = ' 



(72) 



(73) 





in which ni, — r , and -rr are, of course, functions of h and of /. 

 dh dh^ 



In determining the combined implications of (75) and (70) three cases arise 

 accordmg to whether or not -— - = or grad (grad hY = 0. 

 Case 1: 



dh^ ^ ' 



grad (grad hY j^ 0. 



