FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS tl8<) 



In terms of (P and V these solut'ons are given by: 



(H((P) =^(P + (^gJ^(p-\ (61) 



^ ^% Vy(x,3', 2)€-^'- G/F (/' ?^ 0) (62a) 



or 



and 



or 



eA' 



^ ^ kf ^-^'^''' ^' ^^ ~ ^^ ^^ " ^^' ^^^^^ 



•U = 3C(/) + Vfixy y, 2)€-« - G/F {F j^ 0) (63a) 



'O = ac(/) + \//(:«^, 3', z) - Gt (F = 0). (63b) 



For no recombination ((R = 0), these results specialize to (59b), (60), 

 (62b), and (63b) with G set equal to zero. It should be noted (see (55)) that 

 absence of time variation implies absence also of recombination. 



K. Solutions with V = t)((P, /), grad (P 5*^ 



In Theorems 3 and 8 of Section B we have shown that some very inter- 

 esting properties are implied by the condition 



grad V X grad (P = 0. (64) 



In sections G-I we have treated the cases grad 1) = and grad (9=0. 

 We now turn to the remaining possibility leading to (64): 



V = V{(9, t) with grad (P 5^ 0. (65) 



Substitution of (65) into (23b) leads to 



Two cases arise. 

 Case 1: 



V /3 /d(P e 



