FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 



1207 



and 



L ^'^ 



ti-Ji 



Finally we substitute (152) and (153) into (154) to get 



B = — ^^^"^ "^ ^"^P In 

 e flpln — y^nlp 



NilXpIn - finip) 



(154) 



(155) 



Equations (152)-(155) give the desired expressions for M, A, L and B 

 in terms of Ip,In, and (?« for "Uoo = if J 5^ and Z ^ 0. 

 For ^ = we can repeat the above steps using 



and 



V = B 



cP = g(5-M 



L/r) 



(156) 



(157) 



in place of (141) and (142). The result for L 7^ and t)oo = is 



/p = -il2/Xpe.¥Z (158) 



In = h^nn eNL (159) 



/ = iQeN(jin - yip)L . (160) 



with 



jB = 



M = -%(9. 



eN 



and 



L = 



2L 



2In 



fi/Up eN Q/Lin eN 



tlpln — lulj 



^Mp Mn eN 



(161) 

 (162) 



(163) 



It is evident that A = implies V = constant and iipln + yijp = 0. 

 The condition L = makes JC = constant, so we use (62b) and (63b) 



and set 



^ (164) 



and 



Ne 



(P = -VIT57 



V = Q + Vr-\- S/r 



{Q, Rj S: arbitrary constants). (165) 



