EXCESS SEMICONDUCTOR HOLE TRANSPORT 



419 



For convenience in future calculations the equations will be appended 

 which correspond to (31) to (34) when, instead of »/, , the field E is used as 

 dependent variable in the differential equations. In terms of the dimension- 

 less variable 



€ = E/Eo = 



1 



1 + ^1+ Mft/Me) 



(36) 



and the parameter eo corresponding to v = ^'o , the equations are, for ideal 

 volume recombmation (eqs. (31a) etc.), 



t = (1 + Me/M/-)eo - -2 In ( 1 + - eo ) + In (1 



o) 



~ [same with e instead of eo] 

 while, for the recombmation function leading to eqs. (31b) etc., 



1 -60 



(37a) 



(38a) 



^ = eo - e + In 



5 = In 



1 - e 



(37b) 



(3Sb) 



The electrostatic potential U is 



U = — / E dx = — EluhT I € d^. 



In the steady state the relation between e and ^ is given by (37) with eo 



(Me + Mk) je 



set equal to ei which, by (13), is 1 



fJ-h 



(ji + je) 



For this case 



U = -£oM/.Tret - I idt 



= —ElfihT] t(jj.l/fxl — 1) — e"(l + \ij\i})ll 



(39a) 



ln(l-e)-^ln(l-l-^-%)l + 

 Ma \ M. /J 



const. 



