FLOW OF ELECTRONS AND HOLES IN GERMANIUM 



603 



respectively, with the solutions for field opposing and field aiding, as will 

 be seen. 



For Jo = — 1, or field opposing, (82) leads to differential equations of the 

 first order for the determination of the ^'s. The condition that these func- 

 tions vanish identically for P = suppresses all .4's of even order. The 

 first term of the expansion is found by solving 



(83) ^_i + 



whence 

 (84) 



b - 1 



A-, 



[1 + 2P] 



l+'-^P 



[1 + 2P] 



1 + 



b + 



'-'] 



A-i = 



1 + 2P 



The second term is found from 



b - I Ax 



(85) 



^1 + 



[1 + 2P] fl + ^ + 



Ul~L 



l+'^P 



R, 



\_~ ' b J 

 whence, with R equal to unity and (1 + P), respectively, 



(86) 



A, = 



P[l + P] [l + ^-^ P\ 



Ax 



A 



1 + 2P 

 1^-\P +\P'\\\ + 



for constant mean lifetime 



I-H^^] 



1 + 2P 



For the third term, making use of (84), (85) and (86), 

 b-\ As 



for mass-action 

 recombination. 



^3 + 



b [l-t-2P][l + ^-±ip] 



(87) 



^3 + 



= -[1 + P] 

 1 As 



1 + 



6 + 



1 T for c 

 J lifeti 



constant mean 

 lifetime 



[1 + 2P] 



H-'-4^P 



= -[1 +P] 



1 + ^P + ^P^ 



1 + 



6 + 



^'l 



for mass-action 

 recombination 



