

704 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



put By^ = 6 (as if 7 = 7„) and FM = PM, 



2 



1 ^i ^^ 



/3Fp = ^-pp 4/ J- V6 + cosh CO FM (88) 



In this way we retain the correct form of dependence on w, but throw 

 out the dependence on / that comes from 7(/). It can be shown from| 

 (81) that 



tan ^ f sinh - 



sinh ~ (89) 



2 4 



CO CO 



= 1 - — + — - + 



12 ^ 180 ^ 



Thus we define the characteristic (particle) current density of the device 



/o(co) = 



{b + l)7oo 



(b + cosh co)F„(l)2 



(90) 



and (88) can be written 



n2 



CO 



_F^(1) sinh co_ 



= /o</(w) 



2 



i4/£ ^^^H 



This formula corresponds to (42) with C = 2/\/b + 1. In the spirit I 

 of the present theory the exact value of this constant is not important, j 

 so we may replace 2/-\/b + 1 in (91) by C. Then the sum of (87) and 

 (91) gives the total applied bias (66). 



Non Linear Recombination 



In this section we shall consider the forward characteristic of a PIN 

 diode in which the current densities at the contacts obey the law 



/ \" 



J J- I 'ion \ 



,n 



+ 



p 



(92) 

 T = T ( ^"" 1 



where /„,, and /,,., are characteristic of the device and a is a number be- 



