THE FORWARD CHARACTERISTIC OF THE PIN DIODE 699 



arrived at by considering the minima in the sokitions for co » 1. This is 

 really a criterion for conductivity modulation, so we shall assume hence- 

 forth that it is satisfied. 



We now modifv (13) by setting n = p and eliminating E{x) by use of 

 (22) 



, . . 67 + 2Dnn{x) 



^-^'^ = — mh — 



J , . I — 2Dnn (aO 



where n'(x) = dn/dx. Inserting these currents into (22) gives E{x) and 

 integrating gives the potential drop Vp in the middle region 



(6 + 1)D„ Jo n 6+1 no 



This is the generalization of (26) for linear recombination. 



The direct evaluation of (58) and (65) in terms of the total current / 

 leads to a very complicated expression for the applied voltage. It will be 

 jshown in the next section that this result reduces in its simplest approxi- 

 mate form retaining only the essential dependence on w to the formula 



I Jn.9 + ips V io(<^) 



iwhich is identical with (44) except that the characteristic current density 

 lis a function of oj 



7(co) = /o^(w) 



(67) 



g{o:>) = 



cosh - tan ^ f sinh — 



1 _^' + - - 

 6 ^ 48 



(Fig. 5 shows a plot of ^(co). These results show that if co < 1 as we might 

 lexpect in a good diode recombination has no significant effect on the 

 jforward voltage-current characteristic in the conductivity modulation 

 range of operation. 



