p-n JUNCTIONS IN SEMICONDUCTORS 479 



APPENDIX R' 



Time Constant for the Capacity of the Transition Region 



For this case we shall consider the case of holes in an a-c. field with po- 

 tential 



X xe \ 



^ = ^f'^ + - 



where the d-c. retarding field is kT/qLr and the a-c. field is kT/qU where 

 \/L\ is considered small for the linear theory presented here. The expression 

 for the current of holes is 



We shall obtain a solution for p by letting 



p = poe -{- p\[e - e \e , 



while neglecting recombination in this region so that p must satisfy the con- 

 dition p = —d (hole current)/a.v leading to the differential equation 



There are three separate exponential dependencies of the variables leading 

 to three equations (neglecting terms of order (l/Li) ) 



d[poJi-Poj{\ = 



The first equation is satisfied by the equilibrium distribution and the 

 second by 



/>1 = —pQ D/ioJ L\Lr 



and the last by 



1 + Vl 4- ^ii^n/D 

 '^= 2L. 



It is evident that dispersive effects set in when 



CO = D/aC 



