478 BELL SYSTEM TECHNICAL JOURNAL 



and, for continuity of hole current, is dpi/dx = dpi/dx. Expressing these 

 in terms of A, B, C, a and (3 for the a-c. components yields: 



A + B = Ce"^'^'"^''^"''' = CF 



a{A - B) = ^C 



so that 



A ^ {F + /3/a)C/2. 



B = {F - /3/a)C/2. 

 Hence the ratio - [dp/dx\/p atx = -c is 



dlnp _ aiAe^"" - Be'"") ^ ajFa s'nh ac + ^ cosh ac) 

 ~ ~~Q^ (A e+"'= + B e-"") Fa cosh ac -\- ^ sinh ac 



Since at x= —c, the a-c. component of pi is {qvi/ kT) pioe^" , the admittance is 

 = -gPdp/dx ^ ^.^j^p^^/kTX-d In p/dx) 



/ /. \/. , • M/2 F« sinh ac + /3 cosh ac 



= (gM/'io/li)(l + tcon) ^, cosh ac + ^ sinh ac- . 



For c -^ 0, this transforms into 



iqUiPio/Li) (1 + io:nf'^/Fa = {qix{p,,/F)/U){\ + ^corz)'" 



which agrees with Section 4, since pw/F then corresponds to />„ . 



If c/Li and F are not large, an appreciable amount of recombination 

 takes place for x > Q for low frequencies. Dispersive effects will then occur 

 corresponding to t2 . The a-c. will not penetrate to x = 0, however, 

 if ciui/Df'^ » 1 and the dispersive effects will then be determined by n . 



The frequency-dependent part of the admittance, 



Fa sinh ac -\- fi cosh ac 



(1 + iuiTl) 



Fa cosh ac + /3 sinh ac ' 



has been computed and is shown in Fig. 7 for r^ = t2 , F = 1, ri = 7^/9 and 

 c/Li = |. For these values about half the hole current reaches a; = for 

 low frequencies. As the time constant for diffusion through the layer is Tp/81, 

 as discussed in Section 4.6, the layer will act as a largely frequency-inde- 

 pendent admittance well above the point for corp = 1. This is reflected in 

 the behavior of the curves of Fig. 7 and, for frequencies in the V^/ range, 

 it is seen that G is larger than S by about 50% of the low-frequency value of 

 G; this split of G + iS into {^)Co plus approximately (|)Go (1 + io:TpY'^ corre- 

 sponds to the fact that about half the holes are absorbed in layer 1 for the 

 assumed conditions. 



