404 BELL SYSTEM TECJIMCAL JOURNAL 



at very high frequencies Cr will dominate the admittance. At very high fre- 

 quencies Cr itself will have a frequency dependence; however, for the as- 

 sumptions on which the treatment of this section is based, the relaxation 

 time for the transition region tt is much less than Tp . This is a consequence 

 of the fact that, although diffusion of holes into the transition region is 

 required for the charging of Cr , the distance is relatively short, being in 

 fact only that fraction of the width .Vr„ - Xrp of the transition region in 

 which \l/ rises by kT/q; in germanium this will be about one- tenth of 

 xm - Xtp . Since diffusion times vary as (distance)^, the ratio of the times is 



Tt \XTn Xpn) 



Tp iool; 



13 



(4.31) 



Hence if Lp > Xm - Xp„ , tt will be much less than t 



4.5 Admit lance Due to Hole Flow in a Retarding Field 



In Appendix II we treat the case in which a potential gradient, due 

 to changing concentration for example, is present in the n- and ^-regions. 

 This tends to prevent holes from diffusing deep in the //-region and for 

 this reason the w-region acts partly like a storage tank for holes under a-c. 

 conditions, thus enhancing Sp compared to Gp in Ap. If the electric field is 

 -d\p/dx = kT/qLr , where Lr is the distance required for an increase of kT/q 

 of potential (i.e. a factor of e increase in ;;„), then the value of Ap is 



I \ J. /T ^ {2Lr/Lp){\ + io^Tp) .^2-) 



Ap = [qi.p./Lp] 1 ^ [1 _^ (1 +i^rp){2LJLpn" ^ ^ 



For wTp > 1, this admittance is largely reactive provided lErLp is sutTi- 

 ciently small. 



The dependence of Ap upon w is shown in Fig. 7 for two values of Lr/Lp ■ 

 The i)lot shows the real and imaginary parts of 



Ap/[2qt.pnULl] = 1 + [1 + (1 + ,w^)(2VL;?F^ ^^■^''^^ 



for Lp/Lr ^ 10^'" and Lp/Lr = 10, the two curves being relatively displaced 

 vertically by one decade. The second value imi)lies that the field keeps the 

 holes back so that they penetrate only yo their possible diffusion length in 

 \w field. It is seen that for this case the storage effect is very jjronounced and 

 the susceptance ^" is much larger than G for high frequencies. 



The function (1 + io^TpY'', discussed earlier, corresponds to the limiting 

 case of (4.32) for Lr = ■^- . 



'3 In Appendix IV ;in ;uial\-tic treatment of Cr is given. 



