462 BELL SYSTEM TECHMCA L JOLRXAL 



4.4 Tola! Admil lance 



In order to calculate the alternating current, we must include the capacity 

 of the transition region, discussed in Section 2. Denoting this by Cr , we 

 then find for the total alternating current. 



la. - {G, + iS„ + Gn + iSn + icoC r) V, - Avx (4.23) 



where G„ and S,, are similar to G„ and .5"^ hut apply to electron current into 

 the /j-region. The value of the hole and electron admittances can be ex- 

 pressed as 



A, = G, + iS, = (1 + io:r,f"G,,e'"'^"'' (4.24) 



A^ = Gn + iSn = (1 + io^ryGn.e'''"^ (4.25) 



For low frequencies, such that w is much less then l/Xp , we can expand 

 Gp + iSp as follows: 



Gp + iSp = Gp.e'"'"' + i^irp/DGp^e"'''"^ (4.26) 



Hence (rp/2)G;:o(^''°'^^ behaves like a capacity. 



It is instructive to interpret this capacity for the case of zero bias, iq — 0, 

 for which we find: 



Cp = TpGpo/2 = TpqpniJi/2Lp = q pnLp/lkT. (4.27) 



The last formula, obtained by noting that t^m = qTpD/kT = gLp^kT, has 

 a simple interpretation: qpnLp is the total charge of holes in a layer Lp thick. 

 For a small change in voltage v, this density should change by a fraction 

 qv/kT so that the change in charge divided by the change in v is 

 (q/kT){qpnLp) which differs from Cp only by a factor of 2, which arises from 

 the nature of the diffusion equation. 



This capacity can be compared with Ct neut. , discussed in Section 2, (see 

 equation (2.39) and text for (2.42)) for germanium at room temperature 

 as follows: 



Cp _ q' pn Lp kTa _ pnLpU 



(4.28) 



Ct neut. 2kT IQq" n'i lOui 



For a structure like Fig. 6(c), the excess of donors over acceptors reaches its 

 maximum value, equal to ;/„ , at Xm leading to ;?„ = a.Vm . Consequently 

 a = Hn/XTn ■ Substituting this value for a in (4.28) and noting that 

 pniin = tfi gives 



^T iifUt. 2\)XTn 



(4.29) 



As discussed at the beginning of this section, /.;, = 6 X 10 cm for holes 



