806 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



then the ac displacement current is 



j{D, ,S'2)f''"' = ia)C,i;(*S:,)e'"'. (3.0) 



Now the total current is constant through the device, hence 



J = Jip, Sd + j(D, S2) (3.7) 



which leads to 



j = io:C2v{S2)/{l - 13). (3.8) 



If ^(^2) is substantially eciual to the ac voltage across the luiit, then 

 the impedance is 



(3.9) 



= (l/icoCo) + (I/C.C2) I ^ 1 exp t[{7r/2) - d]. 



Evidently ii 6 > tt and 6 < 2ir, the second term will have a negative 

 real part so that the diode will act as a power source. 



If we neglect the ac electric field in N then |3 may be calculated in 

 terms of the thickness L = X2 — rci of the layer and the potential drop 

 across the layer. This latter arises from the concentration ratio Ndi/Nd2 

 between the two sides of N. Since the donor charge density is neutralized 

 substantially entirely by electrons, and since almost no electron current 

 flows, the electron concentration difference must result from a Boltzman 

 factor (at lO^Vcna^ Fermi-Dirac statistics are not needed) and this leads 

 to 



AVn = (kT/q)hi(Ndi/Nd2) (3.10) 



for the potential drop across A^. In A^ the electric field is thus 



E = AVn/L. (3.11) 



The differential equation for hole concentration for a disturbance of 

 frequency co is 



p = i^p = -^pE ^ + i), g . (3.12) 



This linear differential equation has two linearly independent solutions. 

 These must satisfy at .r2 , the left edge of the space charge layer S2 , the 

 boundary condition that the hole density is practically zero. The 

 appropriate solution is 



p = e'"' [e"'^''-''^ - e"'^'"'''), (3.13) 



