.i-c'. I \i rh:i)A\( !■: or co.xt.k r ri-atiiiek 4.m 



about the coiKCiUratiuns of donors and acceptors can be obtained from the 

 \ariation of capacitance with bias. 



In the equivalent circuit of Fij^. 1 the capacitance C is in parallel with the 

 difTerential resistance, R, of the contact, and the parallel components are 

 in series with the resistance R, of the body of the semiconductor. Spenke 

 showed that R and C are independent of frequency if the frequency is low 

 enough so that the charge density is in equilil)rium during the course of a 

 cycle. 



If the applied voltage is suddenly changed, it will take time for the charges 

 to adjust to new equilibrium values. The time constant for the readjustment 

 of charge of the carriers (holes in this case) is x-p Air, where p is the resistiv- 

 ity (in e.s.u.) of the body of the semiconductor and k is the dielectric constant, 

 and is ^ 10^^" sec. for a resistivity of 100 ohm cm. Even if a larger value 

 of p is used, corresponding to a point in the reserve layer, the relaxation 

 time for the carriers is very short.^ A m.uch longer time may be required 

 for readjustment of charge on the donor or acceptor ions, giving a varia- 

 tion of R and C at lower frequencies. If the barrier is nonuniform over the 

 contact area, so that much of the current flows through low-resistance 

 patches, the equivalent circuit may consist of a number of circuits like 

 those of Fig. 1 in parallel. In this case, if an attempt is made to represent 

 the contact by a single circuit of this form, it will be found that R and C 

 vary with frequency. 



The derivation of the current voltage characteristic for the general case 

 of a time dependent applied voltage follows. The total current per unit 

 area is the sum of contributions from conduction, diffusion, and displace- 

 ment currents: 



/(/) = (tE - eDidn/dx) + iK/4Tr)(dE/dt), (1) 



where 



)i{x,() — concentration of holes; 



a = n{x,t)eij, is the conductivity; 

 e = magnitude of electronic charge; 

 IJL = mobility of holes; 

 D = p.kT/e = difTusion coefficient; 

 V(x,l) = electrical potential; 

 E(x,l) — — dV{x,i)/dx = electric lield strength. 

 The coordinate .v extends into the semiconductor from the junction. F^qua- 

 lion (1) may be written in the form 



/(/) = neti(-dV/dx) - pikT{dn/dx) - {K/4Tr)(JfV/dxdl) (1') 



*> Another limit is the transit time of carriers through the barrier layer. This time is 

 generally shorter than the relaxation time of the semiconductor. 



