SURFACE PROPERTIES OF GERMANIUM 39 



The relation between Ct and Rt is obtained by use of (A.l) and (A.2) 

 in (A. 10). Since (A.9) is valid only to terms of the first order in 50n 

 and b<t)p , we make the corresponding approximation in (A. 10) and find 



l/Rt = e^UiCt. (AM) 



If there is more than one type of trap, the net recombination resistance, 

 R, is that of the various traps in parallel. Values obtained for R for 

 specimens A and D from the empirical values of C are about 500 ohms. 



We shall show that for a-traps, Rpa is much larger than the other 

 resistances in series, and that for 6-traps, Rnb is the dominant resistance. 

 This implies that 50a = 50n and 8<j)b = b<i>p , or in other words that a-traps 

 are in equilibrium with the conduction band and 6-traps with the 

 valence band. 



First consider the flow across the space-charge layer. The resistances 

 Rnt and Rh depend on the sign of Vb . When Vb is negative, the net 

 electron current across the space-charge layer is: 



/ = evniusi — ni) exp [^{Vb + 8Vb)] 



(A.12) 



^ e^Vnns(8(f)n — 50ns), 



where Vn is defined by an equation similar to (24). The second form is 

 the linear approximation. Thus we have 



1/RnB = e^VnUs . (A. 13) 



If Vb is positive, Us is replaced by n. 



Correspondingly, for Vb negative, the hole current is: 



/ = evj^ipi - psi) exp 1^(Vb H- 8Vb)] 



^ e^Vpp{8(l)ps — 84>p), 



and 



l/RpB = e^Vpp. (A. 14) 



For Vb positive, p is replaced by ps . 



The maximum value of Rns is obtained for the ambient which makes 

 Vb most negative and RpB is a maximum when Vb is most positive. 



The current from the conduction band to the traps is calculated as in 



(23): 



/ = eiVnSntrisiPn - gtUa) (^-15) 



^ e^VnSntnsPt{84>ns - 8<f>t). (A.16) 



