SURFACE PROPERTIES OF GERMANIUM 27 



It should be noted that the coefficient C is independent of the Fermi 

 level and thus of the conductivity of the specimen, whereas Vs is not. 

 The relation between them is: 



For n-type C = Vs/n, (33) 



For p-type C = v^/v- (34) 



Values of C may be determined empirically from observed values of 

 Vs . Referring to Table I, for sample A, Vs = 60 cm/sec and n = 1.4 X 

 lO'Vcm', so that C = 4.3 X 10~'' cm'/sec. For sample D, Vs = 180 

 cm/sec and p = 3.0 X lO'Vcm', so that C = 6 X 10~'' cmVsec. The 

 values of C are approximately the same, indicating that the traps are 

 not much different for the two specimens. 



The theoretical value of C involves Uao and pto • It is the product 

 naPb = najoPbo , which is related to the parameter H and which can be 

 estimated from empirical data. To obtain the concentrations them- 

 selves, a value must be assumed for Vq . We have 



riao = {UaaPbof exp [ — ^Vq], (35) 



Pbo = (riaoPbo)' exp [l3Vo]. (36) 



As we have mentioned previously, there is no way to determine Vo 

 from our experiments, although postulate II sets limits on its value. 



Let us for simplicity assume that SnbVn = SpaVp = StV. Then, using 

 (35) and (36) in (30) and (32), we have 



C = 2Stv{naoPbo/n]f cosh ^7o . (37) 



This equation may be used to estimate the trapping cross-section S, 

 for an assumed Fo • 



COMPARISON BETWEEN THEORY AND EXPERIMENT 



In Fig. 14 we have plotted c.p. - (c.p.)o - {Vb - Vbo) versus 

 2 sinh 0{Vb - Vbo) for p-type sample D, (see Table I). Each symbol 

 represents experimental points for one cycle. Results are sho^^^l for five 

 different cycles not all in the same run. These results are typical of all 

 the data obtained for this sample. It is seen that these data can be 

 fitted over most of the range by a straight line as dra\vn, giving a value 

 oiH = 0.02 e.v. 



In Fig. 15 we have used the same experimental results to plot 

 8Vl versus c.p. - (c.p.)o . Since the experimental values of 8Vl cover a 

 range of a factor of 20 or more, a logarithmic scale was used to plot 



