1050 THK BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956 



do not fit the observed facts, because, for F — ^n X < — 4, the charge in 

 fast states is found to change more rapidly than is given by the empirical 

 expressions in (13) and (14). The behaviour in this region is perhaps in- 

 dicative of the existence of a discrete trapping level just beyond the 

 range of v which can be explored by our techniques. The observations 

 (see Fig. 6 of preceding paper^) can be described by postulating, in addi- 

 tion to the continuous distribution of states given above, a level of den- 

 sity about 10 ^ cm" , situated at j^ = 6, or a higher density still further 

 from the center of the gap. Statz et al,^' using the "channel" techniques, 

 which are valuable for exploring the more remote parts of the gap, have 

 proposed a level of density '^ 10 cm~^, situated at about 0.14 volts be- 

 low the center of the gap (v = 5.5) : this is not in disagreement with the 

 foregoing. 



In order to compare (22) with the experimental data derived from the 

 surface photo-voltage, it is necessary to choose a value for x- Fig- 2 shows 

 the comparison with the results presented in the preceding paper. On the 

 vertical axis, the values of (dl^s/d8)/(d'2s/dY) plotted have been divided 

 by (X + X" ), in order to show the n and p-type results on the same scale. 

 (Note that the limiting values of this quantity should be X/(X -|- X"^) 

 and — X~V(^ + ^~^)j so that the vertical distance between the limiting 

 values should be 1, independent of X). The theoretical curves have been 

 drawn with the value Inx = 2.5, in order to give best fit between theory 

 and experiment at the points at which the ordinate changes sign. (It 

 may be seen from the form of (22) that, with the actual value of the other 

 parameters, the main effect of adopting a different value of in x would 

 be to shift the theoretical curve horizontally, while a change of X shifts 

 it vertically without in either case greatly modifying its shape). The fit 

 between theory and experiment is not quite as good as could be expected, 

 even taking into account the rather low accuracy of the measurements. 

 The variation of (6Ss/55)/(6Ss/6F) with Y found experimentally seems 

 to be rather slower than the theory would lead one to expect. The main 

 points to make are : (i) the difference in Y between the zeros for the two 

 samples (5.4 ± 1) is about what it should be (4.8) on the assumption 

 that in X is the same for both samples and of the order of unity; and (ii) 

 paying attention mainly to the zeros, the estimate (nx — 2.5 is likely to 

 be good to ±1. 



Now let us consider the surface recombination velocity. Here we are 

 on somewhat shakier ground, in that, in deriving (24), we have had to 

 assume not only that x is independent of v, but (o-„crp)^'^ also. First we note 

 from (24) that the maximum value of s should occur at F — (n X = in x- 

 Comparing with the experimental results given in the preceding paper, 



