1052 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956 



give (in at least some ranges of F) a more rapid instead of a smoother 

 variation of these quantities so long as the surface is homogeneous, (ii) 

 The estimates of the changes in Y might be too large. It is unlikely that 

 our calibration is sufficiently in error, and other workers have obtained 

 results comparable to ours. The only possibility would be that the mo- 

 bility of carriers near the surface is larger (instead of smaller, as found by 

 Schrieffer) than inside • — which seems cjuite out of the question, (iii) 

 The ratio of capture cross-sections varies with v. This, however, w^ould 

 only be in the right direction if one were to assume that the ratio x 'in- 

 creases with the height of the level in the gap — i.e., that the high states 

 behave like acceptors, and the low ones like donors. While not quite 

 impossible, this is an unlikely result, (iv) The surface is patchy. It is 

 probable that a range of variation of two to four times (kT/e) in surface 

 potential would be sufficient to account for the observed slow variation 

 of surface photo-voltage and recombination \'elocity with mean surface 

 potential. We ha\'e refrained from detailed calculations of patch effects, 

 on the grounds that, without detailed knowledge of the magnitude and 

 distribution of the patches, it would be possible to construct a model 

 that could indeed fit the facts, but one w^ould have little confidence in 

 the result. The possibility of patches warns us to view with caution the 

 exact distribution function deduced for the fast states. It would still 

 be conceivable, for example, that one has but two discrete states, as 

 originally proposed by Brattain and Bardeen," and that the apparent 

 existence of a band of states in the middle of the gap arises from the fact 

 that there are always some parts of the surface at which the Fermi level 

 is close to one or other of these states. Fortunately the conclusions as to 

 the cross-sections are not too sensitive to the exact distribution function 

 assumed. 



Using the mean of the two coefficients in (25), substituting //,• = 

 2.5 X 10'^ cnr^ £ - 1.4 X 10"'' cm, {vrnVrp)"' = 1.0 X 10' cm/sec, in 

 (24), and using the experimental result (see Fig. 3) that s,nax/(X -f X~\) = 

 1.2 X 10" cm/sec, one obtains ((Tp(T,y~ = 5 X 10~' cm'. Now setting 

 (ap/a„) = x" '^ c' ^^ 150, one gets for the separate cross-sections: 



o-p = <) X 10"'' cm" 

 an = l X 10"'' cm' 



There values appear lo he emiiicntly reasonable. Burton et al, " who 

 studied re('()inl)ination through body centres associated with nickel and 

 copper ill germanium, found cr^ > 4 X 10 '"^ cm", o-,, = 8 X 10"'^ cm* 

 for nickel, and a„ = 1 X 10 '%„ = 1 X 10"'' for copper. The fact that 



