1042 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956 



and that on an etched surface their density is comparatively low. It is 

 also known that the available results cannot be accounted for by a 

 single level, or even two levels, so that one is evidently dealing either with 

 a large number of discrete states or a continuous spectrum. A given trap- 

 ping centre is completely described by specifying: (i) whether it is donor- 

 like (either neutral or positive) or acceptor-like (neutral or negative); 

 (ii) its position in energy; and (iii) the values for the constants Cp and 

 Cn (related to cross-sections) occurring in the Shockley-Read theory. 

 In this paper we shall deduce what we can about these quantities, using 

 the experimental results previously presented. 



At the outset it must be admitted that it is by no means certain that 

 the same set of surface states appear in the field-effect experiment and 

 give rise to surface recombination. However, (i) it is found that such sur- 

 face treatments as increase s also reduce the effective mobility in the 

 field-effect experiment; (ii) any surface trap must be able to act as a 

 recombination centre, unless one of the quantities Cp and C„ is zero; 

 and (iii) the capture cross-sections obtained by assuming that the field- 

 effect traps are in fact recombination centres are, as we shall see below, 

 eminently reasonable. 



As to the nature of the surface traps, not too much can be said at the 

 moment. The lack of sensitivity to the cycle of chemical environment 

 used argues against their being associated with easily desorbable surface 

 atoms; the intrinsically short time constants (Section 5) suggest that 

 they are on or very close to the germanium surface. The possibility that 

 the surface traps are Tamm levels remains; or they could be corners 

 or dislocations. However, the reproducibility with w hich a given value of 

 s may be obtained by a given chemical treatment of a given sample, 

 followed by exposure to a given ambient, suggests that there is nothing 

 accidental about their occurrence. 



II. STATISTICS OF A DISTRIBUTION OF SURFACE TRAPS 



We start by quoting results from the work of Shockley and Read 

 and Stevenson and Keyes'' on the occupancy factor ft and the flow U 

 of minority carriers (per unit area) into a set of traps having a single 

 energy level and statistical weight unity: 



ft = (Cnfi. + Cpp,)/[Cn(n. + ni) + Cp(p, + p,)] (1) 



U = CnCp(p,ns - ni)/\(\{n. + m) + C,(p.. + pOl , (2) 



where the symbols ha\^e the following mc^anings: 



ns , Ps — densities of electrons and iioles present at the surface 



