1054 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956 



to the new conditions.' This section will concern itself with the trapping 

 time constants (which are not directly related to the rate of recombina- 

 tion of minority carriers). 



One case of trapping kinetics has been discussed by Haynes and Horn- 

 beck.^ A general treatment of surface trapping kinetics is necessarily quite 

 involved, and will be taken up in a future paper. Here we shall restrict 

 ourselves to giving an elementary argument relating to the high-fre- 

 quency field effect experiment of Montgomery. To simplify the discus- 

 sion, we assume that the surface in question is of the "super" type; i.e., 

 the surface excess of the bulk majority carrier is large and positive. At 

 time i = 0, a large field is suddenly applied normal to the surface; the 

 induced charge appears initially as a change in the surface excess of the 

 bulk majority carrier; as time elapses, charge transfer between the space- 

 charge region and the fast states takes place, until equilibrium with the 

 fast states has been re-established. What time constant characterizes 

 this process? 



Take electrons as the majority carrier. Then the flow of electrons into 

 the fast states must equal the rate of decrease of the surface excess of 

 electrons. For a single level one may write: 



Un = NtVTn(rn[(l " ft)ns - Ml] 



(26) 



= -r„ 



For a continuous distribution of levels, one can say that only those 

 levels within a few times (kT/e) of the Fermi level at the surface will be 

 effective, so that one may regard the distribution as being equivalent to 

 a single state with rii = rii exp (Y — In X), which will be about half full. 

 We assume further that the density of fast states is sufficient for the 

 changes in r„ to be large in comparison with those in ft , as is reasonable, 

 having regard to the relative magnitudes of the measured values of 

 (dI,s/dY)i found in the present research, and of (dTp/dY)5 and {dT„/dY)s . 

 Thus/< may be treated as a constant in equation (26). Further, we may 

 set Hs = 4r„ /nj£ , as may be proved from considerations on the space- 

 charge region.' Solving (26) with these conditions, one finds, for the 

 transient change in r„ between the initial and the quasi-equilibrium 

 state : 



Ar„ cc M - th-] (27) 



where 



r = \e-''&/[NtVTn(rnV2 Vftil - ft)] 



