38 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



Changes in imrefs of the traps are defined by: 



n„ = n, + &n, = i + gxp [(£, - E, -e(V, + SVs) + eS^,)/m ' ^^'^^ 



p„ = p, + Sp, = 1 ^. exp [(g, _ £;, + ,(V, + sv,) - e«0,)/fcr] • ^^-^^ 



In these last two equations, t may refer to either type of trap (a or 6) 

 and 6pt = — 5nt . 



For small signals, the recombination current via a given set of surface 

 traps may be considered as a flow produced by differences in the imrefs, 

 50n and 8<t>p , through four effective resistances in series, as shown in 

 Fig. 20. Here RnB is an effective resistance for flow of electrons across 

 the barrier layer, Rnt for flow of electrons from the conduction band at 

 the surface to the traps, Rpt for flow of holes from the filled band to the 

 traps, and RpB for flow of holes across the barrier layer. Under steady 

 state conditions, the net flow of conduction electrons to the surface is 

 balanced by an equal flow of holes. The recombination current may be 

 thought of as a flow of electrons from the conduction band via the traps 

 to the valence band. 



The recombination current per unit area is 



I = -eU = (50n - 5<f>p)/Rt , (A.9) 



where Rt is the sum of the four resistances in series. Here U is the 

 particle current and / is the corresponding electric current. If d<t>n and 

 6<f>p are expressed in volts, Rt is in ohms/cm^. We may define a re- 

 combination constant Ct by an equation corresponding to (34) : 



U = Ctiviui - n]). (A. 10) 



o ^^n 



6¥>^ 



Fig. 20 — Circuit analogy of surface recombination. 



