480 BELL SYSTEM TECIIXICAL JOCKS AL 



This corresponds to the result used in (4.31) in which (.Vr„ — .Vrp)/10was 

 used for L, . For smaller values of oo the current may be calculated and put 

 in simi)le form by expanding 7 up to terms including co". The resulting ex- 

 pression for the current is 



/ = —iicici pi) L.{Lr'L\)e"^ 



This is interpreted as follows: The a-c. voltage across a layer L, thick is 



# = (kT'c]) {L,'U)e'^' 



and, if we consider plus voltage as producing a field from left to right, then 

 the a-c. voltage across /.,. is V = —5\}/. Substituting this for (/,,. /.i)e.\p(/w/) 

 gives 



I = iojc/po Lr(q/kT)V 



Here qpoLr is the total charge in the layer Lr , (qV/kT) is an average frac- 

 tional change in this charge for V so that (qpoL,) (qV/kT) H- F is a capacity. 



APPENDIX V 



The Effect of Surface Recombin.\tiox 



In this appendix we shall consider the effect of surface recombination upon 

 the characteristics of the p-n junction. As for Section 4 we shall illustrate 

 the theory for the case of holes diffusing into «-type material. For sim- 

 plicity we shall treat a square cross-section bounded by y = iw, z = ±w, 

 the current flow being along +-^". 



We shall denote the a-c. component of p as 



pi = pi {x, y, z, I) 



At .V = 0, the edge of the //-region, we shall suppose that tfp and \}/ are inde- 

 pendent of y and z so that we shall have 



pi(0,y,z,l) = pwe"' = {pnqvi/kT)e"^ 



by reasoning similar to that used for equation (4.5). The boundary condi- 

 tion at the surface will be 



— D -p^ = spi for V — +w 



dy ^ 



This states that the recombination per unit area is spi and is equal to the 

 diffusion to the surface —Ddpi'dy. Similar boundary conditions hold for the 

 other surfaces. Ky standard procedures involving separation of variables 

 we may verif\' that the solution satisfying the boundary conditions is 



pi = Z^ a,je ' cos Pi y cos ^jS 



i".;=0 



