1056 THE BELL SYSTEM TECHXICAL JOURNAL, SEPTEMBER 1956 



The integrand has one pole Avithin the contour, at x = ^iw, at which the 

 residue is — c(cos ^cr sh g -\- i sin ^cir ch g). Multiplying by 2x1 and 

 equating the real part to that in the above expression, one obtains: 



/i = xc cosec \cir ch y 



The same contour is used in evaluating lo ; there are now poles at z = 

 ^/tt and at z = \iir — b, and one obtains: 



1-2 = TTC coth b ch g cosec ^ctt 



— 27r cosec ^CTT cosech" b sh ^bc ch{}/'2bc — g) 



To evaluate h , one integrates / [ch{cz + g)/(chz + chh-)] dz around 



the contour shown in Fig. 5. There are poles at iw ± k. Proceeding as 

 before, one finds: 



I3 = 2ir sli ck ch g cosec ire cosech k 



Appendix 2 



limitation of surface recombination arising from the space- 

 charge barrier 



The ([uestion of the resistance to How of carriers to the surface arising 

 from the change in potential across the space-charge layer has been 

 discussed by Brattain and Bardeen. Here we shall recalculate this effect 

 by a better method, which again shows that, \\ithin the range of surface 

 potential studied, the effect of this resistance on the surface recombina- 

 tion velocity is for etched surfaces ciuite negligible. 



Let Ip and /„ be the hole and electron (particle) currents towards the 

 surface, and let x be the distance in a direction perpendicular to the sur- 

 face, measuring .r positive outwards. Then the gradient of the fiuasi- 

 Fermi levels (pp and <pn at any point is given by: 



n n 7i x"'/ 



(1) 



-R +R 



Fig. 5 — Evaluation of I3 . 



