EXCESS SKM/COXDICTOK HOLE TK.WSl'UKT 



while, for the recombination function leadinj^ to (.^Ih), 



t ^ - hid + M/^ )"-■>- 1 - ''1" + 2(1 + ix, nu)v 



4i; 



(35b) 



In Figs. 5a and 6 the lower dotted curve represents the sum of the terms of 

 (35a) or (35b) respectively as far as the term in In v. in this approximation 

 the dei)endence of v on ^ is exponential. An exponential behavior of this 

 sort is assumed in the small-signal theory of the modulation of the resistance 

 of a filament of semiconductor by hole injection.' The upper dotted curve 



2.0 



Fig. 6 — Steady-state curve of hole density Uh against distance .v. fur the case of ideal 

 surface recombination (recombination rate = «/,/r), and asymptotic appro.ximations lo 

 this curve. 



in Figs. 5a and 6 is a plot of (35a) or (35b), respectively, with the linear 

 term included. It will be seen that in both figures the simple exponential 

 apjiroximation is already quite far off when v =^ )ih )in = 0.1, though it 

 improves rapidly for smaller v. 



Figure 7 shows a sample plot of v against ^ for the case of ideal volume 

 recombination (eqs. (31a) etc.), for the numerical conditions s ^ 1, I'l = 0.3 

 (cf Fig. 4). According to (12), whose validity at ^ = is unimpaired by the 

 occurrence of recombination, this value of j-i imi)lies /,. /, = 6.^. The left- 



' \V. Shocklev. O. L. Pearson, and J. R. Haynes, Bell Sys. Tech. Jour., this issue. 



