. The Bell System technical journal . /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 asbefore, 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 arisingfrom the change in potential across the space-charge layer has beendiscussed by Brattain and Bardeen. Here we shall recalculate this effectby a better method, which again shows that, \\ithin the ra
. The Bell System technical journal . /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 asbefore, 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 arisingfrom the change in potential across the space-charge layer has beendiscussed by Brattain and Bardeen. Here we shall recalculate this effectby a better method, which again shows that, \\ithin the range of surfacepotential 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 thesurface, 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 . DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1057 Then the total additional change in (pp and <pn across the space-charget-egion, arising from the departure in uniformity in the carrier densitiest) and n, is: A,, = -£. / (i - 1) ,,. Mn J no/ (2) Suppose now that the true surface recombination rate is infinite, sothat the ciuasi-Fermi levels must coincide at the surface, and: (Pp -f A<Pp = <pn -+- A(pn (3) These equations, together with the known space-charge equations,icomplete the problem. Notice first, from (2), that A<pp will be large onlyif there is a region in which p is small (F ^ 1), while A^„ is large onl}^when, in some region, n is small (F <3C — 1). Introducing the cjuantity 5,approximating for 8 small, equating Ip and /„ and setting the result eciualto sriid, one finds: F « -1 {Dn/£)(\ + X^)e^ F » 1 (4) The coefficients {Dn/S) and (Dp/£) are of the order of 4 X 10
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