. The Bell System technical journal . -effect ex-periment at frequencies less than 10 Mcyc/sec. This conclusion is con-sonant with the findings of Montgomery. Appendix 1evaluation of the integrals in section 4 The integrals occurring in Section 4, giving the experimentally acces-sible quantities (d2s/dY), (dXs/d8) and s in terms of the surface trapdistribution and cross-sections, are conveniently evaluated by contourintegration. In view of the general applicability of this method in deal-ing with integrals of the sort that arise from such a distribution of traps,we include here a short note on
. The Bell System technical journal . -effect ex-periment at frequencies less than 10 Mcyc/sec. This conclusion is con-sonant with the findings of Montgomery. Appendix 1evaluation of the integrals in section 4 The integrals occurring in Section 4, giving the experimentally acces-sible quantities (d2s/dY), (dXs/d8) and s in terms of the surface trapdistribution and cross-sections, are conveniently evaluated by contourintegration. In view of the general applicability of this method in deal-ing with integrals of the sort that arise from such a distribution of traps,we include here a short note on the precedure used. The integrals neededare: .+00 /T-ouch{cx + g) sech x dx00 /+00th{x -\- b) ch(cx -{• g) sech^ x dx00 -L +00 h chicx -\- g) con- e/la; -\- chk To evaluate /i, we evaluate / ch(cz + g) sech^ z dz around the tour shown in Fig. 4. The contributions from the parts z = ±R vanishin the limit R -^ oo, so that the integral has the value: /+00 /.+00 ch(cx -\r g) sech^ x dx — i sin ctt /00 •—00 sh(cx + g) sech^ x dx. Fig. 4 — Evaluation of 7i . 1056 THE BELL SYSTEM TECHXICAL JOURNAL, SEPTEMBER 1956 The integrand has one pole Avithin the contour, at x = ^iw, at which theresidue is — c(cos ^cr sh g -\- i sin ^cir ch g). Multiplying by 2x1 andequating 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 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 Br
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