DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 



1055 



I 



I 



To clarify the order of magnitude of time constant invoh'ed, let us 

 substitute £ '^ 10" cm, Nt ~ 10^^ cm~^, tv,. ~ 10^ cm/sec, cr„ ~ 10"^^ 

 cm ,/t '^ 0.5, Ae~ '~ 1. This gives r -^ 10~' sec, which suggests that one 

 would be unlikely to run into trapping time effects in the field-effect ex- 

 periment at frequencies less than 10 Mcyc/sec. This conclusion is con- 

 sonant with the findings of Montgomery. 



Appendix 1 

 evaluation 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 trap 

 distribution and cross-sections, are conveniently evaluated by contour 

 integration. 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 needed 

 are : 



.+00 



/T-ou 

 ch{cx + g) sech" x dx 

 00 



/+00 

 th{x -\- b) ch(cx -{• g) sech^ x dx 

 00 



-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 vanish 

 in 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 . 



