p-n JUNCTIONS IN SEMICONDUCTORS 483 



approximation is that, at x = 0, pi is independent of .v and y may become a 

 poor one, especially for forward currents, because the transverse currents to 

 the edges will be important. Under these conditions the role of surface re- 

 combination will give rise to patch cfTects of the sort discussed in Section 4. 



APPENDIX VI 

 The Effect of Trapping Upon the Diffusion Process 



In this appendix we shall investigate the effect of the trapping of holes 

 upon the impedance. We denote the density of mobile holes in the valence- 

 bond band by p and the density of holes trapped in acceptors by pa . For 

 thermal equilibrium at room temperature there will be an equilibrium ratio, 

 called a, for pc/p. For germanium a — IQr* and for silicon a — 0.1 to 0.2. 



We shall consider four processes which occur at rates (per particle per 

 unit time) as follows: 



Vr direct recombination of a hole with an electron (free or bound to a donor) 

 vt trapping of a hole by an acceptor 

 Vra recombination of a hole trapped on an acceptor 

 Ve ex'citation of a trapped hole into the valence-bond band. 



Under equilibrium conditions as many holes are being trapped (rate pvt) 

 as are being excited (paVe) '. hence v t = ave . 



We shall study solutions of the customary form for the a-c. components: 



, . iut—yx 



pi = pioc 



Pla = Plaoe 



These must satisfy the equations 



pl = D\ pi — {v t + Vr)pl + Vepla 

 Pla = Vtpl — {Ve -f Vra) pla 



These lead readily to the equation for 7: 



Dy = io} -]r Vr -\- Vt — VeVi/iioi -\- Ve -\- Vrc) = '" 



1 + 7 I ^^2^1 2^ \ -'r Vr -\- Vt 



{Ve + Vra) -r 00 )\ 



1 



(ve + Vra) + W /("e + 



Oj 



From this equation we can directly reach the important conclusion that 

 the trapping process can never lead to a capacitative term larger than the 

 resistive term. This result is obtained by analyzing the complex phase of 7, 

 the admittance being proportional to 7. In particular, we find that the real 

 term in Dy is always positive, as may be seen from inspection, so that the 

 complex phase angle of 7 is less than 45°. 



The form reduces to a simple expression if Ve and v t are very large com- 



