CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 579 



Table III 



equal* (7.10) may be written as 



(iVx - P){Nr> - P) 



= fi 



(9.4) 



where Na and No are, respectively, the total densities of acceptors and 

 donors. 



This equation has the following solution for P/Nd , the fraction of 

 donors paired. 



P_ 



No 



1 



= o 1 + 



1 , Na' 



nNo Nd, 



/i 



1 + 



1 



N, 



mo + ¥j-k ^'-'^ 



Inspection of (9.5) reveals that for given A^^ and 0, P/Nd is a decreasing 

 function of increasing No . 



Very often, P/Nd is measured in an experiment, and from this it is 

 desired to calculate a, the distance of closest approach. For such pur- 

 poses the form (9.5) is not very convenient. In fact an entirely different 

 procedure is to be preferred. Suppose P/Nd is denoted by 6, and 6 is 

 substituted into (9.4), into which (9.2) has been inserted. We obtain 



logio Q{(x) = logio 



d 



{Na - eND)(i - e) 



] 



(9.6) 



A knowledge of 6 thus suffices to determine logic Q(a), from which, in 

 turn, a can be determined by interpolation in Table III. Then (9.3) can 

 be used for the evaluation of a. 



* This is a situation which cannot arise in liquids, since there, charge balance 

 -.must be maintained by the ions themselves. It can occur when the ions are of 

 Idifferent charge, but then things are complicated by the formation of triplets, 

 etc., in addition to pairs. 



