564 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



formation near a silicon atom. Hence the endothermal heat of formation 

 of LiB" in (5.2) is reduced substantially (by the amount of the released 

 energy of elastic strain) below the heat of formation of LiSi. This ac- 

 counts for the greater stability of the former. 



The compressive strain around a substitutional boron in germanium 

 is also illustrated by ion pairing studies to be described later in Section 

 XII. Its action in that case keeps the ions which form a pair from ap- 

 proaching each other as closely as they otherwise might. Although really 

 quantitative studies of pairing have not yet been performed in silicon, 

 the lattice parameters of germanium and silicon are sufficiently close to 

 render it fairly certain that the same strain exists in the latter as in the 

 former. This lends support to the previous argument. 



Before closing this section there is another related topic which is worth 

 mentioning. This concerns part of the explanation of the retrograde solu- 

 bility observable in the curves of Figs. 5 and 9, i.e., the occurrence of the 

 maxima. The solubilities along these curves are given by (3.3) in the form 



Suppose that at low temperatures K* is an increasing function of tem- 

 perature and considerably larger than Ui . Then we have the approxima- 

 tion 



A"" = (K*f' (5.10) 



in which the solubility Do^ must increase with temperature. If Ui in- 

 creases more rapidly than K* with temperature, a point will be reached 

 at which nf in the denominator of the (3.3) in its special form above, 

 exceeds K* by so much that the latter can be ignored. When this is so 

 another approximation holds, 



J. K* 

 Do"- = — (5.11) 



rii 



in which Do"*" decreases with temperature since rii increases more rapidly 

 than K*. Since (5.10) predicts an increase in solubility with temperatmc 

 at low temperatures and (5.11) a decrease at higher temperatures a 

 maximum occurs somewhere between. The maximum may not be due to 

 this cause alone, however. For example K* contains the activity, a, in 

 the external phase, and this may vary with temperature in an erratic 

 manner. 



In any event the influence of the electron-hole equilibrium on Z)o^ in 

 both'silicon and germanium cannot be ignored. The fact that the distri- 

 bution coefficients of donors and acceptors in silicon are usually some 



