CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 581 



10 



10 



10" 10 



12 



10'^ 10' 



10 



15 



10 



16 



10 



17 



10 



18 



N IN CM"^ 



10'9 10' 



Fig. 15 — Fraction of ions paired, assuming equal densities of positive and 

 negative ions, calculated as a function of temperature and concentration from 

 equation (9.5). The situation illustrated might apply to gallium and lithium in 

 germanium in view of the choice of a and /c. 



Fig. 16 covers the range from pi = 0.05 to 0.08 and involves a 

 logarithmic scale because of the sharp variation of i in this range. (This 

 points up the sensitivity of the degree of pairing to the magnitude of a.) 

 Fig. 17 extends the curve to pi = 5. When pi exceeds 5, i{pi. , 0.05) can 

 be obtamed from the formula 



i{pi , 0.05) = 3865 + ^' + ^' 



(9.10) 



In order to determine i{pi , pi) when pi ^ 0.05, the following formula 

 may be used. 



i(p2 , Pi) = i(p2 , 0.05) - 2(pi , 0.05) (9.11) 



