550 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



10 



18 



17 



10 



r<5 



o 

 a. io'® 



UJ 

 Q. 



+ 



10 



,15 



to'' 



10 



,13 



10" 



10' 



15 



10" 



10 



,17 



10^ 



,18 



A" PER CM3 



Fig. 3 — Isotherms showing the solubility of lithium Z)+, in silicon as a func- 

 tion of boron doping A~, for an external phase of tin containing 0.18 per cent 

 lithium. 



ments were made by saturating gallium-doped germanium crystals with 

 lithium by alloying lithium to the germanium surface at a high tempera- 

 ture, and letting it diffuse in. Following this the crystals were cooled 

 and lithium was allowed to precipitate to equilibrium. In this case the 

 external solution is the precipitate and is of unknown composition. 



If the straight line portion of the curve is used to determine D^/A~ 

 appearing in (3.5), the value of Do"*" associated with the precipitate as an 

 external phase can be computed by using the value of n, obtained from 

 Fig. 2 for 25°C. The latter is 3 X lO'' cm"', and the measured D^/A" 

 is 0.85. Application of (3.5) then leads to a value of Dq'^ of 6.6 X 10^' 



+ 



cm at 25°C. Since the highest value of D measured in Fig. 4 is 5.5 X 



10 cm 



, the solubility increase here shows a factor of 10 . Interaction 

 is already apparent at values of A~ as low as 10^ cm~*, and since there 

 are 4.4 X 10 cm~ atoms per cubic centimeter in pure germanium this 

 represents interaction at levels of atom fraction as low as 2 X 10~ . 



IV. FURTHER APPLICATIONS OF THE MASS ACTION PRINCIPLE 



In the last section the possibility was mentioned of inverting the sign 

 of the temperature coefficient of solubility, and so preventing impurity 



