548 



THE BELL SYSTEM TECHNICAL JOURNAL, AL\Y 1956 



volved, the temperature dependence of the solubiHty, D'^, enters only 

 through the ratio, ni/Do^ . If this ratio is very small, then 



D^ ^ A~ (3.6) 



and the solubility is independent of temperature. In this condition Z)"^ 

 may approximate A~ by being either slightly less or slightly greater than 

 the latter. Details are given in Reference 6. 



(3) Whereas D^ at small values of doping may be an increasing func- 

 tion of temperature, it may, depending on the system, be a decreasing 

 function of temperature at high dopings. Thus doping may change the 

 sign of the temperature coefficient of solubility. Because of this, doping 

 sometimes may prevent precipitation of a donor when a semiconductor 

 is cooled, since the latter becomes an undersaturated rather than a 

 supersaturated solution of impurity. Details are given in Reference 6. 



(4) It is also shown in Reference 6 that for the acceptor to have any 

 effect on the solubility of the donor the concentration of A~ should satisfy 

 the following criterion 



A- > (Do"*" or m) (3.7) 



Do or Hi being used depending on which is greater. Obviously at high 



10 '9 



10 



10' 



18 



5 '0'^ 

 O 



lO'S 



10' 



10 



13 



10 



12 



i 



0.001 0.002 0.003 0-004 



i/TEMPERATURE in degrees KELVIN 



Fig. 2 — Temperature dependences of intrinsic carrier concentrations in ger-, 

 manium and silicon. "ft 



