590 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



10' 



10 



16 



10" 

 N IN CM"3 



10'' 



10 



19 



Fig. 18 — Dependence of constant M defined by (10.26) on temperature and 

 concentration, for particular values of a and k. 



Do for germanium to which the system of Fig. 18 refers, since k has been 

 chosen at 16. 



Using Figs. 18 and 19, Fig. 20 was computed. It shows t plotted in 

 seconds versus A^ for the same temperatures appearing in Fig. 18. These 

 curves show that at values of N as low as 10 cm" relaxation times are 

 short enough to be observable down to 200°K, being at the most some 

 50 hours in extent. The value of N makes a big difference.' For example 

 at 200°K the relaxation time is only 4 minutes with A'' = 10^^ cm~^ 

 Presumably, at 10 cm~ , relaxation could be observed down to much 

 lower temperatures. 



It is interesting to note that insofar as M hardly appears in r, the 

 latter is independent of the distance of closest approach, a. Since a is to 

 some extent empirical this is a fortunate circumstance, and the measure- 

 ment of T may provide an accurate means of determining, A^, Do , k, or 

 q, whichever parameter is regarded as unknown. Furthermore k as a 

 macroscopic parameter has real meaning in r since the forces involved 

 may be regarded as being applied over the many lattice parameters 

 separating the di-ifting donor from its acceptor. 



