CHEMICAL INTEKACTIONS AMONG DEFECTS IN Ge AND Si 583 



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Fig. 17 — Plot, for larger values of p-i , of i(p2 , 0.05) from (9.9). 



Suppose a system is first maintained at a temperature high enough to 

 prevent pairing, and then, at an instant designated as zero time, is 

 suddenly chilled to a temperature at which pairing takes place. One 

 thereby has a system which would normally contain pairs but which 

 finds itself with donors and acceptors which are uniformly and randomly 

 distributed. Since the donors are assumed mobile, a process ensues 

 whereby they drift toward acceptors until an equilibrium is established 

 in which each acceptor develops an atmosphere of donors with density 

 c(r), given by (7.7). 



This final state in which the atmosphere is fully developed is the paired 

 state characteristic of the lower temperature. The relaxation time to be 

 defined must measure the interval required for the near completion of 

 the above process. 



In order to acquire physical feeling for the phenomenon, we begin with 

 some simple considerations. In particular a system will be dealt with 

 containing equal numbers of positive and negative ions. This restriction 

 can be lifted later. 



Now, to a first approximation the pairing phenomenon may be re- 

 garded as a trapping process in which mobile, positive donor atoms are 

 captured by the negative acceptors. Thus, suppose each acceptor is imag- 

 ined to possess a sphere of influence of radius R, beyond which its force 

 field may be considered negligible, and inside which a positive ion is to be 

 regarded as captured. This picture immediately emphasizes certain sub- 

 tleties which require discussion before further progress can be made. 



In the crudest sense one might reason that the probability of an en- 

 counter between a positive ion and a negative trap would depend on the 



