CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 621 



for the justification of this view. Briefly it is permissible, after a short 

 transient period, in spherical diffusion, whenever the dimensions of the 

 diffusion field are large compared to the dimension of the sink. This re- 

 sults from the fact that in spherical diffusion from an infinite field a 

 real steady state is reached after a brief transient period. In contrast, in 

 plane-parallel diffusion to a sink from an infinite field, a steady state is 

 never reached. 



Substituting (Cll) into (10.16) then yields 



J* == -AAie-'"'''"' ("^ + ^ G^ (C13) 



\dr r^ / 



Multiplying J* by 47rr" and demanding that the product be independent 

 of r, leads to the relation 



r'^+RG^ = 8 (C14) 



dr 



where 8 is constant. The solution of (C14) is 



G, = exp g) + I (C15) 



This is a sufficient approximation for Gi . 



1 The constants r]i , Ao , Ai , and 5 must now be determined. To accom- 

 'plish this we note that (C2) which specifies that the boundaries at r = a 

 ,and r = L, are impermeable is equivalent to the condition that ions be 

 'conserved with the interval (a, L), or that 



47r ( r'p dr = N (C16) 



Ja 



\ 



\fter infinite time p is specified by the first term of (Cll) and when this 

 is inserted into (CI 6) the result is 



Ao = NM (C17) 



|,vhere M is defined by (10.26). 



': Substitution of (C17) and (CIS) into (Cll) gives 



p = NM exp (R/r) + (ai exp (R/r) + ^ j e""^'"'"' (C18) 



Now (C3) applied to (C18) demands 



NM + Ai = (C19) 



^ ^ N' (C20) 



R 



