CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 587 



The last point raises still another question: What happens when the 

 sink is not perfect, i.e. where the equilibrium state does not involve 

 complete pairing? 



All these difficulties can be removed by a more sophisticated treatment 

 of the diffusion problem. Thus, retain the sphere of volume, 1/A^, en- 

 closing A^ donors at the density N^. However, the equations of motion of 

 these donors are altered to account for the fact that besides diffusing 

 they drift in the field of the acceptor at the origin. Thus the flux density 

 of donors will be given by 



/*(r,o = -z).|^^+l^ 





(10.16) 



where R has been substituted for q/KkT. Equation (10.16) is obtained 

 by adding to the diffusion component, 



— Lfo — 

 dr 



of the flux density, the drift component, 



Mog 



where hq is the mobility of a donor ion and —q/nr' is the field due the 

 acceptor at the origin. The Einstein relation^" 



Mo - qD,/hT (10.17) 



has also been used to replace mo with Do . 



The spherical shell bounding the volume, 1/iV, of radius 



L = {^y (10.18) 



is regarded as impermeable, so we obtain the boundary condition 



J*{L, t) = 0. (10.19) 



Furthermore an arbitrary inner boundary, r = i?, is no longer defined 

 but use is made of the real boundary, r = a, i.e., the distance of closest 

 approach, at which is applied the condition 



J*ia, 0-0 (10.20) 



As before, the initial condition may be expressed as 



p = N- t = a < r < L (10.21) 



