SINGLE CRYSTAL BY ZONE LEVELING 



of these solute concentrations: 



k = 



639 



(1) 



When A- < 1 , the freezing interface may be regarded as a filter permit- 

 ting only a fraction A: of the solute concentration in the liquid to pass into 

 the growing solid and rejecting the rest to remain in the liquid. If the 

 unmelted charge of solvent is pure — ■ that is, if no solute passes into the 

 zone at the melting interface it is readily seen that the liquid zone will be 



: gradually depleted of its solute impurity content during passage through 

 the charge. 



An expression for the solute concentration in the solid, Cs , deposited 

 there by the passage of one zone, for the case of "starting charge into 



' pure solvent" has been derivec^ based on the following assumptions: 



(1) The liquid volume is constant (both cross section of charge and 

 zone length I are constant). 



(2) k is constant. 



! (3) Mixing in the liquid is complete (i.e. concentration in the liquid is 

 uniform). 



(4) Diffusion in the solid is negligible. 

 I The expression is 



i Cs = kCo e-'"'" (2) 



where Clq is the initial concentration of impurities in the liquid, I is the 

 zone length, and x is the distance moved by the solidifying interface. A 

 set of Cs versus x/l curves is shown in Fig. 2 for various k's. From this 



' figure it is readily seen that when k is small the decay of Cs is slow (i.e., 



I the depletion of Cl is slight). 



Largely because of this consideration, most of the practical work re- 



I ported in this paper has utilized solutes in germanium having low segre- 



Fig. 1 — Schematic of zone leveling operation. 



