SINGLE CRYSTAL BY ZONE LEVELING 



653 



thermal contraction. Consider a small increment of the length of a newly 

 formed zone leveled crystal as heat flows through it from its hotter to its 

 colder ends while the crystal moves slowly through the apparatus. Heat 

 flows in by conduction from the higher temperature germanium adjacent 

 to it. Heat leaves not only by conduction out the other end, but also by 

 conduction and radiation from the ingot surface. Because of this latter 

 heat loss, there is a radial component as well as a longitudinal component 

 to the temperature gradient. The cooler surface contracts resulting, as 

 above, in peripheral tension and internal compression. Clearly if the 

 radial component of heat flow could be eliminated, there would be no 

 peripheral contraction. Accordingly, the most desirable temperature dis- 

 tribution is one whose radial heat flow is zero, i.e., a case of purely axial 

 or one dimensional heat flow, which implies a uniform temperature 

 gradient along the axis of the ingot. In practice, it is difficult to obtain 

 a uniform axial temperature gradient except for the special case of a 

 very small one. This may be obtained fairly easily by the use of an ap- 



/ / / ffr 

 / / / ^— 





TRACE OF (ill) 





-TRACE OF (Tll) 



r / 



/ / 

 7 / / 



' ^^^N 



— 7 ' / / / * 



///'// \ , _, 



N / / / /trace of (iii) 

 '', / / / 



[oTi] 



resolved s 



STRESS (u 



stress (Tm)- 



STRESS (lTl) - -" 



IT)- / / \\\\//// 



" ^' \\v/// 



\\v/ 



\v/ 



Fig. 8(b) — Resolved shear stress and slip-plane traces on (111) Plane. 



