SINGLE CRYSTAL BY ZONE LEVELING 641 



treatment is not concerned with lattice imperfections in the ingot such 

 as dislocations, lineage, or grain boundaries. The predictions the theory 

 does make have been well verified by experiment insofar as it has been 

 possible to meet the assumptions enumerated above. However, as with 

 most assumptions, their validity is sensitive to the experimental condi- 

 tions, particularly in the cases of the first three. Much of the develop- 

 ment effort, especially that toward improving resistivity^ uniformity, 

 has been directed toward controlling the process so that these assump- 

 tions will be as nearly valid as possible. 



Early experiments in zone leveling yielded crystals good enough to 

 meet device reciuirements of that time. However, as semiconductor de- 

 vices were designed to meet tighter design requirements, the demands 

 on the germanium material grew" more critical. Under these circum- 

 stances, it became necessary to examine the requirements on the product 

 of the process and what precautions would be necessary to insure that its 

 operation was under sufficient control. Accordingly, we shall chscuss first 

 the requirements on semiconductor material and then those critical as- 

 pects of the leveling operation which must be controlled to insure quality 

 of the final product. 



liEQUIREMENTS ON GERMANIUM FOR SEMICONDUCTOR USES 



The basic electrical bulk property of a germanium crystal is its con- 

 ductivity or the reciprocal of that quantity, its resistivity. For a great 

 majority of semiconductor uses, an extrinsic conductivity* is required in 

 addition to the 3^o ohm"~^ cm~' intrinsic conductivity that results at 

 room temperature from thermal excitation of electron-hole pairs in pure 

 •iermanium. An extrinsic conductivity may be either n-type or p-type. 

 Both of these may be produced by trace impurities distributed through- 

 out the crystal, the n-type by donor impurities and the p-type by accep- 

 tor impurities. At room temperature donors give rise to conduction elec- 

 trons and the acceptors to conduction holes which are free to move 

 within the germanium crystal. If both donors and acceptors are present 

 in the same crystal, the resulting electrons and holes recombine, leaving 

 essentially the extrinsic conductivity contributed by the excess of one 

 over the other, that is by | No — A''^ i . 



The fundamental requirement is, then, to control the net donor and 

 1lie acceptor balance, | No — A^4 I , tea predetermined value throughout 

 the crystal. For most applications, the conductivity is to be increased 

 by one or two orders of magnitude above the 27°C intrinsic value. An 

 idea of the donor or acceptor concentrations involved may be acquired 



* Shockley, W., Electrons and Holes in Semiconductors. 



