G44 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



mony, in a pure element, germanium. The traces are generally desired 

 in concentrations varying from 1 to 100 parts per billion, (p = 35 to 

 0.35 cocm). These amounts are too small to be detected by chemical or 

 spectrographic means, but are readily detectable by electrical resistiv- 

 ity measurements. Although this application of zone leveling is very 

 specific, it should be possible, as we have already suggested, to apply the 

 experimental results to be described to more general systems. The sub- 

 ject of uniformity is conveniently discussed in two sections: (a) longi- 

 tudinal resistivity uniformity, and (b) cross-sectional uniformity. 



(a) Longitudinal Composition Uniformity 



It has already been shown, by (2), that if the k is small, the variation 

 in Cs over four or five zone lengths should be slight. This should be true 

 either if a charge of pure germanium is used, or if a charge containing 

 the same impurity present in the liquid zone is used, provided that the 

 charge concentration of this impurity is of the same order of magnitude 

 as that sought in the product. Where the solute has a small k, the leveling 

 action of the zone is strong and the large C'l, that is required is relatively 

 unaffected by variations of the order of Cs ■ 



The primary cause of observed variations in the longitudinal resistiv- 

 ity is fluctuation of the volume of the liquid zone. If this volume increases 

 for any reason, the solute dissolved in it will be diluted. On the other 

 hand, if the volume decreases, which can occur only when some of the 

 liquid freezes and if k is small, most of the zone's solute will be concen- 

 trated in the smaller volume. Thus for small A;'s the concentration of 

 solute in the liquid zone, Cl , varies inversely with the zone's volume. 

 If Cl is to be constant, the volume must be constant, i.e. assumption (1) 

 must be valid. 



Unfortunately, the zone volume is directly affected by many variables, 

 namely temperature fluctuation and drift, fluctuation in growth rate, 

 variation in the cross-section of the unmelted charge, variation in the 

 inert gas flow, and even cracks in the unmelted charge. For optimum 

 control of longitudinal resistivity uniformity, it is, therefore, necessary to 

 control all of these variables. The remainder of this section will consider 

 their control. 



Toward minimizing the effect of temperature variation on the zone 

 volume, it is important to consider both the means of overall temperature 

 control and the design of the temperature field which melts the liquid 

 zone. It is clear that variation of the temperature field as a whole will 

 directly affect the length of the liquid zone. Accordingly, it will be im- 

 portant to use a precision temperature controller in order to maintain a 



