never met in practice so that the number of passes must be deter mined experimentally but it is pos sible to transfer virtually all the im purity to the last-to-freeze end of the bar if k is less than 1 (and to the first-to-freeze end if fc is greater than 1 ). This provides a powerful tool for raising the level of impurity in a relatively small portion of the sample to a point where standard high purity reagents can be used. Zone refiners are standard equip ment in almost any semiconductor laboratory. Multiple zones and automatic operation require little attention from the analyst and large numbers of passes may be made without difficulty.
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Physical Methods of Analysis The use of physical methods is particularly attractive since it mini mizes any contact between the sample and any other material which might be less pure. In this area emission spectrography is es pecially applicable. The sample comes into contact only with the electrodes and the surrounding at mosphere during burning; high purity electrodes are readily avail able and the atmosphere may be controlled. The method is inher ently capable of high sensitivity and the matrix effect and interaction be tween impurity lines are minimized since the samples are either ele ments or binary compounds with relatively few impurities at a very low level. The problem then re solves itself into one of developing quantitative techniques near the sensitivity limits. The sensitivity of this method, like any other method, is dependent on the "signal-to-noise ratio," in this case, the intensity of an im purity line to that of the back ground. Figure 8 shows the in tensity of radiation as a function of time for three impurity lines and the background from a sample of gallium arsenide. For any given time of burn, the photographic den sity is proportional to the integrated area under the curve. If the full minute exposure were given, the total background would be equal to, or even greater than, the line den sity for any one of the impurities.
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