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The determination of impurity concentrations in silicon Jones, David John Gunning

Abstract

Due to the small concentration of impurities normally present in semiconductors these impurity concentrations cannot' be measured by ordinary chemical analysis. Electrical methods are the common way by which semiconductor impurity concentrations are measured. The specific problem investigated was to determine the concentration Nd of donors and the concentration Na of acceptors at various points in a crystal of silicon. A description of the crystal structure and the energy band scheme of silicon is given. The density of states in the conduction and valence bands is calculated. The population of the conduction and valence bands by electrons and holes as a function of impurity concentration and temperature is derived. A method is given from which the values of Nd and Na may be found from Hall constant measurements at liquid nitrogen and room temperatures. The experimental apparatus used includes a magnet, cryostat, sample holder, and Hall measuring circuit. The results obtained from the measurements are in agreement with those expected from the available knowledge of the method of crystal growth.

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