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Electron mobility in germanium at high temperatures Eastman, Philip Clifford

Abstract

A study is made of the temperature dependence of the lattice scattering mobility of electrons in germanium. Previous work on this subject has been restricted to a range of temperatures from 100°K to 300°K. In this range it is possible to use specimens in which the only scattering the electron suffers is that due to the lattice vibrations; the lattice mobility can then be deduced in a straightforward manner from measurements of the Hall constant and conductivity of the material. It was found that over this restricted temperature range the temperature dependence of the lattice mobility could be represented approximately by the form μαΤ⁻¹‧⁶⁶. It has, however, been predicted, on theoretical grounds, that such a simple power law dependence is insufficient, especially when the temperature range is greater. The present work carries out an extension of the measurements to higher temperatures and studies more carefully the approximation of a simple power law dependence. It is found that if the lattice mobility is expressed in the form μαΤ⁻a, then a has to be considered as increasing from about 1.7 to 1.9 between 200 and 400°K. These results are in qualitative agreement with the theoretical predictions. In order to extend the temperature range, strongly n-type specimens of germanium were required. Several basic and permanent crystal preparation facilities, including a crystal grower and wire-saw cutter, were designed and constructed. The conductivities and Hall coefficients of several specimens, prepared with different concentrations, were measured over the appropriate temperature range. The lattice mobility in these specimens cannot be deduced directly from such measurements as the electrons also suffer scattering from the ionized impurities present. An analysis is given which enables the lattice effects to be separated from the impurity effects. This analysis is based on an assumed power law dependence of the lattice relaxation time on temperature and of the impurity scattering relaxation time on temperature and impurity concentration. The separation of these two scattering effects is performed in a way almost independent of the other factors on which they depend. Some information was also obtained on the impurity scattering mobility. This slightly favours a screened rather than a cut-off Coulomb scattering potential.

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