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Temperature dependence of the energy gaps in semi-conductors Cuden, Ciril Bernard

Abstract

Supervisor; Professor Robert Barrie The question to what extent the poles of the temperature dependent Green's functions have physical significance as temperature dependent energy levels Is considered. Our contention is that such levels should not be thought of in terms of internal energy or free energy. They have no physical significance other than perhaps to say how the statistical mechanical averaging was divided into its two steps. It is shown that the knowledge of the energy and life time of quasi particles is not very helpful in studying the Hall Constant. To study the Hall Constant one would have to use the appropriate two particle Green's Function and a number of approximations have to be made before one has a simple relation "between the Hall Constant and the average occupation numbers for the quasi-particles. (We have discussed the Hall Constant since this is usually the technique discussed in the literature.) In the literature on the energy gap in semiconductors, the single particle excitation energies (mechanical quantities) were found. They were made temperature dependent by replacing phonon occupation numbers by their thermal averages, and it was assumed then that the gap could be simply written down as a difference of two of these energies. It was not clear whether this should be interpreted as the optical or the thermal gap. We have shown that the question, many times raised in the literature, whether the two gaps are the same or not, is not the relevant question at all. Due to the completely different physical nature of the Hall and absorption phenomena, the definitions of the gaps in both cases are entirely different. We have shown that certain approximations involved in our calculation of the Hall constant and optical absorption coefficient lead to the thermal and optical gaps being the same. The optical gap is the same as the thermal one because our calculation of optical absorption involved only the zero-phonon process, neglect of the vertex part of the corresponding two particle Green's Function, neglect of the damping and neglect of the frequency dependence of the level shift. In summary, it appears that the picture in which one thinks of temperature-dependent energy levels and transitions between these is often too misleading and that it is safer to carry out the calculation of macroscopic behaviour in the correct fashion. One may by the latter method, obtain the result one would have obtained using one's physical Intuition, but the approximations for this are now spelled out.

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