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1/2 is used. This discrepancy arises because both these expressions only approximate the true energy dependence of the optical matrix element. The one used in the text is derived using the oscillator sum rule, to get the expression in terms of the effective mass [see, e.g., A. H. Wilson, Theory of Metals, 2nd ed. (Cambridge University Press, Cambridge, UK, 1965)] while the former assumes that the matrix element is independent of energy. To circumvent the ambiguity, fits to both the expressions were done and the energy gaps obtained from either of the two were seen to be, in the worst case, 5% off. This is also the uncertainty inherent in the method used and in the present case, amounting to around 10 meV. The relation mentioned in text fit the data better and was therefore used. [Also see E. J. Johnson, in Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1967), Vol. 3, p. 154.]
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