Modified equations for the evaluation of energy distribution of defects in as-grown thin films by Vand’s theory

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Abstract
It is pointed out that the use of Vand’s original equations for the evaluation of defect density distribution in energy in as-grown thin films lead to results which are in error by at least 6% in the case of thin films vacuum deposited at room temperature. Modified equations that can be applied to thin films formed at any arbitrary temperature T0 K have been obtained. It is found that except for one equation, the remaining three equations are identical to those of Vand. It has also been shown that Vand’s original equations can be applied in the case of thin films formed at an arbitrary temperature if the actual time t in the original equation is replaced by a time t0 measured as if heating had started at 0 K. Experimental plots of decay energy distribution of defect cluster density [F0(E) vs E plots] obtained using the modified equations and Vand’s original equations in the case of bismuth thin films deposited at different substrate temperatures (300–450 K) are also presented to show the extent of the errors and their substrate temperature dependence. These errors are also compared with the errors inherent in the theory and the approximations made in the derivation.