A general formula for the reflectance of a thin film with non-uniform thickness is derived based on expressing its thickness distribution density. Examples of such thickness distribution densities, corresponding to various shapes of the thickness non-uniformity, are presented. In addition, a reflectance formula is derived as the second-order approximation of the general formula expanded into a power series in the root mean square (rms) value of the thickness distribution. By means of a numerical analysis, it is shown that for greater non-uniformities it is necessary to take into account their concrete shapes in the optical characterization, whereas for small non-uniformities the concrete shape is of no importance for the characterization. The theoretical results are applied to the complete optical characterization of a selected non-uniform carbon nitride film.
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