Nondestructive Determination of Thickness and Refractive Index of Transparent Films

Abstract

A simple nondestructive method of measuring the refractive index and thickness of transparent films on reflective substrates has been developed. The technique involves the use of a microscope equipped with a monochromatic filter on the objective and a stage that can be rotated so that the reflected light is observed at various angles. The film thickness, d, is given by d = [ΔNλ]/[2µ(cos r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> − cos r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> )], where λ is the wavelength of the filtered light, µ is the refractive index, and ΔN is the number of fringes observed between the angles of refraction r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> . This technique is especially suited for films thicker than one micron. Techniques are also described for obtaining accurate thicknesses of films less than one micron by the combined use of monochromatic filters and an interference pattern chart. These techniques can be used to determine film thicknesses ranging from several hundred angstroms to several microns with accuracies of 0.2% on films thicker than 2µ, and accuracies of tens of angstroms on thinner films. Since visual comparisons of color can be used fairly easily for film thickness determinations, the techniques were used to construct a color chart for thermally grown SiO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> films up to 1.5µ thick.