A novel method for the determination of optical properties of absorbing thin films with thickness variations
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A novel method for the determination of optical properties of absorbing thin films with thickness variations Jonghoon Baek, Desiderio Kovar, John W. Keto, and Michael F. Becker Texas Materials Institute, The University of Texas at Austin, Austin, Texas 78712 USA ABSTRACT Non-uniformity in the thickness of thin films can severely distort their transmission spectra as compared to those of flat, smooth films. Methods that extract properties such as refractive index, thickness, and extinction coefficient of such films can suffer inaccuracies when applied to wedged or rough films. In order to accurately extract optical properties of non-uniform films, we have developed a novel numerical method and efficient constitutive relations that can determine film properties from just the transmission spectrum. The Optimum Parameter Extraction (OPE) method can accommodate transparent or absorbing films thickness variations that result in significant errors in the values of refractive index and film thickness if not considered. A packing-density model was proposed and used for refractive index to accelerate the fitting routine and to avoid finding local minima instead of the global minimum. In this model, refractive index has one fitting parameter, the packing density, p. Therefore, the OPE method takes a shorter time and produces more accurate results than many other methods. We show that for actual PLD (Pulsed Laser Deposition) AlN thin films, properties such as refractive index, extinction coefficient, and film thickness were very accurately determined using our OPE method. These results are compared with two previous techniques to determine properties of thin films, and the accuracy and applicable conditions for all of these methods are discussed. INTRODUCTION Thin films are widely used to improve the performance of optical components and to form optical waveguides for integrated optics. They also are used in various applications in semiconductor components. For many of these applications, it is important to characterize the films' optical constants (the refractive index, n, and the extinction coefficient, k, and to determine their thickness, d). Accurate determination of the values of the wavelength-dependent optical constants is very useful because it gives fundamental information about the optical band gap, defect levels, oscillator energy and oscillator strength, etc. Moreover, optical constants are believed to be strongly correlated to the film microstructure so that it is possible to ascertain information about film microstructure by investigating optical properties [1-3]. Various methods have been employed for determining the properties of thin films[1,3,4]. However, most of the published techniques and commercial thin film analyzing codes do not consider monotonic variations in thickness (wedge) or periodic non-uniformities in thickness (irregularities) that usually occur in thin films. The presence of thickness variations drastically changes data acquired by both ellipsometry and spectrophotometry and th
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