A novel method for the determination of optical properties of absorbing thin films with thickness variations

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.