The determination of the thickness and optical constants of the ZnO crystalline thin film by using pointwise unconstrained minimization algorithm

Year 2010, Volume: 1 Issue: 2, 181 - 193, 01.12.2010

Nilgün Erarslan Tayyar Güngör

Abstract

Optical constants such as the optical band gap (Eg) and absorption coefficient α(λ), film thickness (t) and film refractive index n(λ) could be computed from transmittance and/or reflectance spectra for thin film on the transparent substrate. The envelope method considering the curve through the extreme points instead of entire spectrum is much preffered method when the spectrum contain finite interference fringes for the given wavelength range depending on the refractive index (n) and thickness (t) product. However, this method can not be used in the case of insufficient number of interference fringes or no fringes and for the interference fringes with too little depth. In this case, the other methods should be used to minimize the difference between the measured and the predicted optical transmittance and / or reflection values. Pointwise Unconstrained Minimization Algorithm (PUMA) is the one of the methods. The refractive index (n) and extinction coefficient (κ) films and film thickness (t) can be calculated using this method by taking into account the entire spectrum. In this study, the validity of the PUMA method was tested on the ZnO thin films with different thicknesses prepared by spray pyrolysis.

Keywords

Optical transmittance, optical constants, PUMA.

ZnO ince filmlerin kalınlıkları ve optiksel sabitlerinin noktasal kısıtlamasız minimizasyon algoritması ile belirlenmesi

Abstract

Optical constants such as the optical band gap (Eg) and absorption coefficient α(λ), film thickness (t) and film refractive index n(λ) could be computed from transmittance and/or reflectance spectra for thin film on the transparent substrate. The envelope method considering the curve through the extreme points instead of entire spectrum is much preffered method when the spectrum contain finite interference fringes for the given wavelength range depending on the refractive index (n) and thickness (t) product. However, this method can not be used in the case of insufficient number of interference fringes or no fringes and for the interference fringes with too little depth. In this case, the other methods should be used to minimize the difference between the measured and the predicted optical transmittance and / or reflection values. Pointwise Unconstrained Minimization Algorithm (PUMA) is the one of the methods. The refractive index (n) and extinction coefficient (κ) films and film thickness (t) can be calculated using this method by taking into account the entire spectrum. In this study, the validity of the PUMA method was tested on the ZnO thin films with different thicknesses prepared by spray pyrolysis.

Keywords

Optical transmittance, optical constants, PUMA.

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