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

Öz

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.

Anahtar Kelimeler

• Optical transmittance, optical constants, PUMA.

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

Öz

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.

Anahtar Kelimeler

• Optical transmittance, optical constants, PUMA.

Kaynakça

1. Birgin, E. G., Chambouleyron, I., & Martinez J. M., (1999) Estimation of optical constants of thin films using unconstraine optimization, Journal of Computational Physics, 151, 862-888.
2. Dolbec, R., El Khakani, M. A., Serventi, A. M., Rudeau, M. T., & Saint-Jacques R.G. (2002). Microstructure and physical properties of nanostructured tin oxide thin films grown by means of pulsed laser deposition, Thin Solid Films, 419, 230–236.
3. Goodman A. M., (1978). Optical Interference method for the approximate determination of refractive index and thickness of a trasparent layer, Applied Physics, 17, 17.
4. Güngör T., (1998). Determination of optical constant and thickness for a-SiNx:H thin film, Journal of Research in Physics, 27, No.1, 1-9.
5. Güngör T., (2001). Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara (yayımlanmamış doktora tezi).
6. Güngör T., & Saka B. (2004). Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum using a genetic algorithm, Thin Solid Films, 467, 319-325.
7. Güngör T, (2007). Saydam iletken oksit ince filmlerin üretilmesi ve elektrooptiksel karakterizasyonu, Hacettepe Üniversitesi Bilimsel Araştırmalar Birimi, Proje No: 030260216.
8. Manifacier, J. C., Gasiot, J., & Fillard, J. P. (1976). A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film, J. Phys. E: Sci. Instrum. 9., 1002.

9. Minkov, D. A., (1989). Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum, J. Phys. D. Appl. Phys. 22, 1157-1161.
10. Minkov, D. A., (1989). Method for determining the optical constants of a thin film on a transparent substrate, J. Phys. D. Appl. Phys. 22, 199-205.
11. Mc Clain, M., Feldman, A., Kahaner, D. & Ying, X., (1991). An algorithm and computer program for the calculation of envelope curves, Computers in Physics, 5. No. 145.
12. Müllerová, J., Jurečka, S., & Kučerová, A. (2003). Extraction of optical parameters of thin films from spectral measurements for design and optical performance of multilayer structures, Acta Physica Slovaca, 53, No. 2, 111 – 119.
13. Ohring M (1991). The Materials Science of Thin Films, Academic Press, New York, NY.
14. Swanepoel, R., (1985). Determining refractive index and thickness of thin films from wavelength measurements only., J. Opt. Soc. Am. A., 2, No. 8, 1339-1343.
15. Swanepoel R. (1983). Determination of the thickness and optical constants of amorphous silicon, J. Phys., E. Sci. Instrum., 16, 1214-1222.
16. Tauc, J., Grigorovici, R., & Vancu, A., (1966). Optical properties and electronic structure of amorphous germanium, Phys.Stat. Sol. 15, 627.