Journal of Applied Spectroscopy, Vol. 85, No. 4, September, 2018 (Russian Original Vol. 85, No. 4, July–August, 2018) OPTICAL CHARACTERISTICS OF ZINC OXIDE FILMS ON GLASS SUBSTRATES N. I. Staskov, a* A. B. Sotsky, a L. I. Sotskaya, b UDC 543.42.062:539.216.2 V. V. Filippov, c B. G. Shulicky, c and I. A. Kashko c An algorithm is developed for solving the inverse problem of multiangular spectrophotometry of a layer on a plane- parallel substrate of finite thickness using s- and p-polarized waves. It allows the dispersive properties of the layer and substrate to be studied both far from and in the vicinity of the resonant wavelengths. The dispersive properties of layers of pure and Al-doped ZnO on glass substrates are investigated using it. It is shown that doping shifts the absorption band maximum to shorter wavelength and decreases the refractive index of the material. The applicability limits of known approximate expressions for determining the spectral dependence of the absorption coefficient of a layer from spectrophotometric data are estimated. Keywords: multiangular spectrophotometry, ZnO, refractive index and absorption coefficient, band gap. Introduction. Zinc oxide (ZnO) doped with aluminum (ZnO:Al) has electrical and optical properties that are widely utilized in optoelectronic materials [1–4]. The thickness (h f ) and main optical characteristics [spectral dependences of the refractive index n f (λ) and absorption k f (λ), band gap E g ] of ZnO:Al films can vary markedly depending on the formation conditions [4–9]. In most instances, such films are produced on glass substrates. The quantities h f , n f (λ), and k f (λ) are usually determined using spectroscopic ellipsometry [10, 11] or spectrophotometry [12, 13] in which spectral dependences of polarization angles or reflectance of the films are measured at several incidence angles of partially coherent light and processed numerically. Spectroscopic ellipsometry measurements were processed using an electrodynamic model that included a nonuniform surface layer and homogeneous film and substrate. Spectrophotometric measurements used a model of a uniform or nonuniform film on a substrate. In the last instance, a Lorentz–Lorenz model in which spatial and spectral variables were separated was effective [13]. The determination of the film parameters is usually simplified by assuming that the film is deposited on a transparent substrate [substrate absorption coefficient k s (λ) = 0]. Then, its absorption coefficient is calculated [14] α f (λ) = 4πk f (λ)/λ (1) using a formula based on Bouguer′s law for incident light normal to the film [15–20]: α f (λ) = 1 f h − ln (1/T t (λ)) , (2) where T t (λ) is the transmittance of the film on the substrate. Light attenuation in the model [Eq. (2)] is due only to absorption in the film. The following expression was used to determine α f (λ) [5, 21] 1 () 1 () ln () t f f t R h T ⎛ ⎞ − λ α λ= ⎜ ⎟ λ ⎝ ⎠ , (3) which contains the reflectance of the film on the substrate R f (λ), in contrast with Eq. (2). The absorption coefficient near the intrinsic absorption band edge of semiconductors is calculated using more complicated expressions [18, 19]: a A. A. Kuleshov Mogilev State University, 1 Kosmonavtov Ave., Mogilev, 212009, Belarus; email: ni_staskov@ mail.ru; b Belarusian-Russian University, Mogilev, Belarus; c Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 85, No. 4, pp. 658–665, July–August, 2018. Original article submitted March 3, 2018. _____________________ * To whom correspondence should be addressed. 710 0021-9037/18/8504-0710 ©2018 Springer Science+Business Media, LLC DOI 10.1007/s10812-018-0709-2