TY - JOUR

T1 - MATHEMATICAL FOUNDATIONS OF INFORMATION PROCESSING METHODS FOR DIELECTRIC SPECTROSCOPY OF THIN FILMS

AU - Karpov, A. G.

AU - Klemeshev, V. A.

AU - Trofimov, V. V.

PY - 2015

Y1 - 2015

N2 - Complex permittivity contains information about the structure and functional properties of the dielectric material. Therefore, the method of spectral measurement and analysis permittivity can serve as a useful tool for research and diagnostics. The original method for computing the real and imaginary parts of permittivity is proposed to process dielectric measurement data in real time. It may be implemented in a compact computing device included in the process control system. This method is based on the use of quadrature formulas for the calculation of integrals. The real and imaginary parts of the permittivity calculated for the frequency values arranged in a geometric progression. Optical properties of the specimen are directly related to the permittivity. The mathematical model to determine the absorption and refractive indices of thin films on a transparent substrate is proposed on the basis of the said relation. Determination of optical properties and thickness of thin films is incorrect inverse problem. The two-step algorithm based on the steepest descent method is proposed to solve it. The method of selecting the initial parameter values is proposed. More stable solutions are obtained for the initial value corresponding to the minimum transmittance in the short wavelength range, when interference effects play an insignificant role. The study of the optical properties of thin films efficient emitters of interest in practical applications was performed.

AB - Complex permittivity contains information about the structure and functional properties of the dielectric material. Therefore, the method of spectral measurement and analysis permittivity can serve as a useful tool for research and diagnostics. The original method for computing the real and imaginary parts of permittivity is proposed to process dielectric measurement data in real time. It may be implemented in a compact computing device included in the process control system. This method is based on the use of quadrature formulas for the calculation of integrals. The real and imaginary parts of the permittivity calculated for the frequency values arranged in a geometric progression. Optical properties of the specimen are directly related to the permittivity. The mathematical model to determine the absorption and refractive indices of thin films on a transparent substrate is proposed on the basis of the said relation. Determination of optical properties and thickness of thin films is incorrect inverse problem. The two-step algorithm based on the steepest descent method is proposed to solve it. The method of selecting the initial parameter values is proposed. More stable solutions are obtained for the initial value corresponding to the minimum transmittance in the short wavelength range, when interference effects play an insignificant role. The study of the optical properties of thin films efficient emitters of interest in practical applications was performed.

KW - mathematical model

KW - permittivity

KW - thin film

KW - optical properties

M3 - Article

VL - 11

SP - 13

EP - 26

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 4

ER -