74-81

UDC 681.586
DOI: 10.15350/2306-2819.2018.4.74

DEVELOPMENT OF A MATHEMATICAL MODEL OF SYNTHESIZING
THIN FILMS OF ZINC OXIDE FOR GIVEN COMPLEX-VALUED RELATIVE
PERMITTIVITY

D. E. Shashin
Volga State University of Technology,
3, Lenin Square, Yoshkar-Ola, 424000, Russian Federation
E-mail: dima_shashin@rambler.ru

ABSTRACT

Introduction. At present there are no mathematical models, which could help to predict optical characteristics of thin films of zinc oxide (the index of refraction and the absorption coefficient within complex permeability) depending on technological modes of their production. Thus, the construction of the mathematical model, connecting technological parameters of production and optical characteristics of thin films of zinc oxide becomes an urgent problem. The purpose of the work is the construction of the mathematical model, connecting technological parameters of production with complex permeability of thin films of zinc oxide. The following problems were being solved: to obtain a set of samples of thin films of zinc oxide by a reactive magnetron sputtering method under different evaporation conditions; to determine dielectric penetrability of obtained films; to create a mathematical expression, connecting technological parameters of production with complex permeability of thin films of zinc oxide. Results. The implementation of the experiment design, which has a number of tests, allows calculating sample coefficients of the regression equation. The accuracy of these coefficients needs to be considered carefully. Magnitudes of variables in the equation X_i have values +1 and –1.. For finding models of the second order, which are more appropriate for describing film coating formation processes, the application of Box design Б_nand Kono design Ко₂₃is justified. In these designs experiments are carried out according to a certain algorithm in points +1,–1 and in the point 0 (the centre of design). For performing physical experiments, rotatable central composite designs (Box-Wilson design) are recommended. These designs are supplemented by experiments in star points. The obtained regression equation looks like the following:

Y = 3,923 + 0,52X₁ +0,03X₁²+0,251X₂

The given equation shows that the parameter X₃ – t_н (evaporation time) in the studied range doesn't invluence the dielectric penetrability of thin films of zinc oxide. The varaiation of values of other parameters X₁ – P_раб(operating pressure) and X₂ – C_кис (content of oxygen in the working mixture), in the given range, allows growing up thin films of zinc oxide with values of complex permeability ԑ from 3,2 to 4,8, that differs considerably from complex permeability of volume zinc oxide (8,5). Conclusion. The mathematical model of the type Y = 3,923 +0,52X₁+0,03X₁² +0,251X₂, connecting technological parameters of magnetron sputtering with complex permeability of obtained films was developed. The adequacy of the obtained regression equation Y = 3,923 + 0,52X₁ +0,03X₁² +0,251X₂ was checked using Fisher's test. The calculation showed that the obtained equation can be considered adequate with a probability of 95 % (F_расч_.=2,368<F_табл_.=2,7).

KEYWORDS

mathematical model; magnetron sputtering; thin films; zinc oxide; dielectric penetrability; regression equation

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For citation: Shashin D. E. Development of a Mathematical Model of Synthesizing thin Films of Zinc Oxide for Given Complex-Valued Relative Permittivity. Vestnik of Volga State University of Technology. Ser.: Radio Engineering and Infocommunication Systems. 2018. No 4 (40). Pp. 74-81. DOI: 10.15350/2306-2819.2018.4.74