Physics

Analysis of relaxation time dependences on influencing factors in conducting oxides based on $SnO_2:Sb$

T. O. Zinchenko, E. A. Pecherskaya, V. D. Krevchik, I. A. Rubtsov, D. V. Yakushov, V. S. Aleksandrov

Penza State University, Penza

Abstract: Background. Transparent conducting oxides (TCOs) based on $SnO_2:Sb$ are promising materials for transparent electrodes in optoelectronic devices. Understanding the mechanisms of charge carrier conductivity and relaxation in these materials is crucial for optimizing their electrophysical properties. The purpose of this work is to analyze experimental data on the dependence of relaxation time on electron concentration, conductivity, and mobility in $SnO_2:Sb$ using various interpolation and approximation methods, as well as to compare the obtained results with the Drude theory. Materials and methods. The study utilized experimental data on electron concentration (n), conductivity ($\sigma$), mobility ($\mu$), and relaxation time ($\tau$) for $SnO_2:Sb$ samples. Three interpolation methods were applied for data processing: linear interpolation, Akima interpolation, and cubic spline. Approximation was performed using the least squares method with first-degree polynomials. The analysis accounted for the logarithmic nature of the dependencies for electron concentration and conductivity. Results. A comparative analysis of interpolation methods was conducted for three dependencies. It was found that the dependence of relaxation time on mobility is well described by linear interpolation, consistent with the Drude theory. For other relaxation time dependencies, Akima interpolation proved most suitable due to its ability to handle nonlinear trends. Cubic spline exhibited oscillations in regions with abrupt data changes. The results align with theoretical predictions of the Drude theory. Conclusions. Experimental data confirm the applicability of the Drude theory for describing the electrophysical properties of $SnO_2:Sb$. The choice of interpolation method should consider both the physical nature of the dependency and the characteristics of the experimental data. For linear dependencies, linear interpolation is optimal. For nonlinear dependencies, Akima interpolation is preferred. The findings can be used to optimize technological parameters for producing $SnO_2:Sb$ with tailored electrophysical properties.

Keywords: transparent conducting oxides, $SnO_2:Sb$, Drude theory, Akima interpolation, approximation, relaxation time, cubic spline, linear interpolation

UDC: 621.3.012.7

DOI: 10.21685/2072-3040-2025-3-8