The role of silver ion doping in the transformation of the phase transition mechanism in vanadium dioxide films

It is shown that both in doped and undoped VO$_2$ films the frequency position and the shape of the maxima of the frequency dependence function of the imaginary part of the complex permittivity $\varepsilon''(f)$ are determined by the values of the physical parameters of the free electron array, for which the frequency of the resonance response to the action of the probing field is due to the difference in their Maxwell relaxation times $(\tau_{\mathrm{М}}=\varepsilon\varepsilon_0/\sigma)$. The same applies to the frequency position of the steps of the frequency dependence function of the real part of the permittivity $\varepsilon'(f)$ and to the position of the semicircle in the Cole–Cole diagrams. It has been established that the characteristics of the dielectric spectra indicate both a decrease in the electron concentration in the conduction band of the VO$_2$ semiconductor phase, caused by doping this phase with silver impurity, and an increase in the equilibrium temperature of the monoclinic and tetragonal phases. Along with this, these characteristics indicate the appearance of two types of crystalline grains with different physical properties upon strong doping with silver. It has been established that selective modification of the dielectric spectra of films by silver impurity is determined by the difference in the degree of silver ion penetration into different-sized nanocrystallites of the VO$_2$ film, which occurs during their synthesis. It has been shown that the cause of this phenomenon is due to the dependence of the resulting concentration of the dopant on the Laplace pressure of the nanocrystallite surface, determined by the curvature of its surface.