Dielectric spectroscopy and mechanism of the semiconductor–metal phase transition in doped VO$_2$:Ge and VO$_2$:Mg films

The frequency dependences of the dissipation factor tan$\delta(f)$ and the Cole–Cole diagrams for germanium- and magnesium-doped vanadium-dioxide films in the range of 0.1 – 10$^6$ Hz are obtained. Measurements at temperatures between 173 – 373 K are performed. It is found that, at room temperature, an additional maximum in the tan$\delta(f)$ dependence and an additional semicircle in the Cole–Cole diagram of the VO$_2$:Ge films as compared with those of undoped films appear at low frequencies. In the VO$_2$:Mg films, similar additional features in the dielectric spectra are observed at high frequencies. It is shown that the shape of the Cole–Cole diagrams for all the films is almost temperature independent in the mentioned temperature range, while the frequencies $f_0$ corresponding to the tan$\delta(f)$ maxima increase with temperature. To interpret the dielectric spectroscopy data, a combined equivalent electrical circuit of the film sample is proposed. The mechanisms of the effect of Ge and Mg impurities on the characteristics of the complex Mott–Peierls semiconductor–metal phase transition are established.