## 2 Materials and Methods
### Materials  
The films were prepared by the thermal vacuum deposition with the subsequent annealing. This method was used for \(Bi_{x-1}Sb_{x}\)-films preparation and was described in [30]. The properties of \(Sb\) and \(Bi_{88}Sb_{12}\) films of 150-nm thickness have been chosen for simulation. Electrical conductivity and relative permittivity of mica substrate, \(Sb\), and \(Bi_{88}Sb_{12}\) thin films in terahertz frequency range were measured using a terahertz time-domain spectrometer (THz-TDS) in thin-film approximation [31] (when a wavelength of THz radiation is by orders of magnitude higher than the film thickness). The waveforms of THz single-pulse (temporal dependencies of THz signal electric field amplitude) were measured for an air (reference signal), mica substrate, and a film. The corresponding amplitude and phase spectra were obtained in the 0.3-0.8 THz frequency range through the Fourier transform method. The complex sheet conductivity of a film was calculated as  
\[\hat{\sigma}(f)=[(\hat{n}_{sub}(f)+1)\hat{E}_{sub}(f)/\hat{E}_{sam}(f)-\hat{n }_{sub}(f)-1]/Z_{0}, \tag{15}\]  
where \(f\) is the frequency of THz radiation, \(Z_{0}\) is the free-space impedance, \(\hat{E}_{sub}\) and \(\hat{E}_{sam}\) are complex amplitudes of THz wave transmitted through the substrate and the sample, and \(\hat{n}_{sub}\) is the substrate complex refractive index--which is calculated as  
\[\hat{n}_{sub}(f)=c[\phi_{sub}(f)-\phi_{air}(f)]/(2\pi fd_{sub})+1-i\ c\ ln(| \hat{E}_{sub}^{2}(f)|/|\hat{E}_{air}^{2}(f)|)/(4\pi fd_{sub}), \tag{16}\]  
where \(c\) is the speed of light, \(\phi_{sub}\) and \(\phi_{air}\) are phases of substrate and air signals, \(d_{sub}\) is the substrate thickness, and \(\hat{E}_{air}\) is the complex amplitude of the THz wave transmitted through the air. The complex film permittivity was extracted from the complex conductivity as  
\[\hat{\epsilon}(f)=1+i\hat{\sigma}(f)/(2\pi fd_{film}\varepsilon_{0}), \tag{17}\]  
where \(d_{film}\) is the film thickness and \(\varepsilon_{0}\) is a permittivity of free space. The results of measurements are shown in Figures 3-5. It should be mentioned that they are in good enough agreement with the classical [PERSON] model (for conductivity \(\hat{\sigma}\) and permittivity \(\hat{\epsilon}\)) due to the semimetallic nature of the films:  
\[\hat{\sigma}(\omega)=\frac{\sigma_{0}}{1-i\omega\tau}, \tag{18}\]  
\[\hat{\epsilon}(\omega)=\varepsilon_{\infty}-\frac{\omega_{p}^{2}}{\omega^{2}+ iy\omega}, \tag{19}\]  
where \(\sigma_{0}\) is the DC conductivity, \(\omega=2\pi f\) is the angular frequency of THz radiation, \(\tau\) is the relaxation time of charge carriers, \(\varepsilon_{\infty}\) is high-frequency dielectric constant, \(\omega_{p}\) is the plasma frequency, and \(\gamma\) is the damping rate. Material properties used in the heat transfer interface are listed in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline
**Material** & **Thermal Conductivity, in-Plane,** & **Thermal Conductivity, Cross-Plane,** & **Heat Capacity,** & **Density,** \\  & **W**-**m**\({}^{-1}\)**-**K**\({}^{-1}\) & **W**-**m**\({}^{-1}\)**-**K**\({}^{-1}\) & **J**-**kg**\({}^{-1}\)**-**K**\({}^{-1}\) & **kg**-**m**\({}^{-3}\) \\ \hline Sb & 63.24 & 24.43 & 207 & 6691 \\ \(B_{\text{ig8}}Sb_{12}\) & 13.21 & 5.1 & 124 & 9790 \\ mica & 5.1 & 0.51 & 880 & 2900 \\ Cu & 401 & 401 & 384 & 8960 \\ \hline \end{tabular}
\end{table} 
Table 1: Thermophysical properties of the materials. Figure 3: The real and imaginary parts of a relative permittivity of thin-film Sb and Bi\({}_{\text{88}}\)Sb\({}_{12}\) on mica substrate in the frequency range of 0.3–0.8 THz. The real part of relative complex permittivity is strongly negative for both the films in the studied frequency range, in accordance with the Drude model, for metals/semimetals below the plasma frequency.