# On the Study of Advanced Nanostructured Semiconductor-Based Metamaterial
## 3 Results  
In this paper, a phenomenon of the propagation of surface waves at the boundary of tunable hyperbolic metamaterial was studied. It is worthwhile mentioning that its resonance can be directly controlled by changing the concentration of the free carriers of the semiconductor. Specifically, we studied the propagation of surface plasmon polaritons at the boundary of the anisotropic media (Figure 1). It should be mentioned that we examined two different samples, i.e., anisotropic InAs semiconductor (Figure 1a) and hyperbolic metamaterial constructed by providing a combination of the alternating dielectric and InAslayers (Figure 1b). The nanostructured metamaterial under consideration can be fabricated by utilizing a synergy of plasma-enhanced vapor deposition techniques [20]. Hyperbolic metamaterials have attracted a great deal of attention over the years [26]. Nanostructured metamaterials, belonging to a class of hyperbolic metamaterials composed of alternating dielectric layers with a permittivity \(\varepsilon_{2}>0\) and conductive layers with a permittivity \(\varepsilon_{1}<0\), can be grown with molecular beam epitaxy on lattice-matched substrates [27]. Moving free electrons in conductive layers can create an electric dipole. The former is crucial in aiming to induce electric resonances in nanostructured metamaterials. Based on the above stated, noble metals are taken into consideration as the conductive layers because of their larger number of free electrons leading to stronger resonances. However, such composites cannot be directly tuned. In this paper, a layered metamaterial is numerically demonstrated, tuning its properties by changing the parameters of the employed semiconductor. The increase in free carrier concentration will raise the free electron collision rate and provide a fertile ground for a reduction in the effective path length of free electrons. In other words, the resonance will move to shorter wavelengths. It is worthwhile noting that doped semiconductors in short-wavelength bands (e.g., near-IR, visible, and UV bands) cannot demonstrate plasma behavior (i.e., \(\varepsilon_{1}>0\)). In this relationship, the suggested cavity will not be obtainable in these bands. However, one can choose a low effective mass and high-mobility semiconductor (e.g., indium tin oxide, zinc oxide doped with aluminum or gallium [28]) or add metallic layers in the nanostructured metamaterial to escape this challenge. The frequency-dependent permittivities [19; 20; 21; 22; 23; 24; 25] of both anisotropic semiconductor and semiconductor-based nanostructured metamaterials are presented in Figure 2. It should be noted that permittivities tend toward the negative values at the lower frequency ranges. As can be observed in Figure 2a, the frequency range of the negative values moves to the higher frequency range as the magnetic field strength increases. The same is valid for the semiconductor-based metamaterial case (Figure 2b). However, the shift is less observable in Figure 2b. It should be mentioned that \(\varepsilon_{\perp}\) only is tunable in the case of varying magnetic field strength along with the permittivity of the dielectric layer in Figure 2a-c. The example depicted in Figure 2d is of particular interest, as it presents the impact of the engineering concentration of the free carriers in the semiconductor. The resonant frequency of \(\varepsilon_{\perp}\) increases with an increase in the \(N\) value. The former is justified by Figure 3. An increase in the concentration allows for a significant enhancement in resonant behavior. Figure 1: A sketch of the problem under consideration, i.e., propagation of surface plasmon polaritons at the boundary of anisotropic semiconductor (**a**) and hyperbolic metamaterials (**b**) with definitions of the geometrical parameters.