# Metal-Organic Hybrid Metamaterials for Spectral-Band Selective Active Terahertz Modulators
## 3 Results and Discussion
(**b**) Normalized THz-transmission spectra measured through the tri-layer sample with different laser powers of the optical beam for photoexcitation in the range from 0 mW to 220 mW (3.1 W/cm\({}^{2}\)) with a step of 20 mW (0.28 W/cm\({}^{2}\)). The insets show electric field distributions of the fundamental (\(f_{1}\)) and second-order LC (\(f_{2}\)) resonances at frequencies of 0.35 THz and 0.85 THz, respectively. It is important to compare the experimental and simulated values of spectral intensity modulation efficiency that is defined as  
\[M=\frac{\int\left|E_{un}(\omega)\right|^{2}d\omega-\int\left|E_{ex}(\omega) \right|^{2}d\omega}{\int\left|E_{un}(\omega)\right|^{2}d\omega},\]  
where \(E_{ex}\) and \(E_{un}\) represent the electric-field amplitude spectra measured with and without photoexcitation, respectively [22]. Figure 4 shows the spectral intensity-modulation efficiency plotted as a function of the laser power of the optical beam. The black squares and red circles indicate the values extracted from the simulations and experimental results, respectively. The most important variables required for simulations, the electrical conductivities of electrons and holes, were selected so that the derived simulation results matched the experimental results well. Furthermore, the electrical conductivity was proportional to the  
Figure 4: Modulation efficiency of THz wave transmission extracted from the simulations shown in Figure 2a (black squares) and experimental results shown in Figure 2b (red circles), plotted as a function of the laser power of the incident optical beam for photoexcitation. Figure 3: The intensity values, extracted at the frequencies of \(f_{1}\),\(f_{2}\) and \(f_{3}\), of the (**a**) simulated and (**b**) measured transmission spectra. product of the carrier concentration and mobility. If a material has both electrons and holes, the total electrical conductivity is given by  
\[\sigma=e(n\mu_{e}+p\mu_{h}) \tag{1}\]  
where \(e\), \(\mu_{e}\), \(\mu_{h}\), \(n\), and \(p\) indicate the elementary charge, carrier mobility of electrons, carrier mobility of holes, carrier concentration of electrons, and carrier concentration of holes, respectively. Figure 5 shows the carrier concentrations of electrons in the PCBM layer and holes in the Si substrate, calculated using the above formula as well as from the simulation results. Here, the hole drift mobility in high-resistivity silicon with a bulk resistivity of more than 10\({}^{5}\)\(\Omega\cdot\)cm was 500 cm\({}^{2}\)/(V\(\cdot\)s), and the electron mobility in a thin film of PCBM molecules thermally annealed at 150 \({}^{\circ}\)C was approximately 2.0 \(\times\) 10\({}^{-4}\) cm\({}^{2}\)/(V\(\cdot\)s) [30]. The values of electrical conductivity selected to perform simulations to realize the experimental results are listed in Table 1 below. Using the values of the electrical conductivity and carrier mobility, the carrier concentrations of electrons in the PCBM thin film and holes in the Si substrate are calculated as shown in Figure 5.  
Considering the excess carrier distribution generated by an optical beam under the continuous photoexcitation by a cw optical laser, the excess carrier concentration gradient over all depths in both the PCBM and silicon layers was not found to be significantly large in a dynamic equilibrium. The carrier concentrations could, therefore, be considered uniform throughout the sample. Spatially separated electrons and holes at the PCBM-Si interface allow sustained maintenance of a relatively high carrier concentration while rendering both the layers sufficiently metallic in the THz frequency region. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline laser power (mW) & 0 & 20 & 40 & 60 & 80 & 100 & 120 & 140 & 160 & 180 & 200 & 220 \\ \hline PCBM [S/m] & & & & & & & & & & & & & \\ (\(\times\)10\({}^{-3}\)) & & & & & & & & & & & & & \\ \hline Si [S/m] & \(<\)1.16 & 17.4 & 27.8 & 36.0 & 40.6 & 46.4 & 48.7 & 55.1 & 58.0 & 61.5 & 63.8 & 69.6 \\ \hline \end{tabular}
\end{table}