# Ultrathin and Electrically Tunable Metamaterial with Nearly Perfect Absorption in Mid-Infrared
## 2 Materials and Methods  
The metamaterial absorbers were fabricated on a Si\({}_{3}\)N\({}_{4}\) membrane with supporting Si frame, as schematically illustrated in Figure 1a. The thickness of the Si\({}_{3}\)N\({}_{4}\) membrane was 200 nm. A series of nano-fabrication processes were performed on the membrane. The reflecting layer underneath the membrane, which was also used as the back-gate of the absorber, was prepared with 5 nm Cr and 30 nm Au by electron beam evaporation. Graphene on top of Si\({}_{3}\)N\({}_{4}\) was grown using the chemical vapor deposition (CVD) method and subsequently transferred onto the membrane. Source and drain contacts, grown with 5 nm Cr and 50 nm Au, were then fabricated onto the graphene by photolithography procedures. Standard electron-beam lithography and lift-off processes were finally used to pattern the cross-shaped Au metamaterial arrays (5 nm Cr/30 nm Au), whose scanning electron microscope (SEM) image is shown in Figure 1b. For each absorber, the total patterned area was about 50 \(\upmu\)m \(\times\) 50 \(\upmu\)m. The period (P) of each square unit cell in these arrays was 2.3 \(\upmu\)m, while the arm width (W) and arm length (L) of the cross-shaped microstructures were to be optimized. All of the following optical and electrical experiments were carried out at room temperature.  
The reflectance spectra of our absorbers are shown in Figure 1c, with the back-gate voltage fixed at 0 V. Considering the transmittance of the device with a reflecting layer underneath the Si\({}_{3}\)N\({}_{4}\) membrane was nearly 0, the absorption (A) of our device is closely related to the reflectance (R). Their relationship can be written as A = 1 - R. From Figure 1c, the reflectance of the absorber without a metasurface was nearly constant and equal to 1, indicating that the absorber reflected almost all the mid-infrared light without noticeable absorption. For those with different patterns, different modes of localized plasmon induced by metamaterial arrays can resonate with light of a specific wavelength. With the help of the reflecting layer, the light trapped in the Si\({}_{3}\)N\({}_{4}\) membrane will finally contribute to the absorption of the device. As a result, mid-infrared light is largely absorbed at the resonant wavelength. The absorber with parameters of L = 1.25 \(\upmu\)m and W = 0.3 \(\upmu\)m exhibited the best performance, with reflectance \(<\) 0.03, or absorptance \(>\) 0.963, at the frequency of 2013 cm\({}^{-1}\). The reflectance of the device was mainly influenced by the length and width of the arm. More systematic studies indicate that a longer arm length results in a red-shift of its resonant frequency, while the arm width affects the depth of reflectance [29]. These patterns can generate different dips in reflectance at its resonance frequency. Figure 1d depicts numerical results based on the Finite-Difference Time-Domain (FDTD) method. The parameters of the MIM structure in the simulation were nearly identical to our experiments. The metals in the simulation were based on the Drude model. The plasma frequency for Au was set to be \(\omega_{\text{P}}=1.365\times 10^{16}\) rad/s and the collision frequency was \(\gamma=5.78\times 10^{13}\) Hz. The relative permittivity for the semiconductor layer (Si\({}_{3}\)N\({}_{4}\)) was chosen to be 3 [30]. The perfect matched layer was introduced as the boundary condition in our system. The simulation results are reasonably consistent with our experimental results, except that the absorption peaks are wider and the absorption rates are lower in the experiments than in the simulation. The discrepancy in peak width may have arisen from the imperfection of the sample fabrication, such as variations in period and length, which were not considered in the simulation. However, it is certain that the MIM structures offers an important and effective approach to design a cavity-like absorber, which can efficiently harvest mid-infrared photons for real applications.