# Ultrathin and Electrically Tunable Metamaterial with Nearly Perfect Absorption in Mid-Infrared
## 3 Results and Discussion
The inset figure in Figure 3a shows the Raman spectrum of the graphene after being integrated into our device using an excitation laser of \(\lambda\) = 633 nm. We can clearly see that the intrinsic G peak and 2D peak of graphene are around 1580 cm\({}^{-1}\) and 2680 cm\({}^{-1}\), which are consistent with precious reports [34], despite the series of nano-fabrication processes. The source-drain current (I\({}_{\text{SD}}\)) in graphene is modulated by back-gate bias (V\({}_{\text{G}}\)), which is shown in Figure 3b. When the source-drain current reaches its lowest level, namely V\({}_{\text{G}}\) = V\({}_{\text{F}}\), which is at around 17 V, the Fermi level matches the Dirac point. As the back-gate voltage increases,  
Figure 2: (**a**) The ratio between Q\({}_{\text{a}}\) and Q\({}_{\text{r}}\), with different W and tan\(\delta\). (**b**) Q\({}_{\text{a}}\) and Q\({}_{\text{r}}\) change when L = 1.25 \(\upmu\)m and tan\(\delta\) = 0.08. (**c**) Black dashed lines indicate the quality factor (Q\({}_{\text{a}}\) and Q\({}_{\text{r}}\)) of the simulated results with fixed W, while red square dots show the experimentally tunable regime of graphene modulated by electricity. (**d**) Q\({}_{\text{a}}\)/Q\({}_{\text{r}}\) of the simulated and experimental results. 2D polarization images depict \(|\)E\({}_{\text{Z}}\)\(|\) distribution at V\({}_{\text{G}}\) = \(-\)8 V and V\({}_{\text{G}}\) = 26 V.  
the source-drain current curve shows an obvious kink shape, indicating that the concentration of carriers in graphene is varying due to the change of Fermi energy level (V\({}_{\rm F}\)). When V\({}_{\rm G}\)\(<\) V\({}_{\rm F}\), the carriers transported in graphene are hole-dominated, and when V\({}_{\rm G}\)\(<\) V\({}_{\rm F}\), transport in graphene is electron-dominated. Figure 3c shows the reflection spectra at different back-gate voltages. It can be seen that the reflection spectra can be tuned continuously by the gate bias, and the change of r(\(\omega_{0}\)) due to back-gating can reach about 5 dB (dip-to-dip). The minimum reflectance, r(\(\omega_{0}\)), at different biases is depicted as black squares in Figure 3d. From Figure 3d, the largest reflection value at resonant dip is near the Dirac point (V\({}_{\rm G}\)\(\sim\) 17 V) and, with increasing the carrier density (no matter electron or hole), the reflection value decreases, which indicates additional absorption. In the meantime, with decreasing V\({}_{\rm G}\), the resonant frequency increases slightly (\(\sim\)1%), which may be ascribed to a smaller effective mode volume. The rather limited tunability of the present device is associated with the quality of the graphene layer, which consisted of impurities and defects due to CVD growth and device fabrication processing. The tunability can be further improved with better sample quality or using BN/graphene/BN sandwiched structures. To reveal the physical insights behind the demonstrated tunability, we followed CMT and numerically fit the experimental data with equation 1 to extract Q\({}_{\rm r}\) and Q\({}_{\rm a}\) values. As the reflectances (R = \(\left|\)r(\(\omega\))\(\right|^{2}\)) of the device under different bias are known, Q\({}_{\rm r}\) and Q\({}_{\rm a}\) of the system can be easily obtained by numerical fitting based on Equation (1). The results are shown by red hollow squares in Figure 2c and it can be seen that the extracted Q\({}_{\rm r}\) and Q\({}_{\rm a}\) agree reasonably with the simulation data. This agreement validates the simplified model to treat graphene as an effective layer with tunable absorption. The apparent deviation in the region of V\({}_{\rm G}\)\(>\) 17 V is attributable to the fact that carriers  
Figure 3: **(a)** Raman spectra of the graphene we used coating on SiO\({}_{2}\) substrate and the graphene integrated in the absorber with cross arrays of L = 1.25 \(\upmu\)m and W = 0.3 \(\upmu\)m (inset figure). The wavelength of the applied laser is 633 nm. **(b)** The source–drain current is controlled by back-gating.