1. Introduction

In recent decades, semiconductors have been employed in a variety of optoelectronic devices such as solar cells, sensors, modulators, photodetectors [1–7]. However, it has been always a dilemma in choosing the thickness of semiconductors, since the high integrability and fast response require thin film semiconductors while the sufficient light absorption can be only guaranteed by bulk. Surface plasmon resonance (SPR), the collective electronic excitation at metal/dielectric interface, provides an effective route to manipulate light-matter interaction beyond the diffraction limit [8–11]. The unprecedented ability of SPR to trap the incident light at the subwavelength scale and lead to the local field enhancement has been extensively exploited to enhance the absorption in the semiconductors, addressing the above concern to a great extent. Based on this, a range of metal-based plasmonic metasurfaces, such as ribbon, disk, ring, cross and other shapes have been presented to load with thin film semicondctors to improve their absorption performance from the ultraviolet to terahertz (THz) regions [12–21]. Unfortunately, the resonant responses of metal-based plasmonic metasurfaces are dependent on the structure parameters, and therefore the operating wavelength of these hybrid optoelectronic devices are fixed in case they are fabricated, which inevitably hinders flexible applications requiring tunable spectral selectivity.

Graphene is a two-dimensional (2D) atomically-thin material with exceptional optical and electrical properties and serves as a promising building block for modern optoelectronics [22, 23]. In the mid-infrared and THz regions, graphene exhibits strong half-metallicity when coupling with the incident light and supports SPR for plasmonic applications [24, 25]. Moreover, the resonant responses of graphene-based metasurfaces can be dynamically modulated by the continuously tunable surface conductivity of graphene with manipulating its Fermi level, which therefore can be considered as serious rivals to the metal-based counterparts [26–34]. Till now, tunable single-, dual- and even multi-wavelength absorption enhancement with graphene-based plasmonic metasurfaces has been investigated, and perfect absorption has further been realized using salisbury screen configuration [35–43]. Most of these works have been concerned with the absorption in graphene itself while the usage of tunable graphene SPR to enhance the light absorption in the semiconductors is yet to be explored. Very recently, the pioneering works have demonstrated the possibility for lighttrapping and absorption engineering with high efficiency and tunable spectral selectivity by loading graphene-based plasmonic metasurfaces with thin film or even 2D semiconductors [44–47].Nevertheless, the graphene resonators in these designs exist in the isolated fashion, which may not be expediently tuned in practice. In addition, the tunable polarization selectivity in this kind of devices also remains to be further explored.

In this contribution, we numerically demonstrate light trapping and absorption enhancement can be realized with graphene-based complementary metasurfaces. The hybrid device consists of a monolayer graphene perforated with a periodic array of nanoholes on the top of a thin film semiconductor separated by an insulator layer. The simulation results show that the excitation of SPR in the monolayer graphene can effectively trap the incident light at the subwavelength scale and enhance the absorption in the surrounding semiconductor by more than one order of magnitude. Furthermore, we explore the polarization sensitivity in the proposed device when transforming the shape of the unit cell from square to rectangle. With manipulating the Fermi level of graphene, the polarization-sensitive absorption here can be dynamically modulated over a broad spectral region, which can find potential applications in the next generation of photodetectors with tunable spectral and polarization selectivity in the mid-infrared and THz regions.

2. The geometric structure and numerical model

Figure 1 schematically depicts the graphene-based complementary metasurfaces. In the proposed hybrid device, the unit cell is arranged in a periodical array with the lattice constant $P=400$ nm and consists of a monolayer graphene perforated with a circular nanohole on the top of a thin film semiconductor separated by an insulator layer. The radius of the circular nanohole is $R=120$ nm, and the effective thickness of the monolayer graphene is set as t_g = 1 nm. The thicknesses of the insulator layer and the semiconductor are t_i = 20 nm and t_a = 100 nm, respectively, and the substrate is assumed to be semi-infinite. The insulator layer and the substrate are treated as lossless dielectrics with a real permittivity of ${\epsilon }_d=1.96$. The semiconductor is modeled using a complex permittivity of ${\epsilon }_a={\epsilon }^{{ }^{\text{′}}}+i{\epsilon }^{{ }^{\text{′′}}}$, where ${\epsilon }^{{ }^{\text{′}}}=10.9$ and ${\epsilon }^{{ }^{\text{′′}}}$ is related to the absorption coefficient $\alpha =\left(2\pi /\lambda \right)\text{Im}\left(\sqrt{{\epsilon }^{{ }^{\text{′}}}+i{\epsilon }^{{ }^{\text{′′}}}}\right)$ accounting for losses. The absorption coefficient $\alpha =0.05\mathrm{\mu }$m⁻¹ is considered, comparable to the typical semiconductor Hg${ }_{1-x}$Cd_xTe ternary alloy exploited for photodetection in the mid-infrared and THz regions [48, 49].

 

Fig. 1 The schematic geometry of our proposed graphene-based complementary metasurfaces. The unit cell consists of a monolayer graphene perforated with a circular nanohole on the top of a thin film semiconductor separated by an insulator layer.

Download Full Size | PDF

The surface conductivity of graphene can be described with the random-phase approximation (RPA) in the local limit, including both the intraband and interband processes [50, 51]

The finite-difference time-domain (FDTD) method is exploited for full-wave numerical simulations (FDTD Solutions, Lumerical Inc., Canada). In the calculations, to balance the simulation time and accuracy, the uniform meshgrid inside the monolayer grapheneis 0.25 nm while the auto non-uniform meshgrid is adopted to the other regions. The periodical boundary conditions are employed in the x and y directions and perfectly matched layers are utilized in the z direction along the propagation of the incident plane wave.

The potential fabrication and tuning of the monolayer graphene are suggested as follows [39, 40]. Firstly, the monolayer graphene is grown on a copper (Cu) foil with a chemical vapor deposition (CVD) method. Secondly, the CVD-grown graphene is transferred onto the insulator layer using a polymethyl methacrylate (PMMA) layer which is then dissolved in the acetone solution. Thirdly, the periodical array of nanohole is patterned via a large area nanoimprint lithography with reactive ion etching (RIE) technique to perforate the monolayer graphene. Finally, a high-capacitance low-loss ion gel layer is drop casted to manipulate the Fermi level of graphene by electric gating. Besides, an optical means to tune graphene SPR hasrecently been demonstrated by ultraviolet illuminations in a dynamical and reversible way, which could further simplify the tuning process [57].

3. Simulation results and discussions

With the electric field of the incident light oriented along the x axis, (x-polarized, i.e., transverse-magnetic (TM) plane wave), SPR in the monolayer graphene is excited in the spectral region of interest. Figure 2(a) illustrates the numerically simulated spectra with an initial Fermi level of graphene $E_F=0.6$ eV. The resonance occurs at 12.0 μm, arising a strong transmission suppression and absorption enhancement. The total absorption is $A=31\%$ at the resonance and the absorption in the semiconductor is $A^{{ }^{\text{′}}}=16.9\%$. Note that the semiconductor is assumed to be an ultrathin film (100 nm) with the absorption coefficient $\alpha =0.05\mathrm{\mu }$m⁻¹, corresponding to an ultralow absorption of about 1% in the impedance matched media, an enhancement factor of 16.9 can be achieved at the resonance. Here the absorption enhancement should be attributed to the excitation of SPR in the monolayer graphene. The simulated x-y plane electric field distribution ($\left|E_z\right|$) at the resonance in Fig. 2(b) shows a strong enhancement of around the circular nanohole, which is symmetric to the y-axis. This is a characteristic behavior of the lowest excitation mode [1,0] of SPR under the Bragg’s condition, which results from the accumulated charges around the circular nanohole due to the TM plane wave [58]. Therefore, SPR effectively trap the incident light and enhance the absorption in the surrounding semiconductor.

 

Fig. 2 (a) The simulated spectra of the transmission T, the reflection R, the total absorption A and the absorption in the semiconductor $A^{{ }^{\prime }}$ with the absorption coefficient $\alpha =0.05\mathrm{\mu }$m⁻¹ and the Fermi level of graphene $E_F=0.6$ eV. The enhancement factor of the absorption in the semiconductor is also shown compared to that in the impedance matched media. (b) The simulated electric field distribution in the x-y plane ($\left|E_z\right|$) at the resonance.

Download Full Size | PDF

It is well known that the SPR is dependent on the structure parameters, and the light trapping and absorption enhancement can thus be tuned with the geometric variation in the graphene-based complementary metasurface. Here we investigate the dependence of the absorption in the semiconductor on the radius of the circular nanohole and the lattice constant of the unit cell, as shown in Figs. 3(a) and (b), respectively. When the radius R starts at 40 nm, the resonance locates at 11.6 μm and the absorption in the semiconductor is $4.5\%$. As R increases to 60 nm, the resonance redshifts to 12.1 μm and the absorption goes up to $A^{{ }^{\text{′}}}=9.5\%$. Finally, when R comes to 120 nm, the absorption reaches the maximum at 12.0 μm as the default. In the interval of $R=80$ to 120 nm, the absorption remains above $13.8\%$ with more than one order enhancement and the resonance stays quite stable at around 12 μm. In contrast, the resonance wavelength is sensitive to the change in the lattice constant P. As P increases to 600 nm, the resonance redshifts to 16.0 μm and the absorption goes down to $A^{{ }^{\text{′}}}=14.3\%$. Finally, when P comes to 1200 nm, the absorption reaches the minimum of $4.6\%$ at 21.8 μm. These phenomena are quite different from those in the graphene-based metasurfaces consisting of isolated resonators, such as ribbon, disk, ring, etc., where the SPR is due to the excitation of cavity mode. The SPR in the complementary metasurface is due to the dressed mode under the Bragg’s condition [58], and thus sensitive to the lattice constant of the unit cell rather than the radius of the circular nanohole, providing much better fabrication tolerance.

 

Fig. 3 The simulated spectra of the absorption in the semiconductor $A^{{ }^{\prime }}$ with different (a) radii of the circular nanohole R and (b) lattice constants of the unit cell P. The enhancement factor of the absorption in the semiconductor is also shown compared to that in the impedance matched media.

Download Full Size | PDF

The optical responses of graphene are also highly dependent on its Fermi level, which is the origin of the dynamical tunability of SPR in the graphene-based metasurfaces. To demonstrate the spectral tunability of our proposed hybrid device, Fig. 4 illustrates the absorption in the semiconductor with different Fermi levels of graphene. When the Fermi level E_F starts at 0.4 eV, the resonance locates at 14.7 μm and the absorption in the semiconductor is $10.5\%$. As E_F increases to 0.7 eV, the resonance blue shifts to 11.1 μm and the absorption goes up to $19.1\%$. Finally, when E_F comes to 0.8 eV, the absorption reaches $21.3\%$ at 10.4 μm with an enhancement as high as 21 times. It can be seen that with the increase of Fermi level, the resonance wavelength becomes shorter and absorption enhancement increases simultaneously. The physics mechanism lies in that as the Fermi level of graphene increases, the wavelength of SPR grows longer (for a fixed frequency or vacuum wavelength) and the nanohole-shaped resonator looks relatively smaller for the incident light, hence the resonance experiences an obvious blue shift. Meanwhile, the increase of Fermi level also leads to the larger surface conductivity of graphene and SPR becomes less lossy, thus the number of charge carriers contributing to the resonance increases. Therefore, the local field enhancement with higher E_F are stronger than that with lower E_F, which results in a higher absorption enhancement in the semiconductor. Therefore, the tunable light trapping and absorption enhancement can be achieved by manipulating the Fermi level of graphene, without altering the structure parameters of the complementary metasurfaces. Here, we would like to highlight that the graphene nanohole-shaped resonators exploited in our proposed hybrid device is in the monolayer morphology rather than the isolated fashion, which is much easier to fabricate and manipulate than previous investigations.

 

Fig. 4 The simulated spectra of the absorption in the semiconductor $A^{{ }^{\prime }}$ with different Fermi levels of graphene E_F. The enhancement factor of the absorption in the semiconductor is also shown compared to that in the impedance matched media.

Download Full Size | PDF

To further explore the polarization sensitivity in the proposed device, we transform the shape of the unit cell from square to rectangle, and complementary resonators from circular nanohole to elliptical nanohole to avoid the mode hybridization. As shown in Fig. 5, the monolayer graphene is perforated with a periodical array of elliptical nanoholes, where the lattice constants are P_x = 300 nm and P_y = 400 nm. The long axis and short axis of the elliptical nanoholes are R_x = 80 nm and R_y = 120 nm accordingly. The thicknesses of the insulator layer and the semiconductor, as well as their optical properties, keep the same as previous settings. The numerically simulated spectra with an initial Fermi level of graphene $E_F=0.6$ eV are depicted in Fig. 6(a) and (c) for TM and TE plane wave at normal incidence, respectively. For TM plane wave, the resonance happens at around 10.2 μm and the absorption in the semiconductor is $16.8\%$. For TE plane wave, the resonance at 11.9μm shows the maximum absorption in the semiconductor as $14.4\%$. The x-y plane electric field distribution ($\left|E_z\right|$) at the resonances are plotted in Fig. 6(b) and (d), where the plasmon-excited local field enhancement around the elloptical nanoholes are symmetric to the y-axis under TM incident plane wave and symmetric to the x-axis under the TE incident plane wave, respectively. Like mentioned above, these are the characteristic behaviors of the lowest excitation mode [1,0] of SPR under the Bragg’s condition. Hence, the excitation of SPR in the monolayer graphene induce the local field confinement and the absorption enhancement in the semiconductor for both the TM and TE plane wave. The different resonance wavelengths for TM and TE modes arise from the different values of the lattice constant of the anisotropic unit cell in the x and y directions.

 

Fig. 5 The schematic geometry of our proposed anisotropic graphene-based complementary metasurfaces. In the unit cell, the monolayer graphene is perforated with a elliptical nanohole, and the rest keep the same as previous settings in Fig. 1.

Download Full Size | PDF

 

Fig. 6 The simulated spectra of the transmission T, the reflection R, the total absorption A and the absorption in the semiconductor $A^{{ }^{\prime }}$ with the absorption coefficient $\alpha =0.05\mathrm{\mu }$m⁻¹ and the Fermi level of graphene $E_F=0.6$ eV for (a) TM and (c) TE plane wave. The enhancement factor of the absorption in the semiconductor is also shown compared to that in the impedance matched media. The simulated electric field distribution in the x-y plane ($\left|E_z\right|$) at the resonance for (b) TM and (d) TE plane wave.

Download Full Size | PDF

With manipulating the Fermi level of graphene, the tunable light trapping and absorption enhancement can be realized for these anisotropic graphene-based complementary metasurfaces as well. Figures 7(a) and (b) show the spectra of absorption in the semiconductor for TM and TE plane wave with different Fermi levels of graphene. Similar with the variations in the square unit cell case, the resonance blue shifts to shorter wavelength and the absorption enhancement increases simultaneously as the Fermi level increases. Note that an interesting phenomenon can be observed by comparing these two figures: the resonance for TM plane wave with the Fermi level $E_F=0.6$ eV and for TE plane wave with the Fermi level $E_F=0.81$ eV share the exact same resonance wavelength at 10.2 μm, which means either TM or TE plane wave at the specific wavelength can be efficiently absorbed by simply manipulating the Fermi level of graphene. Here we introduce the polarization absorption ratio defined by $20*\log (A_{\text{TM}}^{{ }^{\text{′}}}/A_{\text{TE}}^{{ }^{\text{′}}})$, where $A_{\text{TM}}^{{ }^{\text{′}}}$ and $A_{\text{TE}}^{{ }^{\text{′}}}$ are the absorption in the semiconductor for TM and TE plane wave, respectively. The dependence of the polarization absorption ratio on the Fermi level of graphene is explored at the specific wavelength of 10.2 μm. As displayed in Fig. 7(c), the polarization absorption ratio shows continuous variations as the Fermi level of graphene increases. In particular, the ratios with the Fermi level $E_F=0.6$ eV and $E_F=0.81$ eV are calculated as 18.1 dB and -19.0 dB. Therefore, the polarization-sensitive absorption of the incident light at the specific wavelength can be dynamically modulated with manipulating the Fermi level of graphene, which can find potential applications in the next generation of photodetectors with tunable spectral and polarization selectivity in the mid-infrared and THz regimes.

 

Fig. 7 The simulated spectra of the absorption in the semiconductor $A^{{ }^{\prime }}$ with different Fermi levels of graphene E_F for (a) TM and (b) TE plane wave. The enhancement of the optical absorption in the semiconductor is also shown. The enhancement factor of the absorption in the semiconductor is also shown compared to that in the impedance matched media. (c) The dependence of the polarization absorption ratio on the variation of Fermi level of graphene at the specific wavelength of 10.2μm.

Download Full Size | PDF

4. Conclusions

In conclusions, we numerically investigate the tunable light trapping and absorption enhancement in graphene-based complementary metasurfaces. The excitation of SPR under the Bragg’s condition in the monolayer graphene perforated with a periodic array of nanoholes traps the incident light at the subwavelength scale and leads to absorption enhancement in the thin film semiconductor by more than one order of magnitude. Furthermore, polarization-sensitive absorption enhancement can be realized by transforming the shape of the unit cell from square to rectangle. The tunability of graphene makes it possible to dynamically modulate the absorption enhancement in the semiconductor over a broad spectral regime. In particular, either TM or TE plane wave at the specific wavelength can be efficiently absorbed by simply manipulating the Fermi level of graphene, which is promising for potential applications in the mid-infrared and THz photodetection with spectral and polarization selectivity. Although SPR in the graphene-based metasurfaces has mainly been observed in the mid-infrared and THz regimes, it has recently been experimentally demonstrated at much shorter wavelengths ($\sim 2\mathrm{\mu }$m) [59], therefore our proposed hybrid device together with its design principle can be also applied to the near-IR regime.