Design of Optical Metamaterial Mirror with Metallic Nanoparticles for Broadband Light Absorption in Graphene Optoelectronic Devices

A general metallic mirror (i.e., a flat metallic surface) has been a popular optical component that can contribute broadband light absorption to thin-film optoelectronic devices; nonetheless, such electric mirror with a reversal of reflection phase inevitably causes the problem of minimized electric field near at the mirror surface (maximized electric field at one quarter of wavelength from mirror). This problem becomes more elucidated, when the deep-subwavelength-scaled two-dimensional (2D) material (e.g., graphene and molybdenum disulfide) is implemented into optoelectronic device as an active channel layer. The purpose of this work was to conceive the idea for using a charge storage layer (spherical Au nanoparticles (AuNPs), embedded into dielectric matrix) of the floating-gate graphene photodetector as a magnetic mirror, which allows the device to harness the increase in broadband light absorption. In particular, we systematically examined whether the versatile assembly of spherical AuNP monolayer within a dielectric matrix (i.e., optical metamaterial mirror), which should be designed to be placed right below the graphene channel layer for floating-gate device, can be indeed treated as the effective magnetic mirror. In addition to being capable of the enhancement of broadband light absorption, versatile access to various structural motifs of AuNPs benefitting from recent advances in chemical synthesis promises compelling opportunities for sophisticated engineering of optical metamaterial mirror. High amenability of the AuNP assembly with the semiconductor-related procedures may make this strategy widely applicable to various thin film optoelectronic devices. Our study thereby illustrates advantages in advancing the design of mirror for rational engineering of light-matter interaction within deep-subwavelength-scaled optoelectronic devices.

of broadband light absorption, versatile access to various structural motifs of AuNPs benefitting from recent advances in chemical synthesis promises compelling opportunities for sophisticated engineering of optical metamaterial mirror. High amenability of the AuNP assembly with the semiconductor-related procedures may make this strategy widely applicable to various thin film optoelectronic devices. Our study thereby illustrates advantages in advancing the design of mirror for rational engineering of light-matter interaction within deep-subwavelength-scaled optoelectronic devices.

Introduction
In thin film optoelectronic technologies, for example, photodetectors and solar cells, there has usually been a trade-off between efficient photon absorption and the enhancement of electrical performance (increase in the efficiency of charge/carrier collection and photocurrent) [1−8]. The reduction in the thickness of active film (i.e., channel layer or light absorption layer) represents the increase in the efficiency of charge/carrier collection, but it is inherently accompanied by sacrificing light absorption efficiency. More importantly, this trade-off problem becomes more elucidated, when optoelectronic devices mainly rely on the deep-subwavelength-scaled two-dimensional (2D) materials such as graphene and molybdenum disulfide (MoS 2 ) for benefiting from their exotic electronic properties (e.g., high charge carrier mobility even at room temperature) [9−14]. Even if the unique capabilities of 2D materials together with their high amenability to the currently available semiconductor processes promises compelling opportunities in advancing various optoelectronic devices [9][10][11][12][13][14]; nonetheless, the inherently low optical cross-section of 2D materials remains as challenges for their practical applications to optoelectronic devices [12].
Meanwhile, the light trapping technologies have envisioned wide range of optoelectronic devices over the past three decades, from ray optics-based statistical strategy (e.g., Yablonovitch limit) to wave optical near-field manipulation (e.g., plasmonic nanoantennas) [15−24]. Even more exciting is various semiconductor/metalrelevant nanotechnologies' potential (e.g., electron beam/focused ion beam lithography, self-assembly, and synthesis of nanowires) for enabling sophisticated engineering of light trapping with exquisite control over geometries and shapes of 2D/3D nanoscaled mesostructures [25,26]; consequently, such light trapping technologies can further advance the aims of 2D materials-based optoelectronic devices by expanding the range of accessible optical cross-section [27−33]. However, much of the development of light trapping technologies especially for 2D material-based deep-subwavelength-scaled optoelectronic devices has been mainly to regard the use of plasmonic nanoantennas rather than other photonic structural motifs [27−33]. Although this method can address some of the aforementioned optical problems of 2D materials, the requirements for the direct incorporation of antennas into 2D materials place severe restrictions on the available design space of optoelectronic devices. Also, the broadband enhancement of light absorption has been a challenging with the use of such plasmonic nanoantennas. Thus, other optical structural motifs need to be further investigated in order to contain a rich diversity of the deep-subwavelength-scaled optoelectronic device architecture with the rational light trapping design.
Metallic backplane mirror, which itself can act as a contact or gate electrode, has proven to be a versatile component for light trapping in the thin optoelectronic devices, as allowing us broadband photon recycling even with simple structural architecture (just flat film) in stark contrast to plasmonic nanoantennas [34−38]; but, translation of a flat metallic mirror particularly into the deep-subwavelength-scaled optoelectronic devices still requires optical engineer to first address the problem of significantly reduced optical intensity within one-quarter of wavelength, which is generally observed in low surface impedance metallic mirror (i.e., electric mirror) [38]. In other words, the phase of the light reflecting off a mirror (reflection phase) should be quantitatively controlled with a high flexibility, while simultaneously being compatible with optoelectronic device architectures. Very recently, Esfandyarpour et al., has promoted this issue by using electron-beam lithographic texturing of metallic surface [38], but the problems of difficulty in large-area fabrication together with relatively low compatibility with wide range of 2D material optoelectronic device architecture have stymied its practical applications.
Herein, we theoretically propose the concept of multifunctional magnetic mirror, in which a versatile assembly of metallic nanoparticle monolayer can achieve the high impedance and the minimized phase reversal, while fully taking advantage of its nonvolatile memory functionality. Also, the ability to precisely tune the structural features of primitives (i.e., AuNPs) makes this direction highly flexible especially in terms of absorption control within the deep-subwavelength-scaled, 2D material optoelectronic devices. Finally, the assembled monolayer of metallic nanoparticles can be highly amenable to the fabrication process and architecture of the deep-subwavelengthscaled, 2D material optoelectronic device.

Device architectures and numerical calculations
To access whether metallic nanoparticle monolayer-enabled metamaterial mirror can be indeed effective in terms of light trapping in the deep-subwavelength-scaled optoelectronic device, we chose as a model system the pentacene-graphene nano floating-gate transistor memory (NFGTM), which we had identified as a non-volatile photodetector with high optical cross-section and quantum efficiency (schematic for the device architecture is presented in Fig. 1a) [39]. Our device consists of plastic substrate  [40,41]. In order to avoid unrealistic point contact, the interface between the hexagonally close-packed AuNPs (main structural motif of optical metamaterial mirror in the current work) was truncated by 1 nm [42]. Unit cell is also indicated in Fig. 1b (blue dotted box); due to the hexagonal geometry, the optical properties of this structure are independent on the polarization of normally incident light. For the calculation of the complex permittivity of Au, Drude-critical model was implemented into FDTD code [43]; the complex dielectric constants of other materials including PEN, ITO, polyDADMAC, and pentacene (thin film, which was assumed to be dried at 25 °C) were experimentally measured by ellipsometry. The Bruggeman effective medium approximation allows us to obtain the complex permittivity of Al 2 O 3 [42]: where !" and !"#$% are the volume ratios of Al and Al 2 O 3 , respectively; is the permittivity of Al/Al 2 O 3 composite. The both !" and !"#$% were obtained by a modified Drude model and empirical measurement, respectively. In order to calculate the effective complex permittivity of graphene, the optical conductivity, σ(ω) = σ intra (ω) + σ inter (ω), with respect to Fermi energy was obtained by means of Kubo formula [30]: where − ! is the Fermi distribution function with Fermi energy ( ! ), indicates the broadening of the interband transitions, corresponds to the momentum relaxation time (herein, 250 fs was employed) caused by carrier intraband scattering, and ∆ is a half bandgap energy from the tight-binding Hamiltonian near K points of the Brillouin zone.

Optical properties of NFGTM
As presented in Fig Fig. 2a) [39]. Especially, the efficient generation of electron-hole pair within pentacene and subsequent transferring of the generated electron-hole pair to graphene via capacitive coupling was found to dramatically increase the photoresponsibility and photodetectivity of the graphene optoelectronic devices [39].
More importantly, the incorporation of the AuNP layer (individually dispersed AuNPs within cPVP) right below the pentacene-graphene hybrid layer, acting as a charge storage layer as well, can give rise to the plasmonic back scattering and the further enhancement of light absorption, while taking full advantage of non-volatile photonic memory (i.e., floating-gate system) [39]. Indeed, the absorption behavior of such pentacene-graphene hybrid layer (bold purple line in Fig. 2a) strongly relies on the plasmonic scattering behavior of individual AuNP (see back scattering spectrum of the disc-shaped AuNP with 5 nm height and 10 nm diameter, embedded in 20 nm thick cPVP dielectric matrix, as shown in Fig. 2b): at the localized plasmonic resonance wavelength of AuNPs, the absorption of the photodetector can be further increased (Fig. 2a). Herein, the shape of AuNP especially was designed to be disc as with our experimental result [39]. This success to the further increase in the photoresponsibility of the pentacene-graphene photodetector by means of plasmonic light scattering of AuNP charge storage layer, together with high compatibility of the AuNPs implementation with the fabrication procedure of pentacene-graphene photodetector (e.g., sputtering or spin coating-enabled self-assembly), amply inspires the current work on the rational design of a charge storage layer (i.e., AuNP monolayer) to be useful for optical metamaterial mirror, in that provides a way for recycling broadband light, maintaining nonvolatile photonic memory function, and learning some of their perspectives.

Monolayer of hexagonally close-packed, spherical AuNPs as optical magnetic mirror
We now outline how high surface impedance of spherical AuNP monolayer with hexagonally closed-packed geometry, which is useful for a charge storage, can be harnessed to realize optical magnetic mirror with a minimized phase reversal. Much like other periodically bumpy metallic surfaces [38, 44−47], close-packed spherical AuNP monolayer within dielectric cPVP matrix (metallo-dielectric photonic/plasmonic hybrid crystals) itself can efficiently make the path of surface current less straightforward, so as to effectively reduce optical conductivity (σ) of metal surface. This reduced σ in turn results in the enhancement of E z at the surfaces of metallic structure. Particularly, in the case of metallo-dielectric photonic/plasmonic hybrid crystals working at optical frequency [38], both surface plasmon polaritons (SPPs) and photonic (PhC) modes can lead to the dramatic reduction of σ (enhancement of E z ). As the impedance (Z) at the surface of metallic structures is given by the E z /H y (following Ohm's law), the increase in E z at the surfaces, resulting from both SPPs and PhC modes, leads to the reduction of the reflection according to following complex reflection coefficient [38,48]: where Z S1 , Z S2 , φ, θ i , θ t , and ! denote the impedance at the metal surface, the wave impedance of the incident medium, reflection phase, incident angle, transmitted angle, and reflection amplitude, respectively. For the normal irradiation, second terms of the numerator and dominator of eqn. (4) become unity; then, the magnitude of reflection is simplified by Z S1 (or σ) of the monolayer of close-packed spherical AuNPs (r=(Z S1 -1)/(Z S1 +1)). Thus, the increase in Z S1 via SPPs or PhC modes allows us to minimize the phase reversal (φ = π). (symmetric structural motifs), the obtainable bandgap width (Δω/ω) is relatively small (e.g., 0.023 at 686 nm and 0.005 at 520 nm); but, it can be further increased by using anisotropic AuNPs (e.g., Au rice) rather than spherical counterparts [49].

Properties of optical metamaterial mirror
Next, we numerically retrieved the effective impedance (Z) of optical metamaterial mirror: as the size of individual AuNP is much smaller compared to the wavelength of interest (herein, the hexagonally close-packed AuNP monolayer can be treated as a homogeneous medium), the applications of both homogenization theory and effective parameter retrieving method (numerical iterative method) using the scattering parameters (S parameters) can be justified [50]. Note that the peak of impedance of optical metamaterial mirror layer was observed near at the forbidden regions such as plasmonic and photonic bandgaps (Fig. 3c) shows a standing wave with a minimized electric field near at the surface of mirror layer (maximized electric field at one quarter of wavelength from mirror layer) resulting from in-phase superposition between incident and phase reversed (φ = π) reflecting light, the optical metamaterial mirror can exhibit far more electric field right at the surface of mirror layer (Fig. 4a). This is because the phase shift of the light reflecting off the designed metamaterial mirror can be reconfigured to be much smaller than π via SPPs and PhC modes-enabled accumulation of phase (i.e., φ = π/6.3 at wavelength of 707 nm and φ = π/7.1 at wavelength of 511 nm). This reconfigured reflection phase through SPPs and PhC modes of optical metamaterial mirror is well revealed by the shifted sinusoidal envelop of standing wave with respect to field profile above a flat Au mirror. It is also worth noting that overall intensity of standing wave above optical metamaterial mirror is weaker than that above a flat Au mirror; evidencing the stored incident light and accumulated phase into the optical metamaterial mirror. Analyzing magnetic field distribution near at the surface of mirror layer further supports the origin of such metamaterial mirror's behavior. The magnetic field amplitude near at the surface of optical metamaterial mirror is found be weaker than that near at a flat Au layer, as shown in Fig. 4b. As such, the optical metamaterial mirror can harness relatively higher impedance, proper accumulation of phase, and thus more concentrated electric field near at its surface compared with a flat Au counterpart.

Flexibility in tuning reflection behavior of AuNP optical metamaterial mirror
The versatile controllability of optical properties can accrue if we use spherical AuNPs as a building block for the assembly of optical metamaterial mirror rather than conventional lithographic approach to metallic nano-pattern. For example, AuNPs can exist as various structural motifs, such as dielectric core-metallic shell sphere and multilayered metallic alloy sphere [40,51]; also, various sizes of such structural motifs of metallic NPs now can be accessed with recent advances in chemical synthesis [40].
Thereby, through careful tuning of structural features of AuNPs to be assembled into the monolayer, we can explicitly program the properties of SPP or PhC modes (e.g., working wavelength and impedance) and thus reflection behavior of optical metamaterials.
Toward this direction, we further expanded the range of available controllability of optical metamaterial properties by using Au shell (15 nm in thickness) and silica core NPs (120 nm in diameter) (abbreviated as silica@Au core-shell NPs).
In the case of silica@Au core-shell NPs monolayer embedded into cPVP matrix A simple flat Au mirror can still provide the broadband absorption enhancement of the pentacene-graphene hybrid layer. In our case, the thickness of pentacene and graphene hybrid layer (~ 25 nm) is much smaller than the wavelength of interest (deepsubwavelength-scaled); in contrast to semiconducting materials (e.g., Ge) with extremely strong absorption properties [36], the absorption of pentacene is relatively moderate.
Thus, its phase accumulation through round trip propagation or optical resonance within such pentacene-graphene layer should make a negligible contribution to the enhancement of broadband light absorption via a flat Au mirror; this enhancement of broadband light absorption mainly originates from the increased overlap between pentacene layer and increased electric field region (maximized at one quarter of wavelength) resulting from the phase reversed reflection. In particular, as the wavelength is reduced, the absorbed photon fraction becomes more significant mainly due to the interband transition-enabled energy storage and reflection phase accumulation at the surface of Au. This aspect is well reflected by the series of spatial distributions of electric field at different wavelength, as shown in Fig. 6b. We can also observe that the intensity of standing wave above a flat Au mirror layer especially at wavelength of 511 nm is further reduced after the implementation of light absorbing pentacene-graphene layer onto the surface of mirror layer (compare the third panel of Fig. 4a with first panel of Fig. 6b).
Meanwhile, despite of an imperfect magnetic mirror (φ is a bit larger than zero, as demonstrated in sections 3.2 and 3.3), the use of the close-packed spherical AuNP monolayer (both solid AuNPs and silica@Au core-shell NPs) as a charge storage layer in NFGTM can result in far more enhancement of the broadband light absorption within pentacene-graphene hybrid layer, compared with both a flat Au mirror and a individually dispersed disc-shaped AuNP (see Fig. 2a). Importantly, the solid AuNP monolayer is found to achieve dramatic enhancement of light absorption at broadband visible frequencies from 550 nm to 730 nm (55 ~ 65 % of incident photon), where pentacene can maximize light absorption and thereby efficiency of charge/carrier generation [39].
Fundamental to this broadband light absorption benefitting from the use of hexagonally close-packed solid AuNP monolayer is detailed in series of electric field spatial distribution (Fig. 6c). We can observe that the irradiated light in normal direction can properly accumulate the phase via PhC (below wavelength of 650 nm) and SPPs modes (above wavelength of 650 nm), so as to achieve the desired electric field distribution in terms of enhancing broadband light absorption in the device. Due to the deepsubwavelength-scaled thickness of active channel layer, the optical resonance and possible photon recirculation within active layer cannot be effectively activated, as mentioned above, in that the broadband light absorption is dominantly in regards to the highly concentrated near-field effect, which is properly controlled to be overlapped with the active layer. This is main reason that PhC modes with the ability to force the electric field to be strongly accumulated at the surface of solid AuNP monolayer can be advantageous over the SPPs modes in terms of broadband light absorption of deepsubwavelength-scaled active layer. Such enhanced light absorption within the active layer and the accumulated electric field preferably at the surface of solid AuNP monolayer also results in the reduced intensity of standing wave above the mirror layer.
In stark contrast to solid AuNP counterpart, it turns out that silica@Au core-shell NPs monolayer strongly absorbs the incident light within each individual particle through SPP whispering-gallery modes at shorter wavelength of interest (e.g., 511 nm) rather than reflecting back, resulting in much poorer performance of light absorption. Also, as mentioned in section 3.3, this optical metamaterial mirror likely accumulates the electric field at the vicinity of silica@Au core-shell NPs rather than at its surface, thereby being less favorable for broadband light absorption in deep-subwavelength-scaled optoelectronic device. However, this result implies that the working wavelength of metamaterial mirror and thus spectral response of the device can be precisely tuned by adjusting the structural motifs (geometry of AuNPs). For example, the translation of dielectric core into AuNPs is found to increase the working wavelength of SPPs mode 1 (fundamental mode). Such high flexibility, which can be achieved in a versatile way with advances in chemical synthesis [40], will be critical for enabling robust application of AuNP-based optical metamaterial mirror to the wide range of deep-subwavelength-scaled optoelectronic devices. Very recently, thin film coating of various active materials including organic dye and perovskite has proven to be efficient for the enhancement of optical cross-section of 2D materials [52,53]; consequently, being capable of on-demand controlling working wavelength with respect to each different spectral responsibility of such active materials should be satisfied in design of optical metamaterial mirror. In line with this, we believe our strategy will provide a versatile and powerful route to the rational manipulation of light-matter interaction within deep-subwavelength-scaled optoelectronic devices.

Possible options for the assembly and implementation of optical metamaterial mirrors into the NFGTM
The key to success in the fabrication of optical metamaterial mirror-implemented NFGTM is to obtain the highly qualified monolayer of solid AuNPs or silica@Au coreshell NPs. Toward this direction, the highly uniform, super-spherical AuNPs or silica@Au core-shell NPs should be accessible. In general, the citrate-mediated reduction of Au chloride, which has been widely used for the synthesis of AuNPs, results in the polygonal shaped, dispersive AuNPs; but, very recently, G.-R. Yi and his colleagues conceived the radical idea for the monocrystalline, super-spherical AuNPs through the elective etching vertices or edges of Au octahedral [40]. Furthermore, the wellestablished strategy for the selective reduction of Au onto the surface of silica colloidal particles allows us to get an access to the uniformly distributed silica@Au core-shell NPs in a reliable way [54].
Additionally, various methods have been established to organize the large-area monolayer of spherical colloidal nanoparticles, including mechanical rubbing [55], spin coating [56], and controlled dip coating [57], over the last two decades. In general, however, the process yield of such methods has been found to be highly dependent on the substrates (e.g., surface chemistry and roughness); thus, such assembly strategies of AuNP monolayer, in some cases, couldn't be compatible with overall fabrication procedure of NFGTM. This problem of incompatibility between NFGTM fabrication and assembly of AuNP monolayer can be effectively addressed by dry transfer printing with controlled adhesion [58−60]: (i) assembly of AuNP monolayer onto a mother substrate and (ii) transfer printing of it into NFGTM. Finally, the dielectric matrix made of polymer (e.g., cPVP) can be conformably coated by atomic layer deposition (ALD).

Conclusion
Here, we have suggested theoretical designs of optical metamaterial mirror for achieving the enhancement of broadband light absorption in deep-subwavelength-scaled graphene optoelectronic device, while maintaining nonvolatile photonic memory functionality. By examining numerical simulation, we have revealed that the rationally