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Abstract
Graphene has promising applications for novel optoelectronic devices. However, graphene-based photodetectors have two major drawbacks that need attention. The first is how to preserve graphene’s original high carrier mobility, and the second is how to enhance graphene’s absorption to improve its performance. Hexagonal boron nitride (hBN)/graphene van der Waals (vdW) heterostructure-based plasmonic metasurfaces (PMs) are proposed for wavelength-selective infrared (IR) photodetectors. hBN preserves graphene’s high carrier mobility, and PMs enhance graphene’s absorption. Numerical calculations demonstrate sufficient wavelength-selective absorption in the broadband IR wavelength range. Such optical properties are realized by coupling the localized surface plasmon resonance (SPR) of PMs and propagating SPR of graphene. The proposed vdW heterostructure-based PMs could be used for high-performance multi-spectral IR photodetectors.
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1. INTRODUCTION
Graphene, a single layer of carbon atoms with a honeycomb lattice, is a promising material for novel optoelectronic devices because of its high carrier mobility and broadband photoresponse, which are derived from graphene’s unique bandgap structure of Dirac cones [1–3]. Besides, graphene can be easily fabricated by chemical vapor deposition (CVD), which leads to low-cost fabrication. Graphene-based photodetectors are attracting substantial attention because they are expected to realize high responsivity, a rapid response, and compatibility with low-cost manufacturing methods, which cannot be achieved with conventional photodetectors [4,5]. Recently, demand for graphene-based photodetectors that operate at infrared (IR) wavelengths has been increasing as a consequence of the difficulty in fabricating conventional quantum-type photodetectors such as HgCdTe or Type-II superlattice-based IR photodetectors, which offer high performance but require high-quality substrates and complex fabrication procedures [6,7]. Advanced functional IR photodetectors with wavelength [8,9] or polarization tunability [10,11] are also expected to expand their application fields. To achieve such functions, graphene is a promising candidate that can achieve reconfigurable wavelength selectivity by controlling its chemical potential (CP) [12–15], which can be applied for fire detection, analytical devices, and remote sensing [16].
However, graphene-based photodetectors have two major drawbacks. First, their excellent properties are degraded when they are transferred to a conventional substrate, such as ${{\rm SiO}_2}/{\rm Si}$, because graphene is disordered by the substrate surface. Second, they exhibit poor absorption of 2.3% without wavelength dependence, which limits their performance and prevents their use in wavelength-selective applications [3].
One approach to solving the first drawback is to use hexagonal boron nitride (hBN) as the substrate. hBN is an ideal substrate because its lattice constant matches that of graphene, and its surface is atomically smooth and relatively free of dangling bonds and charge traps [17,18]. hBN can preserve the excellent primordial mobility of graphene and act as a good insulator material [17]. hBN has unique optical properties [19,20], mainly because it exhibits anisotropic permittivity. Also, it is a strong candidate for novel optical devices such as ultraviolet photodetectors [21,22], ultra-small filters [23], absorbers [24,25], and single-photon emitters [26]. In terms of the second drawback, plasmonic metasurfaces (PMs) are a promising approach for enhancing the optical absorption of graphene at surface plasmon resonance (SPR) wavelengths [27]. Many methods have been proposed to enhance the photoresponsivity of graphene-based photodetectors using PMs, such as nanoantennas or meta-atoms [28–34] and metal-insulator-metal-based (MIM) metamaterial structures [35]. Therefore, the configuration of graphene on hBN with PMs is key to realizing advanced functional graphene-based IR photodetectors.
Fig. 1. Schematics of (a) vdW-PMs for wavelength-selective IR photodetectors, (b) vdW heterostructure of graphene formed on hBN substrate, and (c) cross-sectional view of a vdW-PM for wavelength-selective IR photodetectors.
Studies have been conducted on graphene and hBN-based PMs, such as patterned graphene-hBN-based absorbers [24,25] and hBN on graphene with MIM-based visible light absorbers [12]. However, patterning graphene or hBN degrades the quality of graphene, which leads to lower device performance. Therefore, there is a necessity to design a PM structure in which flat graphene is placed on hBN with a periodic plasmonic metal structure for enhancing the absorption of graphene. Furthermore, such structures can work as advanced photodetectors with wavelength selectivity. Such graphene-based photodetectors are expected to realize high-performance multi-spectral IR cameras and expand their application fields.
To address this challenge, we propose hBN/graphene van der Waals (vdW) heterostructure-based PMs. Our proposed structure consists of the MIM-based PM, which has hBN as the insulator layer, and graphene is formed on hBN and under a plasmonic metal. This structure can function as graphene-based field effect transistors (FETs). Our previous study [36] realized wavelength-selective absorption, and the wavelength could be controlled by the $CP$. However, the characteristics or photodetector applications for the hBN/graphene vdW heterostructure have not yet been investigated in detail. Here, we report on a detailed numerical investigation of hBN/graphene vdW-heterostructure-based PMs (vdW-PMs) and their potential for application in wavelength-selective IR photodetectors. The study reveals that such vdW-PMs can maintain the high carrier mobility of graphene and realize wavelength-selective absorption in the long-wavelength infrared (LWIR) region (8–12 µm) mainly by controlling the size of the surface pattern of PMs without patterning graphene or by the $\textit{CP}$ of graphene. These vdW-PMs show great potential for electrically tunable advanced-functional IR photodetectors, where their performance can overcome conventional IR photodetectors with small pixel sizes and low dark currents.
2. DEVICE STRUCTURES AND MATERIALS
A. Device Structures
Figures 1(a)–1(c) show the schematics of vdW-PMs for wavelength-selective IR photodetectors, vdW heterostructures of graphene formed on hBN, and the cross-sectional view of vdW-PMs, respectively.
As shown in Fig. 1, the proposed devices consist of top periodic micropatches formed on a vdW heterostructure of graphene, hBN, and a bottom reflector. The top periodic patches and bottom reflector are made of Al because it is low cost and exhibits high reflectivity in the IR wavelength region. This structure is derived from graphene FET-based photodetectors [4].
hBN serves as an insulator layer for graphene and preserves its original high carrier mobility because of its atomically planar surface [17]. This vdW heterostructure can enhance the photodetector performance because the carrier mobility of graphene fundamentally defines the responsivity of the photodetector. The basic structure is an MIM-based PM that exhibits wavelength-selective absorption with incident-angle independence by a localized SPR (LSPR) [37,38]. The absorption of graphene can be enhanced, which corresponds to the enhancement of the responsivity of the photodetector.
Fig. 2. Schematic of a monolayer of hBN and (b) real part of the permittivity of hBN as a function of wavelength.
The period and width of the top micropatches, $CP$ of graphene, and thickness of hBN are defined as $p$, $w$, $CP$, and $h$, respectively.
B. Materials
Figure 2(a) shows a schematic of the monolayer hBN [23]. hBN has two types of phonon modes for IR wavelengths: (1) an out-of-plane ($\parallel$) mode with a transverse optical frequency (${\omega _{{\rm TO}}}$) of ${780}\;{{\rm cm}^{- 1}}$ and a longitudinal optical phonon frequency (${\omega _{{\rm LO}}}$) of ${830}\;{{\rm cm}^{- 1}}$, and (2) an in-plane ($\bot$) mode with a ${\omega _{{\rm TO}}}$ of ${1370}\;{{\rm cm}^{- 1}}$ and a ${\omega _{\rm{LO}}}$ of ${1610}\;{{\rm cm}^{- 1}}$ [39]. Accordingly, hBN has two anisotropic permittivities, ${\epsilon _\parallel}$ and ${\epsilon _ \bot}$. The anisotropic permittivity of hBN is given by [39]
As shown in Fig. 2(b), hBN has another advantage as an insulator material for MIM-based metasurfaces because the two RS bands do not overlap in the middle-wavelength infrared (MWIR) (3–5 µm) or LWIR (8–12 µm) region, which does not prevent the formation of SPR in these two important bands for IR sensors. Notably, conventional oxide-based insulators such as ${{\rm SiO}_2}$ and ${{\rm Al}_2}{{\rm O}_3}$ exhibit strong absorption in the LWIR region, which disturbs SPR [41]. By contrast, SPR can be induced in the MWIR and LWIR regions of hBN without inducing Rabi splitting [23].
The complex conductivity of graphene was obtained from [42]. The temperature, scattering rate multiplied by the reduced Planck constant, and the thickness of the graphene layer were set to 300 K, 5 meV, and 0.7 nm, respectively [43]. The permittivity of Al was obtained from [44].
3. RESULTS AND DISCUSSION
A. Effect of Structural Parameters
A rigorous coupled wave analysis (RCWA) method was used for the calculations [45]. The actual calculation model was a two-dimensional model used to reduce the calculation time. In Fig. 1(a), the incident and polarization angles are defined as $\theta$ and $\varphi$, respectively. The normal incident angle $\theta = {0}^\circ$ is parallel to the $z$ axis. The transverse magnetic (TM) mode at $\varphi = {0}^\circ$ is parallel to the $x$ axis. In this study, the normal incidence and TM mode were used when $\theta$ and φ were not specifically defined because the asymmetricity of the micropatches results in polarization independence (discussed later in this section). The $CP$ of graphene and the thickness of the top micropatches and bottom reflector were fixed at 1.0 eV, 200 nm, and 200 nm, respectively.
Figures 3(a)–3(c) show the calculated absorbance as a function of wavelength and $w$ for micropatches with $p$ of 2.0, 3.0, and 4.0 µm, respectively; $h$ was fixed at 200 nm. Figure 3(d) shows the calculated absorbance as a function of wavelength and $h$ with a fixed $p$ of 3.0 µm.
Fig. 3. Calculated absorbance as a function of wavelength and $w$ for micropatches with $p$ of (a) 2.0 µm, (b) 3.0 µm, and (c) 4.0 µm. (d) Calculated absorbance as a function of wavelength and $h$ with $p$ of 3.0 µm. The color scale represents absorbance.
Figures 3(a)–3(d) reveal the structural dependence of the absorption properties. Figures 3(a)–3(c) show the wavelength-selective absorption with sufficiently high absorbance in all structures at wavelengths from 3.0 to 14.0 µm. The absorption wavelength increases with the increase in $w$. As shown in Figs. 3(a)–3(c), these absorption modes were attributed to the SPR modes SPR1, SPR2, and SPR3 induced by MIM-based PMs and HPP1 induced by the HPPs of hBN. SPP1 to SPP3 were defined primarily by $w$ rather than $p$ or $h$ because these modes result from the LSPR. The wavelength-selective absorption (SPR1 and SPR2) in both the MWIR and LWIR regions was realized for $p$ of 2.0 and 3.0 µm. As shown in Fig. 3(d), the absorption mode at a wavelength of 6.0 µm (SPR1) can be maintained from $h = {0.1 - 0.25}\;{\unicode{x00B5}{\rm m}}$, and its wavelength shifts slightly with a change in $h$.
Two Rabi splitting peaks were observed at approximately 7 and 13 µm, which can be attributed to the interaction between the SPR of the MIM-based PMs and the HPPs of HPP1 and HPP2 in the two RS bands of hBN, respectively. However, unlike conventional oxide-based insulators, these two Rabi splittings do not disturb the main target wavelength regions of IR photodetectors.
Fig. 4. Calculated absorbance as a function of wavelength and (a) $\theta$ and (b) $\varphi$ with $p$ of 3.0 µm. The color scale represents absorbance.
Figures 4(a) and 4(b) show the calculated absorbance as a function of wavelength and $\theta$ and $\varphi$ with $p = {3.0}\;{\unicode{x00B5}{\rm m}}$, respectively; $h$ was fixed at 200 nm. Figures 4(a) and 4(b) indicate the incident-angle dependence and polarization dependence, respectively.
As shown in Figs. 4(a) and 4(b), the absorption modes of SPR1 and SPR3 at approximately 6.0 µm and 13.0 µm, respectively, exhibited incident-angle independence with $\theta$ of over 80° and polarization selectivity, where TM mode ($\varphi = {0}^\circ$) was selectively absorbed. The incident-angle independence was attributed to the LSPR of MIM-based PMs. The polarization selectivity was attributed to the asymmetricity of the micropatches. Several absorption modes at around 7.0–8.0 µm, as denoted by HPP1, were produced by the HPP modes of hBN. A strong incident-angle-dependent mode denoted as plasmonic surface lattice resonance (PSLR) at 3.0–6.0 µm [in Fig. 4(a)] was formed owing to the periodicity of the micropatches [46]. These modes disturb single-mode operation. However, a smaller $p$ such as 1.0 µm can exclude this PSPR from the MWIR wavelength region.
Fig. 5. Calculated electric (${{\rm E}_x}$) and magnetic field (${{\rm H}_y}$) distribution of vdW-PMs at the wavelength of (a), (b) 2.0 µm; (c), (d) 7.0 µm; and (e), (f) 7.23 µm. The white line shows the shape of MIM-based PMs with graphene. The color scale represents the amplitude of ${{\rm E}_x}$ and ${{\rm H}_y}$.
The electromagnetic field distributions of vdW-PMs were calculated using the RCWA method. Figures 5(a)–5(f) show the electric field at the $x$ direction (${{\rm E}_x}$) and the magnetic field at the $y$ direction (${{\rm H}_y}$) distribution at the wavelengths of 6.0, 7.0, and 7.23 µm with fixed $p$, $w$, $h$, and $CP$ of 3.0 µm, 1.2 µm, 200 nm, and 1.0 eV, respectively.
As shown in Figs. 5(a) and 5(b), LSPR was produced at the lower edges of the micropatch, and a strong magnetic resonance was produced between the micropatch and the bottom reflector. Such resonances are analogous to conventional MIM-based metamaterial absorbers [37]. In addition, as shown in Fig. 5(a), propagating SPR was observed on the graphene layer. This indicates that the LSPRs couple with the graphene-based SPR. These SPRs can enhance the absorption of graphene, which in turn enhances the quantum efficiency of graphene-based photodetectors. As shown in Figs. 5(c)–5(f), zigzag modes were clearly formed in the hBN layer owing to the HPP1 of hBN, which is attributed to the mode coupling of SPR and HPP of hBN. Such mode coupling increases the number of absorption modes.
These results indicate that the proposed vdW heterostructure can achieve wavelength-selective detection in the MWIR and LWIR regions using a graphene layer.
B. Effect of the Chemical Potential of Graphene
The effect of $CP$ was also investigated. Figures 6(a)–6(c) show the calculated absorbance spectra for $CP{\rm s}$ of 0, 0.5, 1.0, and 1.5 eV with $p$ and $w$ values of 2.0 and 1.5 µm, 3.0 and 2.0 µm, and 4.0 and 3.0 µm, respectively; $h$ was fixed at 200 nm. $CP$ higher than 1.0 eV may be beyond the practical limit. However, we considered $CP$ of up to 1.5 eV considering previous studies [47,48] to determine the theoretical property. Figures 6(a)–6(c) demonstrate that the peak absorption wavelength shifted to shorter wavelengths with increasing $CP$, independent of the $p$ and $w$ values, because the LSPR is produced in the vicinity of graphene, as shown in Fig. 5(a), where a change in the $CP$ of graphene can modify the LSPR wavelength [29,49]. Figure 6(d) shows the relationship between $CP$ and the peak absorption wavelength. The absorption wavelength shift is 0.5 µm for a $CP$ change of 1.5 eV. The $CP$ of graphene can be controlled by applying a gate voltage, indicating that the detection wavelength of the proposed vdW heterostructure-based IR photodetector can be tuned by varying the back-gate voltage applied from the bottom reflector.
Fig. 6. Calculated absorbance spectra for CPs of 0 eV, 0.5 eV, 1.0 eV, and 1.5 eV for with $p$ and $w$ values of (a) 2.0 µm, (b) 3.0 µm, and (c) 4.0 µm. (d) Relation between CP and the peak absorption wavelength.
C. Isolated hBN Structures
The proposed vdW-PMs exhibit wavelength-selective absorption in both the MWIR and LWIR regions. However, some applications use wavelengths between the MWIR and LWIR regions, such as gas sensing and other analytical applications. To address this issue, isolated hBN-based vdW-PMs have been investigated. Figures 7(a) and 7(b) show a schematic and cross-sectional view of isolated hBN-based vdW-PMs, respectively. The difference from Fig. 1 is that only the hBN layer is patterned, and a flat graphene layer is loaded on each isolated hBN. The graphene is not patterned, and a part of it is suspended. Therefore, the quality of graphene is not degraded because the suspended graphene exhibits better performance than graphene on any insulator layers [50], and the contact of graphene is with hBN, which preserves the quality of graphene. The width of isolated hBN is equal to $w$.
Figures 8(a)–8(c) show the calculated absorbance as a function of wavelength and $w$ for micropatches with a $p$ of 2.0, 3.0, and 4.0 µm, respectively. These figures reveal the structural dependence of the absorption spectra for the isolated hBN structures. As shown in Figs. 8(a)–8(c), the absorption mode denoted as SPR1(2) was produced over a wide wavelength range without the Rabi splitting caused by HPP1 at approximately 7 µm. This absorption wavelength increases with an increase in $w$. The number of absorption modes is significantly reduced compared to those in Figs. 3(a)–3(c). By contrast, Rabi splitting caused by HPP2 is still present. HPP1 is attributed to an in-plane ($\bot$) phonon mode, and its effect decreases in the isolated hBN structure. However, HPP2 is attributed to an out-of-plane ($\parallel$) phonon mode, and its effect persists even in the isolated hBN structure. Please note that the small Rabi splitting in Figs. 8(b) and 8(c) is attributed to the SPR and cavity resonance between the micropatch and the bottom reflector. Figures 9(a) and 9(b) show the calculated absorbance as a function of wavelength and $\theta$ and $\varphi$ with $p = {3.0}\;{\unicode{x00B5}{\rm m}}$, respectively; $h$ was fixed at 200 nm. Figures 9(a) and 9(b) indicate the incident-angle dependence and polarization dependence, respectively.
Fig. 8. Calculated absorbance as a function of wavelength and $w$ for micropatches with $p$ of (a) 2.0 µm, (b) 3.0 µm, and (c) 4.0 µm. The color scale represents absorbance.
Fig. 9. Calculated absorbance as a function of wavelength and (a) $\theta$ and (b) $\varphi$ with $p$ of 3.0 µm for the isolated hBN structure. The color scale represents absorbance.
As shown in Figs. 9(a) and 9(b), the absorption modes of HPP1 were eliminated. The number of absorption modes is significantly reduced, and the main absorption modes of SPR1 are more evident than those in Figs. 4(a) and 4(b). The isolated hBN structures reduced the hBN volume, which can decrease the number of resonant modes in the hBN layer. The main absorption modes of SPR1 maintained incident-angle independence. Such single-mode absorption with incident-angle independence is an advantage for the wavelength-selective IR photodetectors.
Figures 10(a) and 10(b) show the electromagnetic field distributions of the isolated hBN-based vdW-PMs at a wavelength of 6.0 µm with fixed $p$, $w$, $h$, and $CP$ values of 3.0 µm, 1.2 µm, 200 nm, and 1.0 eV.
Fig. 10. Calculated (a) ${{\rm E}_x}$ and (b) ${{\rm H}_y}$ distribution of the isolated hBN-based vdW-PMs at the wavelength of 6.0 µm. The color scale represents the amplitude of ${{\rm E}_x}$ and ${{\rm H}_y}$.
Figures 10(a) and 10(b) show that the same electromagnetic field localization shown in Figs. 5(a) and 5(b) was produced in the isolated hBN structure, and a propagating SPR mode was produced on graphene. SPR cannot be coupled to the HPP1 modes in the isolated hBN structure because the isolated hBN has such a small volume that the propagated HPP mode, as shown in Figs. 5(c) and 5(e), cannot be formed.
The absorption mode in isolated hBN-based vdW-PMs can be controlled in such a broadband wavelength region from MWIR to LWIR simply by changing the width of top micropatches ($w$), which helps in the design of practical multi-spectral applications.
D. Photodetector Applications
Figure 11 shows the concept of the proposed wavelength-selective IR photodetector using vdW-PMs.
As discussed in Section 2.A, the configuration shown in Fig. 11 was derived from a graphene-based FET photodetector. Source and drain electrodes were formed at the sides of periodic micropatches. A back gate was placed under the bottom reflector, and graphene was used as the channel. The graphene layer was connected to the source and drain electrodes, and the bottom reflector layer functioned as a back-gate electrode. The surface of the source and drain electrodes was Au, while the side facing the graphene layer was made of Cr and Ti, which served as adhesion layers for graphene. Cr and Ti were omitted in Fig. 11.
The absorption characteristics as a function of wavelength are the same as those in Figs. 3–6 because the side electrodes do not prevent SPR [28,30]. In Section 3.B, it was shown that the back-gate voltage could electrically control the $CP$ of graphene, leading to electrically tunable multi-spectral photodetection. In this study, an asymmetric micropatch, such as a rectangular structure, was adopted to reduce the calculation time and produce polarization selectivity. However, symmetric micropatches, such as square-shaped structures, can produce polarization-independent absorptions [51]. As shown in Section 3.C, the isolated hBN structure can achieve wavelength selectivity in the broadband wavelength ranges from MWIR to LWIR regions. Therefore, the proposed photodetectors can realize incident-angle independent wavelength-selective IR photodetection with or without polarization insensitivity. The absorption can be enhanced up to ${\sim} 100\%$ using the proposed design. The responsivity can be enhanced by at least ${\sim} 20$ times compared to conventional graphene-based FET photodetectors without PM structures [52] in the MWIR and LWIR regions. Furthermore, our proposed structure does not require nanometer-sized narrow gaps, but the expected performance is similar to those of the graphene-based FET photodetectors with PMs using nanometer-sized narrow gaps [30]. However, notably, the performance of the graphene photodetectors is strongly dependent on the device fabrication process and graphene synthesis method.
Using the proposed design, the photodetector size, which corresponds to the pixel size for image sensors, can be reduced to be smaller than 15 µm compared with a conventional IR image sensor. This is because, to sufficiently produce LSPR, the needed $p$ is a few micrometers and a few periodicities only. The responsivity of this photodetector can be improved by absorption enhancement due to LSPR and the increase in the carrier mobility of graphene due to hBN. Furthermore, as shown in Figs. 5 and 10, the micropatches work as antennas, and the produced LSPR can reduce the physical area of the pixel. This reduces the dark current and improves the signal-to-noise ratio, which can provide higher temperature operations such as a room temperature of approximately 300 K [53,54]. Therefore, the proposed vdW heterostructure-based PMs can be applied to high-performance, advanced functional IR image sensors.
4. CONCLUSION
We proposed advanced functional IR photodetectors using graphene/hBN-based vdW-PMs with an MIM structure. Optical properties were numerically investigated using the RCWA method. The vdW-PMs exhibited wavelength-selective absorption in both the MWIR and LWIR regions with incident-angle insensitivity. The RCWA calculations showed the coupling between the LSPR of MIM-based PMs and the HPP of hBN, and the coupling between the propagating SPR of graphene and LSPR was observed in vdW-PMs. In addition, the $CP$ of graphene controls the absorption wavelength. The isolated hBN structure can eliminate type-II HPP of hBN and realize wavelength selectivity in the broadband wavelength ranges from MWIR to LWIR. Photodetector applications using graphene/hBN-based vdW-PMs can be expected to realize enhanced performance, such as small pixel size, low dark current, and higher temperature operation, owing to the effect of hBN and LSPR of MIM-based PMs. The actual fabrication of high-quality hBN would be a future challenge. However, the rapid growth of CVD methods could address this issue [55]. The results obtained in this study can enable the realization of high-performance vdW heterostructure-based IR image sensors with advanced functions, such as multi-spectral or polarimetric imaging.
Funding
Acquisition, Technology Logistics Agency (JPJ004596).
Acknowledgment
Portions of this work were presented at the SPIE Defense $+$ Commercial Sensing conferences in 2022 [36]. This work was supported by Innovative Science and Technology Initiative for Security Grant Number JPJ004596, ATLA, Japan.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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