1. Introduction

Active solid-state optical filtering presents exciting prospects for integration with a range of technologies including infrared detectors. Presently, frequency selective components often take the form of bulky filter wheels that are placed in front of a detector and rotated for spectral selectivity. However, these filter wheels require mechanical motion making them non-ideal for many high-performance situations where stability is a primary concern and their large size results in increased weight and power requirements. To circumvent this limitation, solid-state filtering has been widely pursued from visible to terahertz frequencies employing both electric-field and thermally tunable materials [1–10]. Graphene has risen to the forefront of the electrically-tunable options, especially in the long-wave infrared, due to its small footprint and the ease with which its optical response can be modified through carrier injection [11–15].

While graphene is only one atom thick, its interaction with long-wave-infrared (LWIR) light can be enhanced by plasmonic excitation enabling graphene to significantly influence the optical response of a microns-thick material stack. Importantly, the plasmonic dispersion of graphene is determined by both its surrounding dielectric environment, as well as graphene’s free carrier density. Changes to the Fermi level cause shifts in the plasmon dispersion (see Appendix A), thereby modifying the excitation energies of plasmons at a given momentum [16–19].

Exploitation of this tunable response requires plasmonic excitation. This process is not trivial as the plasmon dispersion lies at momenta far greater than that of free-space light necessitating a mechanism for excitation of evanescent high-momentum fields near the graphene. Previous studies have employed a range of patterned or sharp metallic features, as well as direct patterning of the graphene to provide the required momentum [12,13,20–22]. However, contact between metals and graphene has been shown to induce Fermi level (E_F) pinning, and graphene patterning not only complicates fabrication, but can also result in residual photoresist on the graphene surface [23,24]. Both effects can greatly limit the range over which the graphene Fermi level can be modified, which, in turn, limits the tuning range of filters based on this effect.

The solid-state graphene-based filters examined here avoid these deleterious effects. They consist of the following layers from the bottom up: a degenerately doped silicon substrate, silicon dioxide (SiO₂), transferred chemical vapor deposition-grown (CVD) graphene, a 1.5 nm Al₂O₃ layer, 20 nm layer of hafnium dioxide (HfO₂), and a 50 nm thick gold grating patterned over an area of 60 × 60 μm². Source and drain contacts for measuring graphene resistance are located just outside the grating. A schematic of one period of the structure is shown in the inset of Fig. 1 (dimensions not to scale). Both the period and SiO₂ thickness vary between devices. In this structure, the HfO₂ dielectric serves as both a spacer layer between the graphene and gold grating to prevent Fermi level pinning and as an efficient high-κ gate dielectric for Fermi level modification when a bias voltage is applied between the grating and graphene. The presence of a capping oxide also helps to ensure the long term stability of the graphene by isolating it from the environment, thereby preventing accumulation of adsorbates on the graphene over time [25,26].

 

Fig. 1 Characteristic transport curves obtained from each device during application of variable bias (V_G) across the gate dielectric with a constant source-drain voltage of 50 mV. (Inset) Schematic of the device showing the various layers. The sample is probed from the grating side during FTIR measurements. Dimensions are not to scale.

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2. Results

Characteristic gate-dependent transport curves obtained while sweeping the bias (V_G) applied to the grating, with a small bias applied across the source and drain electrodes, are shown in Fig. 1 for two different devices. The first has a period of 1.2 μm and an SiO₂ thickness of 150 nm while the second has a larger period of 1.6 μm and thicker 600 nm SiO₂. The gap in the gold grating in both cases is 100 nm wide. For brevity throughout the remainder of the manuscript, we refer to the 1.2 μm period device as the “smaller” device and the 1.6 μm period device as the “larger” device. By fitting the smaller device data (black squares) as in previous studies [27], a graphene mobility of μ ≈ 1080 cm²/V· s and gate dielectric constant of κ ≈ 14.3 can be obtained, in line with values from literature [28]. The larger device, which has thicker SiO₂, does not show the characteristic shape expected from a graphene transistor. Rather, it shows a monotonic increase in source-drain resistance (R_SD) with increasingly negative bias. While it is possible that resistance may reach a maximum value with larger negative values of gate bias, we avoided applying more than ±6 V to across the dielectric to prevent dielectric breakdown. The different electrical behavior may be a result of differences in oxide growth between the two devices. Specifically, the smaller device includes 150 nm of thermally growth SiO₂ while the larger device includes the same thickness of thermal SiO₂ with an additional 450 nm of plasma-enhanced chemical vapor deposition (PECVD) oxide. See Appendix C for details on fabrication. This more complicated process may result in the presence of additional charged traps at the layer interfaces. In spite of this unexpected behavior, the graphene carrier density is still modified by our backgate as is required for optical functionality.

Prior to examining the measured spectra, it is useful to discuss the origins of the response through full-wave electromagnetic simulations assessing the influence of each constituent element. For these simulations, optical properties of the oxides, silicon, and gold were determined from variable angle spectroscopic ellipsometery (IR-VASE, J. A. Woollam) while graphene properties were calculated using the random phase approximation [29]. Due to the thin nature of the Al₂O₃ layer, its presence has little effect on the devices’ response. For this reason, it was not included in simulations throughout the manuscript. In our model, graphene was represented as a sheet conductance at the interface between the SiO₂ and HfO₂ [30]. We begin by simulating a simpler structure that does not contain graphene and for which the SiO₂ has been replaced by a nondispersive and lossless dielectric with an index of refraction of 1.3 (i.e., a material stack comprised of doped Si, a nondispersive dielectric, dispersive HfO₂ and the gold grating). Fig. 2(a) shows that the spectral response of this structure (curve labeled “Grating”) is dominated by the metallic grating (blue curve) as evidenced by the single broad resonance with a minimum at ≈ 750 cm⁻¹. Changing the properties of the non-dispersive oxide to those measured for SiO₂ (curve labeled “Grating+SiO₂”) results in the appearance of three peaks at frequencies of approximately 800, 1095, and 1200 cm⁻¹ as shown by the green curve in Fig. 2(a). While the precise locations of the reflectance peaks depend on the structure (grating dimensions and oxide thicknesses), their locations roughly correlate with the frequencies of the optical phonons in SiO₂. Effectively, the phonon resonances hybridize with the grating mode which results in splitting of the grating resonance into two sharper minima.

 

Fig. 2 (a) Simulated reflectance demonstrating the effects of each additional element. Blue: Grating structure in the absense of graphene and with a dispersionless (n = 1.3) and lossless (k = 0) dielectric in place of SiO₂. Green: Grating structure in the absence of graphene with realistic dielectric optical responses. Black: Simulated full device response including graphene and dispersive dielectrics. (b) Comparison of graphene absorption in full device (red) and total absorption (black) demonstrating increased graphene absorption in bands of tunability.

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With the addition of graphene to the structure (E_F = 0.6 eV, black line, labeled “Grating+Graphene+SiO₂”), these two minima shift to higher frequencies indicating coupling of the grating and phonon resonances to the graphene. Total absorption of the structure is shown by the black curve in Fig. 2(b), along with the absorption in graphene itself (red line). Spectral regions of maximum absorption in graphene corresponds to minima in total reflectance (i.e. maxima in total absorption for this non-transmissive device), with absorption in the graphene layer exceeding 40%. Significant interaction of LWIR light with graphene, indicative of plasmonic excitation, points towards the possibility for tunability owing to the intrinsic gate-tunability of the plasmonic dispersion.

To experimentally demonstrate plasmon-enabled tunability, reflectance spectra of fabricated devices were measured under TM-illumination using a microscope coupled to a Fourier transform infrared (FTIR) spectrometer. Maps of normalized reflectance as a function of applied gate bias for two different geometries are shown in Fig. 3. The data in Figs. 3(a), 3(c), and 3(e) correspond to the smaller device while Figs. 3(b), 3(d), and 3(f) were taken on the larger device. For all devices, two local reflection minima separated by the SiO₂ phonon response are observed. Importantly, the positions of the minima differ between the two devices with shifts of about 200 cm⁻¹ showing the effects that geometric modification can have on the response. However, post-fabrication active tuning, where the optical response can be changed independent of geometry is required for many applications, including that of active infrared sensors.

 

Fig. 3 (a) Measured voltage and frequency dependent reflectance map obtained from the smaller device. Black dots track the minima of each resonance. (b) Experimental voltage and frequency dependent reflectance map obtained from the larger device (c) Measured reflectance for the smaller device at voltages of smallest and largest graphene conductivity. (d) Measured reflectance of the larger device at voltages of smallest and largest graphene conductivity. (e) Measured (black) and simulated (blue) differential reflectance between V_G = 1.75 V and −6 V and 0.3 and 0.7 eV respectively for the smaller device. (f) Measured (black) and simulated (blue) differential reflectance between V_G = −6 V and 6 V and 0.3 and 0.7 eV for the larger device.

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To this end, we examine the bias dependence of the collected spectra. The measured spectral maps show variation in reflectance that results from gate voltage induced modifications of graphene’s Fermi-level. For the smaller device shown in Fig. 3(a), the positions of both minima blueshift as additional carriers are injected into graphene. Carriers accumulate in the graphene when |V_G − V_CNP| > 0 where the voltage at the charge neutrality point V_CNP ≈ 1.75 V is determined from the transport data shown in Fig. 1. As is expected from transport data, shifts in the reflectance minima are nearly symmetric with applied bias, as shown by the black dots in Fig. 3(a) which map out the positions of the local minima. The maximum shift of the resonance position of the higher frequency mode near ∼ 1400 cm⁻¹ is 25 cm⁻¹, which significantly exceeds that of the lower frequency resonance which shifts by 8 cm⁻¹. Differential reflectance is a convenient figure of merit for a reflectance mode filter. From the data at V_CNP (1.75 V) and the maximally shifted data (V_G = −6 V) shown in Fig. 3(c), the calculated differential reflectance (ΔR = R(−6 V) − R(V_CNP)) approaches 10% for the higher frequency mode, as shown in Fig. 3(e) (black line). The measured and simulated differential reflectance are in relatively good agreement with the simulated data (blue) accurately reproducing the frequencies of the most salient spectral features. While the simulated spectra suggest that larger tuning should be expected, imperfections in device fabrication that are difficult to include in simulations likely have a deleterious effect on measured tunability by contributing to increased damping of the graphene plasmon and reducing graphene’s mobility. Specifically, topographic variation at interfaces and residual contaminants on the graphene surface have both been shown to have this effect [19,31].

For the larger device shown in Figs. 3(b) and 3(d), sizable shifts in both resonances result from gate voltage induced Fermi level changes. Specifically, the high and low frequency resonance locations change by 42 cm⁻¹ and 91 cm⁻¹, respectively. Thus, the differences in geometry yield a more than tenfold increase in the spectral shift of the low frequency mode. These larger spectral shifts result in an increased differential reflectance, seen in Fig. 3(f), in both measured (black) and simulated (blue) results (ΔR = R(6 V) − R(−6 V)) exceeding 15% at both 890 and 1260 cm⁻¹ in the measured data. This value of ΔR suggests that this reflective filter could be used to enable a frequency-agile infrared detector where the amplitude of reflected light can modulate the detector signal. Unlike in the smaller device, this device shows asymmetric behavior with bias as both resonance minima shift monotonically as illustrated by the black dots in Fig. 3(b). This behavior is consistent with the transport data shown in Fig. 1 (red circles). Importantly, the unipolar transport behavior does not eliminate tunability. Ultimately, the size of changes in carrier concentration directly correlate with the overall performance.

 

Fig. 4 Maps of the real part of the y-component of the electric field near the graphene in one period of the larger device. Yellow rectangles represent the gold grating while the black dotted line corresponds to the location of the graphene. (a) Field map at 1053 cm⁻¹ (9.5 μm) and E_F = 0.4 eV. (b) Field map at 1053 cm⁻¹ (9.5 μm) and E_F = 0.8 eV. (c) Field map at 1250 cm⁻¹ (8 μm) and E_F = 0.4 eV. (d) Field map at 1250 cm⁻¹ (8 μm) and E_F = 0.8 eV.

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With tuning established, we more closely investigate the underlying tuning mechanism through examination of the the electric field within the larger device during optical excitation. Plots of the simulated real part of the y-component of the electric field (ℜ(E_y)) near the graphene are shown in Figs. 4(a)–4(d) for one period of the device at two different frequencies and Fermi levels. At ω = 1053 cm⁻¹, which is between the reflection minima seen in Fig. 3(b), the electric field maps are unremarkable. The field is antisymmetric with respect to the gap, and field strength (|ℜ(E_y)|)decays monotonically with distance from the gap. Only minimal changes in this response are observed when E F is varied, as seen by the nearly identical field maps in Figs. 4(a) and 4(b). This is in good agreement with the measured results in Fig. 3(f), where the reflectance stays relatively constant at this frequency as bias is applied with ΔR < 0.5%.

In stark contrast, field plots at 1250 cm⁻¹, as shown in Figs. 4(c) and 4(d), where large changes to reflection are measured (ΔR > 17%), exhibit a periodically oscillating field around the graphene that varies with Fermi level. The periodic oscillations are indicative of excitation of surface plasmon modes in the graphene [32], which are evanescent along the y-direction and propagate in the x-direction. Vital to the functionality of our device, changing the graphene Fermi level from 0.4 eV to 0.8 eV modifies the field profiles significantly with a definitive change in both the periodicity and amplitude of the oscillating maxima and minima, suggesting a change of the plasmon wavelength. It is the coupling between the incident field and graphene plasmons that lends our device its tunability.

This understanding of tunability arising from plasmonic excitation helps to explain the limited tuning range of the lower frequency resonance in the smaller device. At frequencies between ∼1000 and 1100 cm⁻¹, graphene plasmons cannot be excited due to mode repulsion between the graphene plasmon and the SiO₂ phonons [30, 33]. In the absence of plasmon excitation, tuning does not occur. In the larger device, the selected dimensions move the two resonances to frequencies away from the strongest SiO₂ phonons resulting in increased tuning of both minima.

3. Conclusion

The devices described and measured here demonstrate the potential for graphene-based active tuning for infrared filtering. Notably, the choice of surrounding dielectrics, and the geometry itself, have a strong influence on the regions of tunability enabling devices to be designed for functionality in specific wavelength regimes. By selecting cladding dielectrics based on their phonon modes, the tuning range can be designed. Lastly, the use of unpatterned large-area commercial CVD graphene ensures the scalability of the design reducing the complexity inherent in fabrication, and also suggesting a path towards improvement through use of higher quality graphene (see Appendix B). This work points the way towards frequency agile solid-state filters that can enable hyperspectral infrared sensing without the necessity for modification of the detector itself.

Appendix A: Ideal device response

Simulations of reflectance from an ideal larger device are shown in Fig. 5. As the quality of CVD graphene is continually improving, it is useful to examine the future potential of the devices discussed here [34, 35]. These simulations assume that there are no charged impurities on the graphene (E_F = 0 eV at V_G = 0 V) and the use of a high quality HfO₂ gate that can be taken to its breakdown voltage. We employ literature values for both the breakdown field (E_BD ≈ 5.4 MV/cm), equivalent to 11 V applied across the 20 nm thick HfO₂, and the dielectric constant of HfO₂ (κ = 20) [28,36]. Based on these assumptions, we simulated a device where the graphene Fermi level can be tuned from 0 eV to 0.9 eV where the Fermi level at a given bias is obtained from the following relationship [16]:

(1)$$E_F=\sqrt{\frac{∊{∊}_0{\hslash }^2{v}_F^2\pi \left|V_G\right|}{ed}}$$

where ∊₀ is the free space permittivity, ħ is the reduced Planck constant, v_F = c /300 is the Fermi velocity with speed of light c, V_G is the applied gate voltage across a dielectric of thickness d, and e is the electron charge. The change in frequencies of the reflectance minima in these simulations are 160 and 130 cm⁻¹ for the low and high frequency dips respectively. Only positive bias is shown as the expression used for E_F depends only on the absolute value of the voltage. These simulations suggest the possibility of improved functionality through advances in fabrication quality.

 

Fig. 5 Simulated reflectance map for the larger device assuming ideal behavior. Black dots track the location of minima.

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Appendix B: Plasmonic dispersion

The plasmonic dispersion calculated for graphene on an infinite slab of SiO₂ at two different Fermi levels of 0.4 and 0.7 eV is shown in Fig. 6 [37]. Significant shifts in the excitation frequency for a given plasmon momentum are present with changing E_F. As a result, the wavelength of the plasmon excited by a given free space wavelength is modified through changes to the graphene carrier density, resulting in the changes to the periodicity of the electric field maps shown in Figs. 4(c) and 4(d).

 

Fig. 6 Graphene plasmon dispersion calculated for Fermi levels of 0.4 eV (black) and 0.7 eV (red).

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Appendix C: Sample fabrication

Commercially available chemical vapor deposition (CVD) monolayer graphene (ACS Material, Trivial Transfer Graphene) was transferred onto an n++ Si/SiO₂ substrate. The SiO₂ was composed of either a 150 nm thermally grown oxide or a 600 nm layer in which 150 nm was thermally grown and the remaining 450 nm realized with plasma enhanced chemical vapor deposition (PECVD). The graphene was then patterned using AZ5214 photoresist to protect the graphene channels and ashed in an O₂ plasma until the channels where defined. The graphene was passivated by first depositing a 1.5 nm Al layer by e-beam evaporation for proper wetting of the graphene followed by exposure to oxygen to form Al₂O₃. This allows for the adhesion of Al to graphene to be weak (physisorption) with minimal interaction with graphene’s π- or σ-bonds thereby preserving its electronic structure [38]. Furthermore, the Al₂O₃, also acts as the seed layer for the 20 nm of atomic layer deposited HfO₂ at 250°C using Tetrakis[DiMethylAmido]Hafnium (TDMAH) [39,40]. This method of passivation does not damage the graphene or degrade FET performance as we have shown previously [41]. The gratings were defined using PMMA resist and e-beam lithography. E-beam evaporation was used to deposit 50 nm of Au to construct the gratings. A Cl₂ inductively coupled plasma etch was then used to etch through the passivating HfO₂ allowing for the the source, drain and gate metals to contact the graphene via e-beam evaporation (Ti/Au 200 nm/2000 nm).

Funding

Laboratory Directed Research and Development (LDRD), Sandia National Laboratories; U.S. Department of Energy (DE-NA0003525).

Acknowledgments

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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