1. Introduction

Infrared detector arrays based on narrow bandgap, III-V semiconductors have made tremendous progress in the last decade. In particular, III-V semiconductor alloys containing antimony (i.e., InAlAsSb, including ternary and binary alloys) have a unique band structure that enables certain heterostructures to exhibit a broken gap which is advantageous in some newer detector designs [1]. These narrow bandgap semiconductors also show promise in other electronic applications such as high-frequency, low-noise high-electron-mobility-transistors [2]. The plasmonic behavior of these materials in their highly doped state has also been explored [3–5]. The ability to dynamically tune the spectral response of such detectors with a filter that may be integrated on top of the absorbing region will enable the realization of a spectrally tunable detector at the pixel level that may be of interest to many communities. Recently a metasurface for active beam steering based on these materials was theoretically discussed [6, 7].

As a step towards this highly rewarding goal, we propose here a structure that may enable spectrally tunable and/or modulated devices based on the strong coupling between a metasurface composed of complementary metamaterial resonators and epsilon-near-zero (ENZ) modes [8, 9] supported by thin, high mobility layers. The semiconductor part of the device we propose and demonstrate is made from the same constituents as a mid to long-wave infrared (IR) detector pixel (heterostructures of InAlAsSb), and thus could be grown monolithically with the detector. Figure 1(a) shows a schematic of the integrated device, where the bottom purple layer represents the detector, while the top layers show the filter portion discussed in this work.

 

Fig. 1 (a) Schematic of a voltage tunable spectral filter (top layers) monolithically integrated on a photodetector (purple). (b) Semiconductor layer stack used in this work; the epsilon-near-zero (ENZ) layer is marked with the diagonal pattern. Two thicknesses of the ENZ layer were investigated in this work: 30 and 80 nm. The cap layer is undoped InAsSb. (c, d) Experimental measurement of the ellipsometric angle Ψ for two 80 nm ENZ samples with doping levels as noted in the plots. The Berreman feature associated with the ENZ crossing is clearly visible as a dip around 14.5 µm and 11.8 µm, respectively.

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The spectral filter device is based on a principle demonstrated in earlier work in different semiconductor systems [10, 11]. In general terms, very large modifications of the transmission and reflection spectral response can be obtained when metasurfaces designed to exhibit strong dipole resonances couple strongly to different fundamental excitations present in semiconductors and their heterostructures [12]. This effect is termed strong coupling and has been observed both in the classical and quantum regimes [13–16]. It leads to the periodic exchange of energy between the two resonant systems at the Rabi frequency. In the spectral domain this is manifested as an opening of a spectral gap at the frequency corresponding to the uncoupled cavity or metasurface [17, 18]. Due to the very large coupling strength between infrared resonances created with metallic metasurfaces and some of these excitations, this spectral gap (or Rabi splitting as it is termed) can be very large throughout most of the infrared spectrum. Such large modifications of the spectral response using dipole coupling can be harnessed for active and tunable behavior provided that this coupling can be modified with external stimuli (e.g., voltage, temperature, illumination, etc.).

In this work, we choose strong coupling of metasurfaces to ENZ modes present in thin, highly doped semiconductors as the mechanism for spectral modification. ENZ modes are nearly flat-dispersion plasmon modes occurring at the plasma frequency of an extremely thin layer of a “Drude” material (e.g. metals, highly-doped semiconductors, etc.) [8, 9]. They are best observed when the electrons in the Drude layer have high mobility. The main reason for this choice is the simplicity of the additional layers that should be grown above the infrared detector stack: our design requires additional growth of a spacer layer, a thin (~20–50 nm) high-mobility region, and a barrier layer (the latter could be replaced with a gate dielectric for more efficient biasing). Additionally, we implement a complementary metasurface for the strongly coupled system that has a more desirable transmission spectrum, i.e. the transmission of the uncoupled metasurface resembles a bandpass filter. Importantly, this complementary metasurface offers a continuous gold top layer that can be used later to bias the spectral filter portion of the device should this be desired.

With this platform, we experimentally demonstrate a large Rabi splitting of approximately 29% of the center frequency (~900 cm⁻¹, ~11.8 µm). We further observe that the splitting in the ENZ/metasurface system increases with the thickness of the epitaxial layer supporting the ENZ mode, in agreement with previous works [19, 20]. Finally, we present a numerical study of the electrical tuning capabilities of the proposed device. This demonstration is an important step towards the implementation of a tunable filter and detector in one integrated semiconductor stack.

2. Design and Fabrication of the Strongly Coupled Metasurface-ENZ System

Since our end goal is to make an electrically tunable passband filter, we take this into account in every step of the design, fabrication, and measurement, as explained below. Our target spectral region is the long-wave IR and thus we choose the doping density of the ENZ layer that provides a plasma frequency of ~900 cm⁻¹ (~11 µm). Using published values of effective masses in the binary semiconductor constituents and models to account for changes with high doping densities, we chose an initial target doping density of 2.5 × 10¹⁸ cm⁻³. The ENZ layer is made from InAs_0.91Sb_0.09 which is lattice matched to the GaSb substrate and provides the best compromise between low strain-induced defects and high electron mobility. Additionally, the low effective mass of InAsSb alloys enables targeting plasma frequencies higher than 1000 cm⁻¹, which could be an important consideration in scaling these concepts to shorter IR spectral bands. Due to unknowns in donor activation and conduction band nonparabolicity, spectral ellipsometry and growth iteration were necessary in order to hit the target plasma frequency.

Semiconductor layers of highly n-doped, lattice-matched InAsSb (the ENZ layer) were grown using molecular beam epitaxy on GaSb substrates with a GaSb and InAsSb buffer and an AlSb/InAsSb spacer/cap layer. The spacer layer will function as an electrical barrier to prevent current flow if the device should be electrically biased. The mildly doped InAsSb buffer layer will act as a back contact for the application of bias. Samples were grown with two ENZ layer thicknesses but with identical nominal doping, and will be referred to as ‘30nm ENZ’ and ‘80nm ENZ’, respectively. Figure 1(b) depicts a cross section of the grown layers including the top Au complementary metasurface. The ENZ point was measured (prior to gold deposition) with ellipsometry by observing the absorption feature associated with the Berreman mode [21, 22].

Ellipsometry measurements (performed using a J.A. Woolam IR-VASE Ellipsometer) provide the quantity $\tan \left(\psi \right)e^{\left(i\Delta \right)}=\frac{R_p}{R_s}$, where$R_p$and$R_s$are the complex p- and s-polarized reflection coefficients. The measured$\psi$and$\Delta$quantities are then fit to desired models using the WVASE software to extract the optical parameters of the models. Figures 1(c) and 1(d) show the measured ellipsometric angle$\psi$as a function of wavelength for two ‘80nm ENZ’ samples having different doping densities (2.5 × 10¹⁸ cm⁻³ and 4.5 × 10¹⁸ cm⁻³, respectively) as noted in the plots. The data depicted in Fig. 1(c) was used to calibrate the nominal-doping-to-plasma-frequency (zero crossing of the real part of the permittivity) relationship while the data presented in Fig. 1(d) also depicts the fitted data using the model reported in the Appendix. As can be seen in Figs. 1(c) and Fig. 1(d) the “Berreman dip” [21] appears at 14.5 µm and 11.8 µm for the two wafers, in accordance with the ENZ frequency location. The aforementioned calibration was done by adjusting the carrier concentration used to calculate the Drude parameters (see Appendix and [23]) in order to reproduce the frequency position of the measured Berreman dip. This effective carrier concentration can be slightly different than the nominal doping target due to limited dopant activation and variations in dopant incorporation. From this ellipsometry data together with additional control measurements we are able to extract the permittivities of the various layers; these data are tabulated in the Appendix and are used for the numerical simulations reported in this manuscript. The electron mobility calculated from the data presented in Fig. 1(d) can be estimated at 48000 - 73000 cm²/Vs depending on doping activation. The wafers used for the experiments described below are only from the second growth run [Fig. 1(d)]. Ellipsometry data of the ‘30nm ENZ’ did not resolve the Berreman dip due to the lowered thickness, but the presence of the ENZ crossing is confirmed by the Rabi splitting discussed below.

We optimize the metasurface design using finite-difference time-domain (FDTD) simulations [24]. In prior publications, we have demonstrated that metasurface designs with high capacitance (such as metallic dogbones) are required to maximize the Rabi splitting in metasurface strongly coupled systems [25, 26]. We use the permittivities extracted from the ellipsometric data as input for our FDTD simulations. The optimized metasurface dimensions are given in Fig. 2(a). The optimization is done so that the resonance overlaps with the measured ENZ crossing of the doped semiconductor layer i.e., in these simulations we artificially ‘turn-off’ the Drude component of the doped layer permittivity. We then fabricate the metasurface by electron beam lithography (100 keV accelerating voltage, 2 nA nominal current, 60 µm aperture, base dose 330 µC/cm²) exposing a negative tone resist (maN-2403) followed by metal evaporation (5 nm Ti and 100 nm Au). We finish the process with standard lift-off. A scanning electron micrograph (SEM) of a typical array is shown in Fig. 2(b). Figure 2(c) depicts a simulated transmission spectrum of the bare cavity resonance as was used in the optimization process.

 

Fig. 2 (a) Dimensions of the metasurface unit cell as optimized by finite-difference time-domain simulations. (b) Scanning electron micrograph of a typical fabricated metasurface. (c) Simulated transmission spectrum of the bare cavity resonance as was used in the optimization process.

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Several metasurfaces were fabricated on the same die with the lateral unit cell dimensions scaled above and below the optimal size using a parameter we define as ‘scaling factor’; this enables us to ‘scan’ the metasurface resonance across the ENZ frequency and map the polaritons of the strongly coupled system. Transmission and reflection measurements are performed in a microscope equipped Fourier-transform-infrared (FTIR) spectrometer. The measured spectra are referenced to a region of the sample with continuous gold for reflection, and a region with no gold (i.e. only the semiconductor stack) for transmission.

3. Results

Figures 3(a) and 3(b) present the measured and simulated transmission curves as a function of the metasurface’s scaling factor for the ‘30nm ENZ’ sample. In these figures each vertical slice corresponds to one transmission measurement and then all the graphs are stacked as a color-coded two-dimensional plot. By following the peaks in transmission we can observe a clear anti-crossing behavior both in the simulated and the measured spectra and a corresponding Rabi splitting; both experiments and theory are in very good agreement. The discrepancy visible for the smaller scaling factors can be attributed to various fabrication imperfections having a higher impact for smaller features: (a) Proximity effects (resulting in smaller resonators with higher resonance frequency). (b) Edge roughness, as seen in the SEM image in Fig. 2(b), resulting in increased losses and wider resonance features. For comparison we give in panel (c) a similar plot for the simulated case where no free carriers are present thus removing the ENZ mode; one can note that the polariton splitting signature of strong coupling is absent in this simulation. Figure 3(d) [Fig. 3(e)] presents the measured [simulated] reflection data for the ‘80nm ENZ’ sample. Transmission measurements of this sample were very noisy due to the high absorption of the thick ENZ layer. In this data, the reflection dips provide a possible signature of strong coupling.. For comparison, Fig. 3(f) depicts the simulated ‘no ENZ’ case for the ‘80nm ENZ’ sample: one can again note the absence of the polariton splitting signature of strong coupling. All curves are renormalized to the [0,1] interval for clarity.

 

Fig. 3 (a) Experimental FTIR transmission curves as a function of scaling factors for the ‘30nm ENZ’ sample. (b) Same as (a) but simulated in FDTD. (c) Simulated transmission spectra for the bare cavity: no polariton splitting is observed in this case. (d) Experimental FTIR reflection curves as a function of scaling factors for the ‘80nm ENZ’ sample. (e) Same as (d) but simulated in FDTD. (f) Simulated reflection spectra of the bare cavity. All curves are normalized to the [0,1] interval.

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In Fig. 4 we examine the reflection spectra at the exact anti-crossing point for the two samples. Panel (a) is from the ‘80nm ENZ’ sample, scaling factor 1.4 and panel (b) from the ‘30nm ENZ’ case, scaling factor 1.2. As opposed to Fig. 3 here we present the spectra without the [0,1] renormalization. We see very good agreement between simulation and experiment with regard to the energetic position of the two polaritons: the discrepancy in amplitude can be explained by our measurement setup’s sensitivity to the exact position of the sample with respect to the focal plane. We estimate the coupling strength through the ratio of the energy splitting between the two polaritons (i.e., Rabi frequency) and the uncoupled ENZ frequency. We arrive at a value of 22% for the ‘30nm ENZ’ sample and 29% for the ‘80nm ENZ’ sample. Such high ratios of Rabi splitting to the uncoupled modal frequency are indicative of strong (to ultra-strong) coupling [13, 27–29]. We also note that the ‘80nm ENZ’ sample shows a more significant variation between the minimal and maximal reflection. The latter observation may be significant when considering that this device will act as a filter: this is because one of the important parameters characterizing a filter is the transmission ratio between the blocked and passed bands.

 

Fig. 4 (a) Experimental and simulated reflection curves at the anti-crossing point, scaling factor 1.4 for the ‘80nm ENZ’ sample. (b) Same as (a) but for the ‘30nm ENZ’ sample and 1.2 scaling factor.

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In the following, we discuss the possibility of controlling the spectral behavior of the coupled metasurface shown above using a voltage bias. As we stated earlier, controlling the spectral response using a voltage bias would turn an IR pixel into a 3-terminal device that could be attractive for new applications requiring hyperspectral capabilities or new modalities in modulated detection. The obvious solution to tune the spectral response of the coupled metasurfaces is to modulate the electron density in the ENZ layer using an external bias. Depletion of carriers as a tuning mechanism for metasurfaces has been extensively discussed in the past [10, 11, 30, 31] and the largest impediment is the inversely proportional relationship between depletion width and carrier density [32]. Thus, at the high doping densities used here, the maximum expected depletion width is of the order of ~10 nm, as determined by electrostatic band-structure calculations for this system. This small value is also due in part to the “early” onset of inversion which characterizes low bandgap semiconductors. Moreover, in some preliminary studies (not reported here) we find that the effective electrical barrier in this semiconductor heterostructure does not permit significant reverse bias without large leakage currents; this further limits the actual depletion widths achievable. Some of these issues can be circumvented using a gate dielectric instead of a semiconductor barrier with the added advantage of creating a small accumulation region under positive bias. This represents the largest possible swing in carrier density, but such study is outside the scope of this paper. Nevertheless, we present some numerical results to highlight the potential of such an approach.

Figure 5 shows the effect of carrier redistribution in the ENZ layer on the transmission spectrum. We compare three cases relative to the ‘30nm ENZ’ sample analyzed above: a fully depleted ENZ layer, a partially depleted ENZ layer (with depletion depth of 10 nm, which was chosen based on an achievable depletion length in electrostatic band-structure calculations [33]) and an ENZ layer under charge accumulation. Depletion (accumulation) is modeled here by removing (changing) the Drude component in the permittivity function of the ENZ layer; these cases are schematically shown in the inset of Fig. 5. We model the cases described above by artificially splitting the ENZ layer into two separate layers: (a) ‘depleted (accumulated) layer’, represented in the sketch by a dotted layer, in which the Drude component in the ENZ permittivity is modified and (b) ‘undepleted layer’ (hashed layer in the sketch) which includes the original Drude permittivity. The plot in Fig. 5 suggests that a partial depletion of the ENZ layer will have a significant effect on the transmission properties of the device, for example at 800 cm⁻¹ there is a 25% difference in transmission between the unbiased case and the partially depleted device. We also note that according to this simplified model, no significant change is expected due to operating the device in accumulation mode.

 

Fig. 5 FDTD simulations showing the transmission spectrum of the device with 30 nm ENZ layer under various carrier depletion/accumulation conditions. The inset depicts a schematic of the simulated structure with carrier density modification.

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4. Conclusion

We have experimentally demonstrated the first steps toward achieving a spectrally tunable band-pass filter that is monolithically integrable with infrared photodetectors based on the so called “6.1Å semiconductor system” (i.e, InAs, GaSb, AlSb, their ternaries and quaternaries). These included the demonstration of strong-coupling between the resonance supported by a complementary metasurface made of voids in a metallic thin film and matter-resonances consisting of ENZ modes in a highly doped semiconductor. We witness a large coupling strength, with a Rabi frequency of ~29% of the uncoupled resonance frequency (~900cm⁻¹). We show that an increased thickness (while still smaller than the decay length of the near fields around the cavities) leads to stronger coupling. This coupling may enable tuning of the optical properties by changing the electronic characteristics of the ENZ layer. We explore this numerically by artificially depleting the ENZ layer and observing a modulation on the order of 25% in the transmission characteristics when employing a reasonable depletion width. Finally, we note that the high electron mobilities obtained at room temperature and at high doping densities for InAsSb alloys could open new opportunities for tunable plasmonics and metasurfaces using heterostructures of low bandgap semiconductors.

Appendix Optical constants of the III-Sb based system

For the ellipsometry fitting, we use Drude oscillators: $\epsilon (\omega )=\frac{i}{\rho \omega \left(1-i\omega \tau \right)}$, where τ is the mean time between collisions, ρ is the resistivity, and ω is the angular frequency. We assume the relations [23]: $\rho =\frac{1}{ne{\mu }_e}$ and $\tau =\frac{{\mu }_e{m}^{*}}{e}$, where e is the elementary charge, n is the effective free electron density, ${\mu }_e$ is their mobility and m* their effective mass. We also use Gaussian oscillators: ${\epsilon }_2(E)=A{e}^{-{\left(\frac{E-E_n}{Br}\right)}^2}-A{e}^{-{\left(\frac{E+E_n}{Br}\right)}^2}$, where A is the amplitude, E_n is the transition energy associated with the oscillator, Br is the linewidth of the transition, ε₁ is calculated through the Kramers-Kronig relations, and Sellmeier coefficients. All values are given below. Our Gasb Substrate is modeled with ε_∞=14.436 and Drude parameters of: ρ~1.256x10⁻³ Ωcm and τ~392 fs. The lightly doped InAsSb layer is modeled as ε_∞=9.051, Drude parameters of ρ~25.3x10⁻³ Ωcm and τ~88 fs and Gaussian oscillators as in Table 1.

Table 1. Gaussian Oscillator parameters in our lightly doped InAsSb layer.

View Table

The 30nm ENZ layer has ε_∞=0.566 and Drude parameters of: ρ~1.62x10⁻³ Ωcm and τ~25 fs, one Gaussian with A=307520, E_n=0.1 meV and Br=8.72 eV and one Sellmeier Pole at 1 meV with a magnitude of 0.04.

The 80nm ENZ layer has ε_∞=2.498 and Drude parameters of: ρ~1.69x10⁻³ Ωcm and τ~42 fs one Gaussian with A=283620, E_n=0.1 meV and Br=10 eV and one Sellmeier Pole at 1 meV with a magnitude of 0.08.

The AlSb data is taken from the WVASE database [34] and fit to a model having one Sellmeier pole at 1.5809eV with a magnitude of 3.9634 and ε_∞=8.7967.

Note that ε_∞ should not be interpreted as the high frequency dielectric constant; this value can be obtained by summing the contributions of all the oscillators, e.g. for the ENZ layers these include the Drude and Gaussian oscillators and a Sellmeier pole.

Funding

U.S. Department of Energy Office of Basic Energy Sciences; Laboratory Directed Research and Development; Center for Integrated Nanotechnologies; Sandia National Laboratories (DE-AC04-94AL85000).

Acknowledgments

The theory and design part of this work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering and by Sandia’s Laboratory Directed Research and Development program. The experimental work was supported by Sandia’s Laboratory Directed Research and Development program and performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

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