1. Introduction

The fields of plasmonics and metamaterials have seen rapid recent growth, in part fueled by the desire to control and utilize light on a subwavelength scale. Exciting new phenomena, including negative refraction and superlenses [1,2], electromagnetic cloaks [3,4], and ideal optical couplers [5] have demonstrated the potential promise of metamaterial structures. Simultaneously, applications such as enhanced sensing [6] and energy collection [7], beam steering and shaping [8], subdiffraction-limited waveguiding [9], and subwavelength light emitters [10–13] have made plasmonics an exciting and vibrant new field of research. Central to both fields is the use of metals, either as a constituent material of subwavelength geometry in composite metamaterials, or for wave -guiding or -localization in plasmonic structures. Traditionally, most metamaterial and plasmonic structures utilize the noble metals silver (Ag) and gold (Au) as their metallic components across a wide range of optical frequencies. At short wavelengths, where the permittivities of traditional metals are negative and small in magnitude, optical losses in the metals of plasmonic and metamaterial structures present a formidable obstacle to large scale implementation of such structures for optoelectronic and photonic applications. At longer wavelengths, such as the terahertz (THz) and mid-infrared (mid-IR), the permittivities of these metals are negative and quite large in magnitude, significantly altering the optical properties of metal/dielectric composites, especially in the near field.

The mid-IR is a vital wavelength range for a variety of sensing, security, and defense applications, as it is the home to numerous fundamental molecular absorption resonances as well as the blackbody emission from biological and mechanical objects over a wide range of temperatures. There has been significant recent interest in applying the advances in metamaterials and plasmonics at shorter wavelengths to a new class of structures in the mid-IR. Such structures have been used, for example, as designer meta-surfaces for control of thermal emission [14–16], or integrated into sensing systems designed to enhance the interaction between incident radiation and molecular absorption resonances [17].

For plasmonic materials, it is useful to differentiate between two distinct plasmonic excitations. The first, propagating surface plasmon polaritons (SPPs), are collective charge oscillations in a metal coupled to an electromagnetic wave in a dielectric which propagate at and along the metal/dielectric interface. The second, localized surface plasmon resonances (LSPRs), are coherent charge oscillations bound to the surface of metallic particles much smaller than the wavelength of the exciting light source. At wavelengths where the real part of the metal permittivity is small and negative, both SPP and LSPR excitations can be confined to length scales much smaller than the wavelength of light. It is this subwavelength volume of the plasmonic modes which makes them so attractive for both nanophotonic (subwavelength waveguides and laser cavities) and sensing (strengthened interaction with molecules by means of field localization and enhancement) applications.

For SPPs, scaling from short wavelengths to the longer wavelength mid-IR can be achieved simply by appropriate scaling of the plasmonic device geometry, resulting in very similar far-field optical signatures, as has been demonstrated, for instance, with extraordinary optical transmission gratings and plasmonic beam steering structures [18,19]. In the near field, however, the behavior of these structures is markedly different [20]. The large and negative permittivities of the noble metals at long wavelengths result in weakly bound propagating modes which extend deep into the dielectric material. While these modes can propagate for long distances, their confinement is nowhere near subwavelength in the mid-IR, precluding the strong field enhancement achievable at shorter wavelengths. For the LSPR, excited on a single subwavelength plasmonic particle, the difference is even starker. Such an LSPR can be supported when the real part of the metal’s dielectric constant is negative and approximately equal to that of the surrounding dielectric, as will be discussed in greater detail below. The very large negative permittivity of the noble metals in the mid-IR thus precludes the excitation of the LSPR on single subwavelength-sized particles in this wavelength range. However, the mid-IR does offer significant flexibility for the plasmonics researcher willing to look past traditional plasmonic materials. In particular, highly doped semiconductors offer a potential replacement for noble metals at long wavelengths. The optical response of a doped semiconductor can be modeled using the Drude formalism:

The optical properties of highly doped semiconductors are not entirely unexplored. In fact, early long-wavelength quantum cascade lasers utilized highly doped semiconductor layers for surface plasmon polariton-based mode confinement [22]. SPP-mediated selective thermal emission from patterned doped silicon with ε<0 has been observed [23], and more recently, further studies of highly doped silicon have demonstrated SPP excitation across a wide range of the mid-IR [24,25]. Highly doped semiconductors have also been used to demonstrate enhanced transmission at epsilon-near-zero wavelengths when a single layer is placed under a subwavelength aperture [26] as well as negative refraction in anisotropic metamaterial structures consisting of alternating highly doped and undoped layers [27]. Especially relevant to this work, highly doped InAs in GaSb/InAs heterostructures has recently been proposed as a promising material system for active plasmonic devices in the mid-IR [28]·

Here we experimentally demonstrate epitaxially grown InAs with design-able metal-like optical properties at longer wavelengths. We show that by controlling the doping of our material, we can shift the material plasma wavelength across a broad range of mid-IR wavelengths (5.5-15µm). In addition, we demonstrate that subwavelength features fabricated from our highly-doped InAs exhibit localized surface plasmon resonances. Finally, not only do our materials behave as plasmonic metals at these longer wavelengths, but they can be designed to be optically transparent out to telecom wavelengths, and thus have the potential for integration with existing semiconductor-based optoelectronic devices and materials. These results indicate the potential of highly-doped InAs as wavelength flexible, epitaxially-grown, designer metals for mid-IR plasmonic and metamaterial structures.

2. Material growth, fabrication and experimental set-up

The highly-doped semiconductor films studied in this work consist of silicon-doped InAs grown on semi-insulating GaAs substrates using an SVT molecular beam epitaxy (MBE) system. Single-side polished GaAs wafers are used to prevent the Fabry-Perot oscillations seen in double-side polished substrates from interfering with our sample spectra. The large lattice mismatch between the InAs epilayer and the GaAs substrate results in extremely poor quality epitaxial growth near the GaAs/InAs interface. For this reason, thick InAs films were grown (>1μm) in order to allow the majority of dislocations to terminate, resulting in reasonably high quality InAs material for a significant fraction of the total epilayer thickness. A streaky RHEED pattern indicative of 2D film growth was visible during growth and RHEED oscillations were used to calibrate the InAs growth rate. Following growth, portions of the InAs layers were selectively wet-etched from the GaAs substrate and profilometry measurements made in order to verify epilayer thickness. Sample thicknesses, shown in Table 1 , include the uncertainty resulting from thickness measurements using RHEED, profilometry, and optical characterization. Hall measurements were taken to characterize the films and the resulting mobilities and carrier concentrations for our samples can be seen in Table 1.

Table 1. Experimental and Calculated Film Data

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As can be seen from Table 1, the carrier concentration for the most heavily-doped films is extremely high. For many semiconductors, dopants become amphoteric (able to act as either an acceptor or donor) at much lower concentrations than those utilized in this work. InAs, however, differs from the vast majority of semiconductors in its ability to sustain extremely high doping concentrations. As discussed by Tokumitsu [29] and Zhang [30], when n-type dopants are added to a semiconductor, the Fermi level increases until it reaches an energy described as the Fermi level stabilization point. As the dopant concentration is increased past this point, subsequent dopants are amphoteric, and the electron concentration of the material cannot be increased. These early works studying dopant limits in III-V semiconductor crystals suggest that the reason InAs can be doped so heavily is a result of its unusually high Fermi level stabilization point. For InAs, the stabilization point is well within the conduction band, allowing InAs to support a large electron dopant density. Tokumitsu predicted n-type InAs could contain up to 1 × 10²⁰cm⁻³ carriers, a concentration even higher than the values reported here.

Optical transmission and reflection data was collected on both the as-grown InAs epilayers, in order to determine the bulk optical properties of the highly doped InAs, as well as our patterned disc arrays, in order to demonstrate localized surface plasmon resonances of subwavelength particles formed from our designer metal material. In order to fabricate the discs, the bulk InAs films were patterned into an array of dots using standard UV-lithography followed by a wet chemical etch using a HBr:HNO₃:H₂O (1:1:10) etchant. The geometries of the fabricated disc samples were characterized by surface profilometry and scanning electron microscopy (SEM). Two disc samples for each film were fabricated: one with a disk diameter of 1.7μm and an array periodicity of 3.4μm and the second with a disk diameter of 1.2μm and an array periodicity of 2.4μm.

The reflection and transmission of both the films and discs were measured with a Bruker V70 Fourier transform infrared (FTIR) spectrometer across a spectral range spanning from 650cm⁻¹ to 8000 cm⁻¹ (1.25μm to 22.5μm) using both the mid-IR and near-IR internal sources of the FTIR. For the transmission measurements, light is focused on the sample surface through a ZnSe focusing lens and collected on the back side of the sample with a ZnSe lens pair, which collimates and refocuses the transmitted light onto the external detector. Transmission measurements for the as-grown epilayers are normalized to a semi-insulating GaAs substrate. This is done to remove the effects of the GaAs substrate from the transmission data and allow a more accurate comparison with our model. Transmission data from our patterned discs, however, are normalized to free space transmission spectra (no sample), as the signal from the patterned discs above a GaAs substrate cannot be extracted from that of the GaAs substrate with a simple normalization process. For reflection measurements, a ZnSe 50/50 beamsplitter is placed in the beam path of the focusing light. Half of the light reflected off the sample surface is directed by the beamsplitter to a second lens pair, which collimates and focuses the light on the detector. Reflection spectra are normalized to an optically thick layer of evaporated gold, which will behave as a near perfect reflector in the mid-IR. For the experiments in this work, we use an external HgCdTe (MCT) detector with a 22.5µm cut-off wavelength.

For the modeling, a 2-D COMSOL simulation was designed with a single disc of dimensions 1.7 μm (width) x 1.6 μm (height) in a unit cell of width 3.4 μm flanked on either side by boundaries with Floquet boundary conditions applied, effectively resulting in an infinite 1-D array of pucks. The space in the cell beneath the puck was modeled with a relative permittivity of 10.9, corresponding to semi-insulating GaAs, and the rest of the space was modeled as air. The top and the bottom of the cell employed perfectly matched layers in order to eliminate non-physical reflections. To accurately model the dispersion of the doped InAs material comprising the puck, the simulation included the optical data for the InAs epilayer material as determined from the experimental optical characterization of the layers. The simulation ran a frequency sweep over the range of 5-15 μm, with each step parameterized with the appropriate material properties for the puck, and having a spectral resolution approximately corresponding to that of the FTIR with which the experimental optical data was obtained. In this manner far-field spectra for the structure could be obtained, as well as contour plots of the resistive heating loss (absorption) in the puck itself.

3. Results and discussion

In order to characterize the bulk optical properties of our highly doped InAs films, we first perform reflection and transmission measurements on the as-grown material. Figure 1(a) shows the reflection data from our samples, normalized to reflection from a flat gold surface. For an undoped semiconductor, the reflection of incident light is given by Fresnel’s equations, and remains relatively constant (R~30%) at normal incidence for a wide range of mid-IR wavelengths. The reflection data shows a transition from the ~30% reflection expected at shorter wavelengths, to a high reflectivity state at longer wavelengths, as the material moves through the transition from positive to negative real permittivity. Figure 1(b) shows the transmission data through the as-grown samples, normalized to transmission through a GaAs substrate. For both transmission and reflection data, oscillations are observed (the strongest of which results in the near null of reflection for the most highly doped samples) resulting from the Fabry-Perot cavity formed by the InAs epilayer and the GaAs/InAs and InAs/air interfaces. At short wavelengths, the normalized transmission can give a value greater than one, also due to Fabry-Perot reflections in the InAs epilayer, which can, at certain wavelengths, give transmission greater than the GaAs substrate used for normalization.

 

Fig. 1 (a) Experimental (solid lines) and modeled (dashed lines) reflection spectra for as-grown InAs layers of varying doping concentrations, normalized to reflection from a flat, optically thick, gold surface. (b) Experimental transmission spectra for the same samples. The experimental transmission spectra in (b) have been normalized to transmission through a GaAs substrate.

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In order to extract the permittivity data for our as-grown InAs, we assume the material permittivity can be approximated using the Drude formalism, given in Eq. (1). With the InAs background permittivity known, as well as the InAs layer thickness, we can fit our transmission and reflection data using the process described in [31], using only the scattering rate (Γ) and plasma frequency (ω_p) as fitting parameters. The extracted values for scattering time (1/Γ) and the plasma wavelength (λ_p = 2πc/ω_p) are given in Table 1 along with the calculated plasma wavelength for each sample which was determined by using Hall measurements of our doping concentration and the InAs effective mass, taking into account the doping dependent non-parabolicity of the InAs conduction band [32]. Because the reflection data fitting process is an indirect measurement of permittivity, there is some finite range of scattering times which allow for an accurate fit to the experimental data, a fact that is reflected in the scattering time uncertainties given in Table 1. As can be seen in Fig. 1(a), the modeled reflection spectra calculated using our fitting parameters match well to the experimentally obtained data. While the fitting for the transmission data replicates the experimentally observed spectral behavior of our films, it does not accurately capture the amplitude of the transmitted signal, due to the large (sample-variable) disorder and losses which occur at the GaAs/InAs interface. This effect was noted in previous work with highly mismatched doped layers [26].

Figures 2(a) and 2(b) show the real and imaginary components of the extracted dielectric constants for our five highly doped InAs samples. As can be seen from Fig. 2(a), by controlling the doping of our InAs layers, we are able to shift the spectral position of the transition from positive to negative ${\epsilon }^{\prime }$in our material from 15µm (for the most lightly doped sample) to wavelengths as short as ~5.5µm (for our most heavily doped sample). This clearly shows the wavelength flexibility of our highly doped InAs across a large portion of the mid-IR spectrum. Figure 2(b) shows the magnitude of the imaginary component of the InAs permittivity ($\epsilon \text{"}$) as a function of wavelength. Clearly, at any IR wavelength, both the real and imaginary components of the doped InAs permittivity are significantly smaller than that of traditional plasmonic metals, such as gold or silver [33]. A better, if still imperfect, method for comparison of different material systems designed for different wavelength ranges, might be the values of $\epsilon \text{"}$at ${\epsilon }^{\prime }\approx 0$. For the five samples shown here, $\epsilon \text{"}$ at ${\epsilon }^{\prime }\approx 0$ varies from magnitudes $\epsilon \text{"}<0.5$ (for samples 012 and 009) to $\epsilon \text{"}\approx \text{2}$(for samples 005 and 013). Comparison of the imaginary component of our material permittivity to that of traditional plasmonic metals such as gold and silver at ${\epsilon }^{\prime }\approx 0$gives smaller values for our doped InAs [33]. However this comparison is somewhat skewed, due to the presence of interband absorption resonances in the noble metals near the metals’ plasma frequency. When comparing our highest-quality samples to the more recently demonstrated plasmonic oxides and nitrides [21], we see very similar values of $\epsilon \text{"}$for both material systems.

 

Fig. 2 Wavelength-dependent (a) real and (b) imaginary parts of the permittivity of our five InAs epilayers, calculated from the modeled fits of our experimental reflection data from the as-grown samples using the Drude model. Range of real and imaginary permittivity values results from the uncertainty in the fitted scattering rate, Γ.

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While our InAs material losses compare favorably with plasmonic metals in other wavelength ranges, we do observe a significant variation in $\epsilon \text{"}$at ${\epsilon }^{\prime }\approx 0$across our grown samples, due in part, we believe, to variations in growth rate, substrate temperature, and epilayer thickness. However, we believe our material system is not yet fully optimized, and that adjustment of MBE growth parameters (i.e. substrate temperature, deposition rate), as well as mitigation of strain-induced defects by growth on alternative substrates (InAs, GaSb) or by utilization of metamorphic buffer layers could significantly improve material quality. Efforts are currently underway to better understand the relationship between our MBE growth process and our material quality.

The use of narrow gap semiconductor material for mid-IR applications brings with it natural concerns over the spectral bandwidth of these material systems. Interband absorption at energies higher than the semiconductor bandgap would normally preclude integration of narrow band semiconductors into optoelectronic systems designed for shorter wavelengths. However, at short wavelengths the optical properties of the highly doped InAs studied in this work are rather different from undoped InAs. Figure 3 shows the transmission at short wavelengths through our as-grown material, normalized to transmission through the GaAs substrate (which is still transparent in the range studied). For each sample, a cut-off in transmission is observed with decreasing wavelength, a result of interband absorption in the InAs. Interestingly, the spectral position of this cut-off varies significantly with doping, with the more highly doped samples showing high transmission out to wavelengths shorter than 1.5µm. The short wavelength transmission observed in Fig. 3 is consistent with the well-understood Burstein-Moss effect [34,35]. As the doping of the semiconductor increases, states in the conduction band are filled, preventing the excitation of a valence band electron into these filled states. The larger the doping, the higher in energy the state filling extends, effectively increasing the bandgap of the InAs epilayer. As shown in [36], the band gap energy shift is given by

 

Fig. 3 Short wavelength transmission though our as-grown InAs epilayers showing, for the most highly doped samples, strong transmission beyond 2 µm. Inset shows the product of the doping-dependent effective mass ($m_n^{*}(n)/m_e$) and the bandgap energy shift as a function of n^2/3. Red line is a linear fit to the data.

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In order to demonstrate the potential of highly doped InAs as a mid-IR plasmonic material, we fashioned subwavelength particles from our epi-grown InAs. As noted above, and quantitatively described in Eq. (3), individual subwavelength noble metal particles cannot support LSPRs in the mid-IR, irrespective of particle size, due to the large negative real component of the metals’ permittivity. In order to demonstrate our designer metals’ ability to support such modes in the mid-IR, disc arrays of the five films were fabricated and their reflection and transmission spectra measured. Representative spectra for discs fabricated from sample 009 are shown in Fig. 4 , with transmission represented as solid lines and reflection as dashed lines. Data for dots with diameters of 1.2μm and 1.7μm are shown. The transmission data is normalized to free space transmission and the reflection normalized to a gold mirror.

 

Fig. 4 (a) Transmission (solid lines) and reflection (dashed lines) data for 1.7µm (red lines) and 1.2µm (black lines) dots fabricated from wafer 009. The transmission data is normalized to air and the reflection to a gold mirror. (b) SEM image of the dots measured in (a) taken at a 45 degree tilt.

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The optical properties of the subwavelength highly-doped InAs particles in the mid-IR should resemble those of noble metal nanoparticles in the visible frequency range. In each case, the particle can be thought of as a background of positive ions surrounded by a cloud of electrons. Incident electromagnetic radiation, at resonance, will excite charge density oscillations in the particle, leading to strong absorption signatures and an enhancement of the local electric field. For strongly-subwavelength particles, we can approximate the incident field using the quasi-static approximation, where it is assumed that the particle is excited by a time-varying electric field which is constant across the nanoparticle, thus allowing the quasi-static Maxwell’s equations to be applied.

Here we will use the quasi-static approximation to determine the extinction coefficient for our nanoparticles. This approximation is not strictly valid for these devices, as it assumes that the particles are both spherical and much smaller than the wavelength of light (a/λ<0.1 where a is the particle radius), but we will see that the prediction matches the data well, an agreement that is supported by our numerical simulations. The expression for the electric field outside of a spherical nanoparticle can be written as a sum of the incident radiation field and the field of the excited plasmon resonance [37], and from this we can write the extinction coefficient for a metal nanoparticle as [38]:

Dips in both the transmission and reflection spectra at approximately 9μm correspond to the LSPR of our subwavelength structures. These resonances are strongly visible in the 1.7μm spectra, weakly visible for the 1.2μm transmission data, and absent for the 1.2μm reflection data. It should be noted, however, that though the strength of the resonance changes with the size of the disc, its spectral position does not, as is expected for the LSPR in spherical particles which can be modeled using the above dipole approximation. In addition, it can be seen that the reflection minima are slightly red-shifted from the transmission minima. For plasmonic nanoparticles, the extinction efficiency as a function of wavelength is a sum of the wavelength-dependent absorption and scattering efficiencies, whose maxima, while close, do not coincide spectrally. In addition, the intensity of scattered light collected from the plasmonic particle array is dependent on the collection angle. Our reflection experiment measures absorption and back-scattered light over a fixed solid angle, while our transmission experiment measures absorption as well as forward-scattered light over fixed solid angle. The difference in the intensity of the collected forward and backward scattered light between our reflection and transmission measurements can slightly shift the observed minima in each spectra.

We can also use Eq. (3) to determine the expected strength of the resonance for samples with different dot radii. A sample with larger dots will have a larger Q per dot but fewer dots sampled in a given beam spot size. By determining the number of dots sampled on both the 1.7μm sample and the 1.2μm sample and using the different radii for each sample, we can see that a 40% larger resonance is expected for the 1.7μm sample, qualitatively consistent with our experimental observation. Quantitatively, we see a larger signal (>40%) from the 1.7μm diameter sample when compared to the 1.2μm sample, possibly due to the increased effect of fabrication-related damage as a function of the individual discs’ surface area/volume ratio.

A plot of the modeled extinction coefficient and the measured transmission for the 1.7μm particles measured in Fig. 4 can be seen in Fig. 5(a) . Both the position and width of the predicted resonance fit the data nicely. The slight shift in the predicted resonance position can be attributed to a combination of the non-spherical nature of our plasmonic particles as well as the fact that the calculated extinction includes both scattering and absorption, while our transmission measures only a small solid angle of the forward-scattered light.

 

Fig. 5 (a) Experimental transmission data (red curve) for the 1.7μm dots fabricated with sample 009 compared with the calculated dipole extinction curve (blue curve) and the numerically simulated absorption (green curve). Contour plots of resistive heating (W/cm³) showing the simulated resistive losses (absorption) for the pucks at (b) λ = 8.05µm (c) λ = 8.94µm (on resonance) and (d) λ = 10.05µm.

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An even stronger agreement is seen between our experimental results and our numerical simulations. In Fig. 5, the simulated magnitude of the resistive heating in our plasmonic particles is plotted as a function of wavelength (green). This signal represents the modeled absorption efficiency in the plasmonic nanoparticles, with no scattering signal. Spectrally, the simulated absorption peak aligns well with the dip in our experimental transmission, suggesting that our transmission experiment is a reasonably accurate representation of the plasmonic particle absorption. The slight shift in the modeled absorption peak, when compared to our experimental data, may be the result of the 2D model used to simulate the 3D fabricated and characterized structures. Figures 5(b)–5(d) show contour plots of the resistive heating in our particles (each on the same color scale). A strong signal is seen at resonance (Fig. 5(c)), as expected, corresponding to the incident light absorbed at the LSPR resonance.

4. Conclusions

In summary, we have grown designer mid-infrared plasmonic metals using silicon-doped InAs films with doping densities ranging from 2.7 × 10¹⁸ cm⁻³ to 7.5 × 10¹⁹ cm⁻³. The films were characterized by Hall measurements as well as optical transmission and reflection in the mid-IR and near-IR wavelength ranges. The optical data were fit and the plasma frequencies and scattering times of our materials determined. Using the Drude model formalism, the films’ real and imaginary dielectric constants were modeled, and it was demonstrated that samples can be designed with plasma wavelengths across a broad range of mid-IR wavelengths. In addition, near-IR transmission measurements demonstrated that our highly doped materials are effectively transparent to telecom frequencies, due to the Burstein-Moss effect, allowing for potential integration of mid-IR plasmonic materials with semiconductor optoelectronic devices designed for shorter wavelengths. Finally, the films were patterned into subwavelength plasmonic particles and a localized surface plasmon resonance was observed, with experimental spectra that agreed well with both the modeled dipole extinction curve and our numerical simulations.

The materials demonstrated in this work provide an important building block for the design and development of plasmonic structures at mid-IR wavelengths. Because these are MBE-grown materials, we have the ability to accurately and reproducibly control plasmonic structures’ optical properties with nanometer-scale accuracy in the vertical (growth) direction. The further development of highly doped InAs designer metals offers the potential for a new class of epitaxially-grown, wavelength flexible, and semiconductor-based plasmonic and metamaterial structures designed for mid-IR wavelengths. Future work will look to minimize our material losses by careful optimization of the InAs growth process, as well as to integrate our materials into a variety of plasmonic and metamaterial structures for potential mid-IR applications.