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We simulate, fabricate, and characterize near perfectly absorbing two-dimensional grating structures in the thermal infrared using heavily doped silicon (HdSi) that supports long wave infrared surface plasmon polaritons (LWIR SPP’s). The devices were designed and optimized using both finite difference time domain (FDTD) and rigorous coupled wave analysis (RCWA) simulation techniques to satisfy stringent requirements for thermal management applications requiring high thermal radiation absorption over a narrow angular range and low visible radiation absorption over a broad angular range. After optimization and fabrication, characterization was performed using reflection spectroscopy and normal incidence emissivity measurements. Excellent agreement between simulation and experiment was obtained.
©2013 Optical Society of America
1. Introduction
Surface plasmons in the mid-wave and long-wave infrared, nominally 3-12 μm, have notable differences to plasmons in the visible and near infrared part of the electromagnetic spectrum. Two defining characteristics of SPP modes are the propagation length, δspp, and the dielectric surface penetration depth, kd. These features are directly proportional to one another over all frequency ranges but exist in opposite extremes for the visible and IR, with propagation length and dielectric penetration being small in comparison to wavelength in the visible, and quite large in the infrared. These physical properties of the LWIR SPP’s have made it a challenge to find efficient applications in this frequency range, though some have been demonstrated [1,2]. Performance of the quantum cascade laser (QCL) was improved through the use of SPP waveguide modes, while the beam profile and polarization state of Mid-IR QCL’s have been modified using SPP’s as well. However, there are further applications that can be developed if one can generate long-wavelength plasmons with the high confinement and high loss of conventional SPP’s. One of these applications is directional emission, where plasmon loss can be beneficial. Careful design of a periodic structure allows this absorption (emission) to occur only over a narrow angular range, as will be shown.
The surface plasmon dispersion relation is given by:
where k0 is the free space propagation vector and εm and εd are the complex metal and dielectric permittivities respectively. All plasmon mode characteristics can be determined from this relation which is dependent on the relative magnitudes of εm and εd. The variation in the magnitudes of εm for the visible and IR is the source of the physical distinctions and can be easily understood by using the Drude model to describe the optical dispersion of a medium with free electrons subject to collisional damping. Here, the frequency dependent permittivity is expressed as:where is the high frequency permittivity, ω is the exciting frequency, τ is the collision rate, and the plasma frequency:is a function of the carrier density n, the effective mass m*, and . In conventional metals, the plasma frequency is in the UV, and for excitation frequencies which are slightly lower, the real part of the permittivity is negative and of single digit order. As excitation frequency decreases, the effective permittivity increases and rapidly reaches vary large values. A material with a plasma frequency in close proximity to the infrared will provide a smaller permittivity, which in turn could support IR SPP’s with the desired properties.One alternative to noble metals which exhibits a controllable plasma frequency is highly doped silicon (HDSi) [3]. There has been significant research conducted on this material in the last 30 years. Hesketh et al. demonstrated control over the emissivity of a one-dimensional grating [4] fabricated from HDSi and also investigated the angular dependence of those properties [5], while Auslender and Hava furthered this work by demonstrating perfect absorption with one-dimensional HDSi gratings designed for resonance at 10.6 μms [6]. In more recent years, Cleary et al. explored the use of doped silicon for surface plasmon waveguides in the long wave infrared as they offer high confinement and acceptable propagation lengths [7], while Shazad et al. demonstrated coupling LWIR laser radiation to an HDSi one dimensional grating [8]. In this work, we further develop the use of HDSi for IR plasmonics and design a nearly perfect absorbing two-dimensional grating structure which is optimized for thermal management applications through directional absorption control at thermal wavelengths and minimization of visible light absorption at all angles. Our device exhibits >90% absorption of thermal radiation over a narrow angular cone, extending +/−15° around the surface normal. In accordance with Kirchoff’s law [9], the thermal emissivity of a material is directly proportional to its thermal absorption characteristics for a system at thermal equilibrium. As our structure’s transmission is essentially zero, the reflected signal is equivalent to 1 - emissivity as will be shown.
2. Design and simulation
The near perfect absorption of unpolarized normal incidence thermal radiation is achieved using a two-dimensional grating structure comprised of an HDSi mesa array with gold spanning the troughs. The HDSi material was n-doped with phosphorous to a density of 2.4 E 20 cm−3 as reported in reference 3, wherein the doping technique and characterization results are reported. The SPP dispersion relation for an air/HdSi interface predicts a mode with tight confinement and high loss, similar to the characteristics of visible SPP’s. A plot of these properties is shown in Fig. 1 , which indicates that subwavelength SPP confinement is predicted for wavelengths up to 9.5 μm. As expected, the propagation length is also decreased throughout that infrared range resulting in a very high loss mode. It is this high loss mode that we exploit for the perfect absorption functionality of the device.
Fig. 1 Dielectric penetration depth, kd, and propagation length, δspp, of HDSi air plasmons with both quantities normalized to wavelength, λ.
Initial simulations indicated that near perfect normal incidence LWIR absorption was achievable with a biperiodic device consisting of the HDSi material alone, but in order to maximize high visible light reflectivity, a thin layer of highly conductive metal was deemed necessary to fill the array troughs. For device fabrication convenience and characterization in the IR frequency range, we employed gold for this function despite its non-ideal behavior in the visible region. This was an acceptable alteration as simulations showed inconsequential variation in the IR region of the device behavior when the gold was replaced by silver or aluminum. Parameter sweeps were conducted using low resolution RCWA simulations to explore and optimize the thermal absorption dependency on periodicity Λ, mesa side length w, and mesa etch depth h, as shown schematically in Fig. 2(d) . Figure 2(a-c) shows simulation results for the three cases of fixing two parameters while varying the third. The analysis makes it clear that the maximum in absorption cannot be solely determined by periodicity, i.e. by the simple surface plasmon conservation equations. We speculate that all of the supported plasmon modes, the HdSi-air, gold-air, and the HDSi-air-HDSi gap plasmon modes existing in between the mesas all play a role in the enhanced absorption process, but do not investigate that exact process here.
Fig. 2 Reflectivity contour plots resulting from RCWA parameter sweeps of device geometry. (a) w = 6 μm, h = 1.5 μm, varying period. (b) Λ = 9 μm, w = 6 μm, varying mesa height. (c) Λ = 9 μm, h = 1.5 μm, varying mesa side length. (d) Schematic of device array.
From these simulation results, a geometry consisting of periodicity 9 um, mesa side length 6 um and mesa height 1.5 um was chosen for more rigorous simulation analysis and for fabrication. The devices were fabricated in a process which relied on a single optical lithography patterning step for both inductively coupled plasma reactive ion etching (ICP RIE) of the silicon mesas and the titanium gold (5, 50 nm respectively) metallization patterning for the troughs. A scanning electron microscope (SEM) image of an array portion is shown in Fig. 3 . A rounding of the mesa corners and damage to mesa sidewalls is evident and is attributed to the single lithography step; however, no changes to the fabrication process were made to maintain the simple procedure.
3. Device characterization
Normal incidence reflection measurements were performed using a Jasco scientific 6300 Fourier transform infrared spectrometer (FTIR), f/4 optics, and a liquid nitrogen cooled MCT detector. High resolution 3 dimensional FDTD simulations for the normal incidence reflection were conducted with k-vector corrections to account for grating order losses not recovered in the experiment, i.e. the simulation rejected power diffracted outside of the 10° angular cone that the experiment collected. Figure 4 shows the normal incidence reflection spectrum and FDTD model results for our device. As can be seen, near perfect absorption, ~99% is predicted at 10.6 μm, and a value of ~91% is measured at 10.3 μm. The discrepancy is attributed to the curved and damaged silicon sidewalls and variation in structure geometry over the device surface. It is expected that agreement could be improved with additional fabrication steps, but was not experimentally explored. Angle dependent reflectivity scans were acquired using a Surface Optics Corporation hemispherical directional reflectometer (HDR) and a Nicolet 6700 FTIR spectrometer. The HDR system was used to make polarized measurements of both the specular and diffuse components of the radiation reflected and transmitted by a sample for angles ranging from 8° - 80°. As these structures exhibit no transmission throughout the measured spectrum, reflection is equivalent to 1 - emissivity. Contour plots of the HDR measurement and RCWA simulations of reflection are shown in Fig. 5 for S, P, and averaged polarization states of the composite specular and diffuse reflection spectra. In the HDR measurement data, an artificial loss is present which is caused by satisfaction of the Littrow condition. The Littrow condition occurs when a diffractive structure is measured in a configuration such that the first order reflected mode is directed to the same angle as the incident beam, thereby reflecting energy back to the source in the HDR system. Due to the optical configuration of the HDR, this light is not recoverable thus giving rise to the spurious loss source. For clarity, a plot of the Littrow solution, given by Eq. (4), is overlaid on the DHR P polarized data of Fig. 5(a).
The Littrow curve is also present in the P polarized and averaged data contours, though with intensity decreasing and eventually disappearing at higher wavelengths.Fig. 4 Normal incidence specular reflection measurement and FDTD simulation with angular correction.
Fig. 5 Contour plots of angle dependent device reflectivity from HDR measurements for (a) P polarized with Littrow condition overlaid, (c) S polarized, and (e) the average of the two and angle dependent device reflectivity from RCWA simulations for (b) P polarized, (d) S polarized, and (f) the average of the two.
While these plots demonstrate the suitability of the structure for highly directional thermal emissivity, it was also desirable to obtain efficient rejection of the solar spectrum. To evaluate device performance, RCWA simulations using Palik’s values [10] for the permittivities of silicon and silver and gold in the 0.2 to 3 μm spectral range were conducted for the unmetallized and metallized geometries. By integrating the product of the absorption spectra and the black body spectral irradiance for the sun at 5250 Co, we found the uncoated silicon grating structure absorbed ~65%, the gold coated structure absorbed ~56%, and the silver trench structure absorbed only ~35% of the sun’s energy at an incidence angle of 45°, with similar values persisting up to normal incidence.
Normal incidence emissivity measurements were conducted on the device with a custom built thermal chamber and a Nicolet 6700 FTIR spectrometer [11]. The sample was mounted on a gold coated cryostat finger along with a matte black painted silicon control sample. A cold shield with a 1x1 cm window was positioned in front of the sample holder. The entire assembly was placed in a vacuum chamber and pumped down to 10−6 Torr, at which point the cold shield was cooled to 27K to suppress background emissions. Multiple cartridge heaters were used to heat the cryostat finger to the desired temperature and FTIR spectra were collected employing the background correction techniques discussed in reference 11. The collection optic of the emissivity system is an f/2.5 lens which collects a broad cone of angles thereby convoluting the sample’s emissivity up to approximately 11°. To account for this, the image of the sample was projected onto the lens for particular emission angles, and the fraction of the surface area captured by the optic was used as a weighting factor for the RCWA simulated emissivity. Those weighted emissivity numbers were then combined to replicate the measurement system. Figure 6 shows these results and again demonstrates good agreement.
5. Conclusion
In this work, highly doped silicon with a plasma frequency in the mid-wave infrared was used to fabricate nearly perfect absorbing two-dimensional gratings structures that function as highly directional thermal radiators. The absorption and emission characteristics of the devices possess a high degree of angular dependence for IR absorption in the 10-12 μm range, while maintaining high reflectivity of solar radiation (~64%) at large incidence angles. We project that alternative metallization such as HDSi mesas on a full ground plane can increase the solar rejection to ~72% without deteriorating the desired control of thermal emission. With further modification of the two-dimensional pattern, it is expected that increased bandwidth tailoring could be achieved as well.
Acknowledgments
This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. This work was supported by the Sandia laboratory directed research and development (LDRD) program. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
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