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Mirror-backed Dark Alumina: A Nearly Perfect Absorber for Thermoelectronics and Thermophotovotaics

We present here a broadband, wide-angle, and polarization-independent nearly perfect absorber consisting of mirror-backed nanoporous alumina. By electrochemically anodizing the disordered multicomponent aluminum and properly tailoring the thickness and air-filling fraction of nanoporous alumina, according to the Maxwell-Garnet mixture theory, a large-area dark alumina can be made with excellent photothermal properties and absorption larger than 93% over a wide wavelength range spanning from near-infrared to ultraviolet light, i.e. 250 nm–2500 nm. The measured absorption is orders of magnitude greater than other reported anodized porous alumina, typically semi-transparent at similar wavelengths. This simple yet effective approach, however, does not require any lithography, nano-mixture deposition, pre- and post-treatment. Here, we also envisage and theoretically investigate the practical use of proposed absorbers and/or photothermal converters in integrated thermoelectronic and/or thermophotovoltaic energy conversion devices, which make efficient use of the entire spectrum of ambient visible to near-infrared radiation.


Results
Optically Lossy Nanoporous Alumina Films. In this work, a set of optically lossy porous alumina (i.e. AAO) films on top of aluminum substrate were fabricated. A 2cm× 2cm commercial 6061-T6 aluminum alloy was treated by a standard electrolytic polishing. Then, the aluminum sheet was immersed in a 0.3 M sulfuric acid solution for hard anodizing. During the hard anodizing process, the DC bias was fixed to 30 V and the medium temperature was controlled by a precise cooling system. We prepared three species under different process Figure 1. Schematics of (a) a thermoelectronic and (b) thermophotovoltaic microdevices using the mirrorbacked nanoporous alumina absorber, which can be readily integrated with an electron or thermal emitter depending on applications.
temperatures: 0 °C, 5 °C, and 10 °C. The hard anodizing process was performed for 1 hour, followed by the standard deionized water rinse and blow dry. Due to the high concentration of sulfuric acid and the high electrostatic biasing field in the hard anodizing process, the active surface oxidation results in rapid Joule heating and imposes morphological damages to the surface, which is quite sensitive to the process temperature. To study the effect of electrostatic biasing, we also prepared two species under higher DC bias voltage of 40 V and 50 V, at the process temperature of 10 °C. Conventional AAOs are made based on the costly high-purity (99.997%) aluminum foils 33 , which yield an optically transparent porous alumina that hardly absorbs infrared and visible light. Our approach, although based on similar electrochemical process, utilized the high-impurity alloy that is naturally lossy in infrared and visible regions, as its collision rate in the fitted Drude model is ~10 times larger than pure aluminum. The resulting alumina presents an exotic dark color, as a clear evidence of broadband absorption of visible light. Table 1 summarizes the thickness and air-filling ratio (ratio of air in this porous medium) of synthesized dark alumina under different anodizing conditions. The morphology, air-filling fraction, and thickness of nanoporous alumina film are determined by several factors, including the electrolyte concentration, the temperature and the DC bias in the anodizing process. Figure 2(a) shows the corresponding CCD images for different AAO-covered, anodized aluminum in Table 1; the untreated aluminum is also shown here for a fair comparison. It is surprising to see that an AAO coating, i.e. nanoporous alumina, can turn the highly reflective surface of aluminum into dramatically dark, by absorbing most of the impinging visible light. We also note that greater opacity of AAO-coated aluminum is obtained by raising the process temperature, due to the increased thickness and air-filling ratio of AAO, which will be explained in the following. Figure 2(b,c) show the top-view and cross-sectional scanning electron microscope (SEM) images of sample 4 in Fig. 2(a). We found that unlike those conventional AAO membranes having crystal-like hexagonal periodicity, the synthesized AAO film exhibits irregularly distributed nanopores with inconsistent sizes. The cross-sectional SEM image also reveals that nanopores have high aspect ratio, and are misaligned and randomly orientated in the vertical direction.

Infrared and Optical Absorption.
Here we demonstrate that the concept and feasibility of broadband and wide-angle absorption enabled by the mirror-backed mesoporous metal oxide (MMO), as shown in Fig. 3(a). The surface-anodized aluminum alloys studied here, i.e. AAO plus aluminum, could be a representative structure, which, however, can be readily, prepared using the simple and cost-effective electrochemical process 48 . For an N-phase composite medium consisting of randomly distributed subwavelength inclusions, its macroscopic effective permittivity ε eff can be analytically derived from the Maxwell-Garnett theory 49 as: where p n and ε i,n are the volume fraction and relative permittivity of the N-th inclusion in this mixture, and ε m is the relative permittivity of host matrix. Consider the two-phase mesoporous material in Fig. 2(b,c): irregularly-distributed, subwavelength nanopores filled with air (i.e. ε m = 1) and embedded in a metal oxide host matrix of relative permittivity ε MMO , the effective relative permittivity is given by: where δ is the volume fraction of air nanopores. Since air nanopores with average diameter less than 20 nm are deeply subwavelength, this MMO medium can be treated as a homogenous medium of relative permittivity ε eff . By properly tailoring the complex effective refractive index (or optical impedance) of metal oxide, the maximum light absorption can be obtained in certain conditions. Here we used a transmission line (TL) approach 18,50 depicted in Fig. 3(b) to model the light scattering from such a mirror-backed composite medium, i.e. MMO. The TL approach is particularly suitable for studying the plane waves incident on the bulk homogeneous medium, without the excitation of higher-order diffracted Floquet modes. The free-space region and metal substrate are modeled as semi-infinite TLs and the MMO region is treated as a TL segment of length l. For a given angle of incidence θ with respect to the surface normal direction [see Fig. 3a], the effective free-space wave number is β θ = k cos   Table 1; here solid lines represent the experimental data and dots represent the theoretical results based on the Maxwell-Garnet effective medium theory and transmission line approach.
, are the propagation angle, wave vector, and intrinsic impedance of the i-th medium, ω is the radian frequency, ε i is the relative permittivity of the i-th medium, and ε 0 and μ 0 are vacuum permittivity and permeability. According to the TL model in Fig. 3(b), the reflection coefficient at the input of MMO surface can be derived as: 3   TE TM  MMO  TE TM  M  TE TM  0  TE TM  MMO  TE TM 2  M  TE TM  0  TE TM  MMO  TE TM   MMO  TE TM  M  TE TM  0  TE TM  MMO  TE TM 2  M  TE TM  0  TE TM  MMO  TE TM and the total absorption of this system is given by TE TM TE TM 2 The relative permittivity of metal substrate follows a Drude-type dispersion 51,52 where ω p is the plasma frequency and γ is the collision rate. For aluminum, parameters extracted from experimental data are ε = , and γ π = × . × 2 0296 10 Hz 15 . We note that the value of γ used here is 9.5 times larger than that of the best quality purified aluminum, owning to the existence of various residual impurities and alloying elements in 6061-T6 aluminum, which would increase the material loss that depends on the volume fraction of air and lossy alumina. Figure 3(c,d) report the measured spectral absorption for 6061-T6 aluminum and various anodized alumina in Table 1. The UV-VIS-NIR spectrophotometer (integrating sphere detector) shown in the Fig. 3(a) was used here to rigorously characterize the light absorption of samples in a wide wavelength range of 250 nm-2500 nm. The measured average absorption by spectrophotometer over all angles of illumination is defined as: The experimental data (solid lines) was verified by the theoretical results (dots) obtained from the TL model, and excellent agreements are obtained for all cases; here realistic physical parameters in Table 1 were used in our theoretical calculations. The refractive index of the MMO layer (AAO here) is 34,35 , valid at wavelengths of interest. We note that the imaginary part of n AAO is significantly larger than that of most AAO membranes and is expected to enhance the absorption of incident radiation. The TL approach is an effective tool to design, analyze and optimize the scattering and absorption of mirror-backed MMO structures. From Fig. 3(c,d), it is evident that the 6061-T6 aluminum is more lossy than the high-quality aluminum (e.g. those prepared by physical vapor deposition or sputtering 51,52 ), with almost ten times larger collision rate in the fitted Drude model. We note that the interband transition of aluminum is observed at the wavelength λ = 879.4 nm 51,52 , which introduces extra absorption and is not considered in the Drude model. From Fig. 3(c,d), we found that hard anodizing can dramatically increase the absorption of aluminum, and the absorption increases with increasing the anodizing temperature and DC bias. The sample 4 of larger AAO thickness and higher porosity exhibits a 93.5% average absorption in the UV/visible and a 92.3% average absorption in the near-infrared region. Such high absorption can be attributed to the optical impedance matching, for which a nanoporous AAO thinfilm can have real-part effective impedance (or refractive index) close to that of free space region (background medium). Based on the mixture law in Equation (2), the effective impedance of AAO can be tailored at will by designing the volume fraction of air pores, and a close-to-zero reflection may be obtained when AAO and incident medium have the equal value of characteristic impedance. Figure 4(a,d) show the theoretical contours of absorptions for a mirror-backed porous alumina at different wavelengths: (a) 500 nm, (b) 1000 nm, (c) 1500 nm, and (d) 2000 nm, varying the porosity and thickness; all measured samples in Fig. 3(c,d) are indicated by dots. Intuitively, a zero air-filling ratio results in a poor impedance match at the air/ AAO interface, while an air-filling ratio near unity has a large reflection, similar to a pure aluminum surface. From Fig. 4, it can be observed that the sample 4 may have the optimum absorption property within the wavelength range of interest, which is consistent with the experimentally measured absorption spectrum in Fig. 3(c,d). We should note that the AAO films synthesized here have relatively large imaginary-part refractive indices such that a sufficiently thick AAO film may considerably absorb the impinging light in a relatively short optical path length. As a result, the surface-anodizing of lossy 6061-T6 aluminum may offer an effectual platform to tune the absorption and reflection properties of the AAO surface coating, of which the morphology, porosity and thickness can be readily controlled by varying the temperature, electrolyte concentration, and the DC bias in the anodizing process.
Photothermal Effect. We investigate here the photothermal conversion efficiency of fabricated samples under excitation from a tungsten halogen illumination source, typically used to simulate the solar radiation in experiments. All samples to be characterized were insulated to avoid possible thermal conduction and convection, except for the surface to be illuminated. The intensity of impinging light is = / P 5W cm inc 2 . Figure 5(a) reports the transient temperature variation for different samples in Fig. 3(c), showing that the photothermal conversion efficiency is proportional to the absorption of the sample. The temperature was measured directly using K-type thermocouples connected to a temperature logger, with 0.1 K accuracy. It is astonishing to see that the steady-state temperature difference between an untreated aluminum and the sample 4 is more than 100 °C.   Table 1, are indicated by dots.

B hS m C s [ ]
p 0 1 is the rate constant of heat loss, m and C p are effective mass and heat capacity of the background medium. We used Equation (6) to fit the temperature profiles in Fig. 5(a), and the extracted empirical parameters A 0 and B 0 are shown in Fig. 5(b), which are plotted as functions of the averaged spectral absorption. It is clearly seen that the measured temperature profile is perfectly described by the physics-based model of Equation (6), and the steady-state temperature can be estimated as ( → ∞) = + / T t T A B 0 0 0 , where taking the limit → ∞ t means the steady-state condition. Figure 5(b) shows the linear relationship between the energy absorption/dissipation rate and the optical absorption. Thermoelectronic Conversion. We study here the applicability of this mirror-backed MMO structure to practical TC and TPV applications. We first consider a thermoelectronic device in Fig. 1(a), where the emitter electrode is composed of an AAO-coated aluminate sheet. The front-side AAO layer can absorb sunlight and/or blackbody radiation over a broad spectrum, converting absorbed photon energy into heat. The heated back-side metal, if coated with low-Schottky-barrier thermionic emitters will trigger the thermionic emission of hot electrons. Some low-dimensional nanomaterials are idea thermionic emitters, which show high thermal conductivity and low effective work function (e.g. LaB6 nanowires 54 , carbon nanotubes 55 , and graphene flakes 56 ) or negative electron affinity (e.g. diamond nanotips 57 ). When the vacuum gap between two electrodes is at the micrometer scale, one could neglect the space charge effect that limits the maximum current density received by the collector electrode 58 . The thermionic emission current density can be described by the well-known Richardson-Dushman formula as 9 : . Previous works 8,9,59 suggest that the work function of emitter electrode Φ e should be larger than that of collector electrode Φ c , which renders . Although the ideal conversion efficiency neglecting heat losses, η The practical efficiency is much lower due to unavoidable heat losses. According to the familiar Stefan-Boltzmann law 59 , the radiation heat loss is given by , where σ is the Stefan-Boltzmann constant, ε e and ε c are emissivity of emitter and collector (here we assume ε ε = = . ≈ 0 2 e c absorption of aluminum). Other possible heat transfer P c , e.g. thermal conduction loss in the proximity of collector and conversion loss of absorption to heat, is extracted from the measurement results in Fig. 5. The energy balance suggests the following relationship: where P inc is the illumination irradiance. Therefore, the optical-to-electrical conversion efficiency is defined as: Assuming the electrical contacts are perfect thermal insulator and perfectly electric conductor, the conversion efficiency can be calculated by simultaneously solving Equations (10) and (11). The optimum conversion efficiency is achieved at the voltage V m , which produces the maximum power, delivered to the load, namely The value of V m and the optimum conversion efficiency must be numerically obtained using an iterative method, analogous to the diagram of a photovoltaic cell 60 : performing an I-V sweep from short circuit to open circuit condition and recording the optimum operating point. Figure 6 presents the calculated theoretical maximum conversion efficiency against the intensity of impinging light for the different species shown in Fig. 2(a). We found that the surface anodizing can significantly boost the optical-to-electrical conversion efficiency of aluminum sheet at low illumination intensities, due to the enhanced light absorption and heat generation rate. We must emphasize that for the optimal design, i.e. sample 4, the device can be operated at a moderately low light intensity, readily achievable with a Fresnel lens. On the other hand, the untreated aluminum alloy requires an intense light ~25 W/cm 2 to turn on the device. We note that by using specific thermodynamic structures, e.g. thermal metamaterials 61 , the thermal insulation and energy conversion efficiency (which in theory could be up to 30% 59 ), could be improved.
Thermophotovotaic Application. We note that the proposed mirror-backed dark alumina structure can also be of interest for thermophotovotaic applications. The TPV device in Fig. 1(b) is known as a highly efficient tool to generate electricity. In this case, the front-side nanoporous alumina layer can collect light in a wide wavelength range, while the back-side metal can be nano-engineered to reradiate light in a narrow wavelength range, matched to the bandgap energy of photovoltaic diode receivers. In this scenario, nanostructures on each side of the metal substrate can be designed to tame the spectrum of absorption and reradiation. We note that the recently proposed metamaterial approach 62-64 may be suitable here for the wide-angle, wavelength-selective thermal radiation. Figure 1(b) illustrates the proposed metamaterial structure, where a metamaterial slab is formed by a screen of thickness h, corrugated by slit of width w and period d. Provided the grating periodicity is subwavelength (d < λ/2), all diffraction orders, except for the zero-th mode, are evanescent, and therefore the TL approach in Fig. 3(b) can again be used to analyze the scattering properties. The homogenization theory for this metamaterial structure is more complicated than the mesoporous binary mixture in Equation (2). The metallic grating can be viewed as an array of subwavelength metal-air-metal waveguide that supports the fundamental TM mode (non-polarization-selective emitters are also possible by engineering the symmetric nanopatterns on the aluminum surface, as has been discussed in 26 ). For a TM-wave illumination, the characteristic impedance per unit length is η θ = , Z dcos 0 0 calculated as the ratio between the voltage across one period  Table 1; the inset shows the energy band diagram of a thermoelectronic microdiode with hot electronics thermionic emission.  Figure 7(a) reports the contour of emissivity (or absorption) calculated according to Equation (4) at the wavelength λ = 800 nm under the normal incidence (θ = 0°), varying the width and length (w, h) of air slits (here d = 250 nm). Bands of emissivity, with maximum value close to unity, are clearly visible in this figure. Figure 7(b) reports the contour of emissivity for a metamaterial using particularly structural parameter indicated in Fig. 7(a), varying wavelength and incident angle; here (w, h) = (50 nm, 100 nm). We found that the emissivity is fairly intense around the design wavelength λ = 800 nm, over a broad angular range. Figure 7(c,d) are similar to Fig. 7(b,c), but for a design wavelength of 1 μ m, with structural parameters (d, w, h) = (250 nm, 50 nm, 100 nm), as indicated by the spot in Fig. 7(c). It is clearly seen that by tailoring the metamaterial geometry, narrowband emissivities can be designed at the desired wavelength range. This metamaterial approach may offer a worthwhile alternative to tame the thermal emissivity of back-side metal.

Discussion
In summary, we have developed a mirror-backed dark alumina as an absorbing and photothermal conversion platform for harvesting sunlight and Earth's infrared emissions. In particular, the nanoporous alumina made from  Fig. 1(b), varying the width w and length h of nanoslits; here the period is d = 250 nm and the design wavelength is λ = 0.8 μ m. (b) Contours of emissivity for a metamaterial-based thermal emitter using structural parameters indicated in the spot of (a), varying the wavelength and incident angle. (c,d) are similar to (a,b), but for the design wavelength λ = 1 μ m.
impurity-rich aluminum via the electrochemical anodization can be optically lossy, while having a real-valued optical impedance matched to that of the free space. By optimizing the process conditions, the anodized aluminum turns completely dark, whereas the untreated aluminum shows brilliant reflection. The photothermal experiment further demonstrates the viability of proposed absorber in practical energy conversion applications. Finally, we have also theoretically investigated the conversion efficiency of a thermoelectronic solar cell based on the proposed absorber, showing a remarkably improved efficiency compared to an aluminum hot electrode. In addition, by integrating nanostructured metamaterials on the back-side of proposed absorber, the absorbed photon energy can produce a narrowband thermal emission to illuminate the PV module of thermophotovoltaic solar cells. The large-area and low-cost dark alumina shows a promising potential for various energy harvesting and conversion applications.