Inverse design and realization of an optimized photonic multilayer for thermophotovoltaics

Eva De Leo; Ferry Prins; Ferry Prins; David J. Norris

doi:10.1364/OSAC.434849

1. Introduction

Conventional photovoltaic (PV) cells can only convert incident light with an energy above the bandgap into electricity and are, therefore, unable to exploit the full solar spectrum [1]. Thermophotovoltaic (TPV) devices, on the other hand, can overcome this limitation by first converting light into heat with the use of an absorber element and subsequently, using a radiator element, re-emit thermal radiation that is spectrally tailored to contain frequency components primarily above the bandgap energy of the photovoltaic cell [2,3]. This two-step process potentially doubles the efficiency of conventional photovoltaic cells. The key challenge in TPV lies in creating radiator elements with carefully tailored thermal emission spectra that can sustain high operating temperatures (>1000°C) throughout its lifetime and at the same time have good thermal conductivity to allow for uniform temperature distributions.

Concepts from photonics and plasmonics can be used to manipulate thermal emission [4,5]. Periodic structuring of metallic or dielectric films allows for spectrally and angularly selective thermal emission, as well as control over the polarization state of the emitted light. To ensure thermal stability, such structures are usually based on refractory metals and high-refractive-index dielectrics [6,7]. The most successful examples of photonic structuring for tailored thermal emission have been based on photonic crystals, including examples of 3D [5,8,9] and 2D [10,11] photonic crystals, as well as 1D multilayer architectures [12,13]. In these structures, the periodicity of the lattice can be designed to generate a photonic bandgap through the creation of spectral regions of constructive and destructive interference [14]. By aligning the photonic bandgap with the electronic bandgap of the photovoltaic cell, emission can be maximized at the electronic band edge and minimized for below-bandgap energies [15]. Of the different types of photonic structures, multilayers have the distinct advantage of the simplicity of their planar architecture, allowing for cost-effective lithography-free fabrication. In terms of simplicity, recent demonstrations of coherent total absorption in few-layer structures is of particular interest [16,17].

Crucially though, the optimal design of a multilayer emitter requires consideration of the full parameter space of spectral, angular, and polarization responses. To efficiently explore the multidimensional parameter spaces in photonic design, inverse-design principles using numerical optimization techniques have gained popularity in recent years [18]. Rather than evaluating the performance of a large number of given geometries to optimize the performance, inverse photonic design uses algorithms to find the optimal geometry for a desired performance. Inverse design has been applied successfully to a variety of photonic device applications, including optical fibers [19,20], cavities [21–23], and photonic multilayers [24–26]. Recently, Sakurai et al. have presented the inverse design of a Si/SiO₂ multilayer structure for potential use in thermophotovoltaics [27]. The optimized design with high quality-factor resonances was confirmed experimentally, though the experimental verification of the resulting structure was only evaluated at room temperature. Critically, to match theoretically optimized designs with final high-temperature performance, a number of challenges must be overcome. Importantly, the optical constants used in the design are usually room temperature dielectric functions, since high-temperature values are not generally available and difficult to obtain experimentally. As the optical constants can differ quite significantly at higher temperatures, this may lead to inaccuracies in the optimized design. Moreover, structural changes at high temperatures, which may include oxidation and annealing of the film as well as local delamination, can cause further modification of the optical response. To overcome these challenges, high-temperature evaluation of the optimized designs is critical.

Here, we present the inverse design and experimental realization of a photonic multilayer with an optimized thermal emission spectrum, and evaluate the performance using high-temperature reflectance measurements. The design of the emitter is optimized for use with an InGaAs photocell with a bandgap at 1.65 µm (0.75 eV) and for an operating temperature of 1300°C. Since our target operating temperature is 1300°C, we limit the design of the multilayer to the use of tungsten, which has the highest melting point among metals (∼3400°C), and aluminum oxide (Al₂O₃) as the dielectric spacer. Moreover, with the aim of minimizing the complexity of the structure, we focus the design toward a four-layer structure, similar to the few-layer structures reported by Blandre et al. [16] and Wang et al. [17]. In a first step, we employ an evolutionary optimization algorithm to optimize the multilayer geometry, taking into consideration the spectral, directional, and polarization response of the structure. In a critical next step, we optimize the deposition conditions for the multilayer, achieving high-quality optical constants while avoiding delamination at high temperatures. Finally, we characterize the optimized structure using high-temperature reflectance measurements, obtaining close to unity emission at above bandgap energies while suppressing up to 40% of below bandgap energies. We discuss the differences in performance of the original design and the final performance, emphasizing the difficulties of high-temperature induced changes in the optical properties of multilayer structures.

2. Design and fabrication

2.1 Inverse numerical design of an optimized multilayer

An ideal emitter radiates the absorbed energy in a narrow frequency range that matches the absorption edge of the photocell. For the design of the emitter, we assume the use of an InGaAs photocell with a bandgap at 1.65 µm (0.75 eV) and an operating temperature of the emitter of 1300°C using a solar concentrator.

For the design of our thermal emitter, the emissive power from a surface in the selected wavelength and angular ranges can be obtained as:

(1)$$P = \mathop \smallint \nolimits_{{\lambda _1}}^{{\lambda _2}} \mathop \smallint \nolimits_{{\varphi _1}}^{{\varphi _2}} \mathop \smallint \nolimits_{{\theta _1}}^{{\theta _2}} {L_{e\lambda }}\; \varepsilon ({\lambda ,\; \varphi ,\; \theta } )\;\cos \theta \sin \theta \; d\theta \; d\varphi \; d\lambda$$

where [λ₁, λ₂] is the wavelength range, [φ₁, φ₂] is the azimuthal angle range, [θ₁, θ₂] is the polar angle range, $\varepsilon ({\lambda ,\; \varphi ,\; \theta } )$ is the polarization averaged emissivity of the surface which depends on the material and structure of the emitter, and ${L_{e\lambda }}$ is the spectral radiance:

(2)$${L_{e\lambda }} = \frac{{2hc}}{{{\lambda ^5}}}\; \frac{1}{{\exp \left( {\frac{{hc}}{{\lambda {k_B}T}}} \right) - 1}}$$

where c is the speed of light in vacuum, h is Planck’s constant, k_B is Boltzmann’s constant, and T is the temperature of the emitter. According to Kirchhoff’s law, the emissivity of a body equals its absorptivity [28], yielding:

(3)$$\left\langle {A\; ({\lambda ,\phi ,\theta } )} \right\rangle = \left\langle {\varepsilon \; ({\lambda ,\phi ,\theta } )} \right\rangle$$

The absorption of the structure, A(λ,φ,θ), can be derived from an electromagnetic solver [26] via the calculated reflection, transmission, and diffraction efficiencies:

(4)$$A({\lambda ,\; \varphi ,\; \theta ,\; \tau } ) = 1\; - \; R({\lambda ,\; \varphi ,\; \theta ,\; \tau } ) - T({\lambda ,\; \varphi ,\; \theta ,\; \tau } ) - \sum \; D({\lambda ,\; \varphi ,\; \theta ,\; \tau } )$$

where τ denotes the polarization state.

To optimize the emission, we utilized a fitness function, FF, which is a parameter that quantifies the quality of the emitter. Here, the fitness function is defined as:

(5)$$FF = {\tilde{P}_{used}} - {\tilde{P}_{unused}} \le \; 1$$

where:

(6)$${P_{used}} \equiv {P_{0 \to {\lambda _g}}} = \mathop \smallint \nolimits_0^{{\lambda _g}} \mathop \smallint \nolimits_0^{2\pi } \mathop \smallint \nolimits_0^\pi {L_{e\lambda }}\; \varepsilon ({\lambda ,\; \varphi ,\; \theta } )\;\cos \theta \sin \theta \; d\theta \; d\varphi \; d\lambda$$

(7)$${\tilde{P}_{used}} \equiv {P_{0 \to {\lambda _g}}} / P_{0 \to \; \; {\lambda _g}\; }^{BB}$$

(8)$${P_{unused}} \equiv {P_{{\lambda _g} \to \infty }} = \mathop \smallint \nolimits_{{\lambda _g}}^\infty \mathop \smallint \nolimits_0^{2\pi } \mathop \smallint \nolimits_0^\pi {L_{e\lambda }}\; \varepsilon ({\lambda ,\; \varphi ,\; \theta } )\;\cos \theta \sin \theta \; d\theta \; d\varphi \; d\lambda$$

(9)$${\tilde{P}_{unused}} \equiv {P_{{\lambda _g} \to \infty }} / P_{{\lambda _g} \to \infty }^{BB}$$

in which P_used and P_unused represent the emitted power that can and cannot be used (i.e. converted) by the InGaAs photocell, defined by the cutoff wavelength ${\lambda _g}$ = 1.65 µm (or 0.75 eV). P^BB = σT⁴ is Boltzmann’s law for a black body.

Using the evolutionary optimization algorithm [26] to maximize FF, we obtain an optimized Al₂O₃/W/Al₂O₃/W multilayer structure as shown in the inset of Fig. 1(a). Thicknesses of the layers from top to bottom measure 155, 18, and 160 nm and a final optically thick W layer. It is important to emphasize that for the optimization procedure, the available room temperature optical constants from Palik et al. were used [29]. The resulting maximum absorptivity (emissivity) is positioned just above the bandgap energy of the PV cell. The corresponding emittance of the design at 1300°C is shown in Fig. 1(b). Compared to the emittance from a flat W thin film, a significant enhancement of above-bandgap emission is obtained. For above-bandgap energies, the multilayer emits up to 96% of the black-body limit, while suppressing up to 65% of the black-body radiation at below-bandgap energies. Our inverse design strategy yields a performance that compares favorably to the highest performing example of a multilayer emitter in literature, where 56% above-bandgap emission and 69% below-bandgap suppression were reported [12,30].

Fig. 1. a) Absorptivity (φ- and polarization-averaged) of the optimized Al₂O₃/W multilayer as a function of energy and polar angle θ (see inset for details on the calculated optimal materials thicknesses). b) Calculated emittance for the multilayer structure (red) and a bare W film (blue) at 1300°C, compared with the black-body spectrum (dashed-dotted line). The vertical dashed line represents the InGaAs bandgap at 1.65 µm (0.75 eV).

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2.2 Multilayer fabrication

The optical performance of 1D photonic-crystal cavities is highly sensitive to fabrication-controlled properties such as surface roughness and thickness variation of our dielectric stack, as well as the dielectric functions and thermal stability. For this reason, we performed an initial parameter study of the deposition parameters with a particular emphasis on the argon pressure during deposition. While low pressures generally result in denser films with superior optical constants (reduced losses), the higher density may lead to stresses in the film and cause delamination at high temperatures [31].

Thin-film deposition was performed using magnetron sputtering (Kurt J. Lesker PVD 75). In a first step, W layers were deposited on SiC substrates with a DC sputtering power of 250 W. Deposition was performed at different argon pressures, varying from 0.5 to 25 mTorr. The optical constants of the thin films were measured using spectroscopic ellipsometry (V-VASE, J.A. Woollam Co.). As expected, lower argon pressures resulted in improved room temperature optical constants, with 0.5 mTorr closely matching optimal literature values [29] (see Figure S1). Inspection of the thin films using scanning electron microscopy moreover shows that the films deposited with the lower argon pressures display larger grain sizes and smoother surfaces (see Figure S2).

To evaluate the high-temperature stability of the different films, the structures were placed in a heating stage (Linkam TS1500). After evacuation of the heating chamber to 10⁻⁵ mbar, the temperature was raised to 900°C at a rate of 20°C/min and then cooled to room temperature at the same rate. Scanning electron micrographs in Figure S3 show delamination of films deposited with the lowest deposition pressures (0.5 mTorr). On the other hand, no significant structural modification or significant change in the surface roughness was observed for the other films. Therefore, while lower deposition pressures lead to higher densities, they can also increase the stress incorporated in the films. This stress is usually of a compressive nature caused by tightly packed columnar grains [32]. At high temperatures, the thermal expansion of the material can therefore cause delamination from the substrate. A good compromise in terms of film density, incorporated stress, optical properties, and surface roughness was achieved with the use of 6 mTorr argon pressure during the deposition of the W films. Aluminum oxide layers were deposited with a reactive RF sputtering process at 200 W and a pressure of 1 mTorr. The refractive index for Al₂O₃ films was measured to be around 1.64 in most of the NIR range, matching standard literature values [29].

Using the optimized deposition conditions, we fabricated the Al₂O₃/W multilayer with the optimized design parameters on SiC substrates (Fig. 2(a)). The thermal stability of the multilayer was tested under vacuum conditions (10⁻⁵ mbar), maintaining the temperature at 1300°C for 6 h. After this heating period, the cross-section of the multilayer was examined using scanning electron microscopy. While some small defects are observed in scanning electron micrographs, the multilayer does not suffer from delamination (Fig. 2(b)). Moreover, surface investigations revealed that the surface roughness was similar to values determined prior to the heating process.

Fig. 2. Cross-sectional scanning electron micrograph of the multilayer before (a) and after (b) heating up to 1300°C.

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3. Optical characterization

3.2 Room-temperature reflectivity measurements

To verify the optical response of our Al₂O₃/W multilayer, we first performed room-temperature optical reflectivity measurements. For this, a home-built optical setup was used in which illumination from a broadband light source (ORIEL, Newport) is directed to the sample using a KBr beamsplitter. Reflected light was collected at normal incidence using a 1 inch diameter CaF₂ lens with a focal length of 40 mm (+/- 18 degrees collection cone) and sent to a Fourier-transform infrared spectrometer (FT-IR, Bruker Vertex 80) equipped with a liquid-nitrogen-cooled InSb detector for spectral analysis in the NIR spectral range. For the visible spectral range, a spectrograph (Princeton Instruments, SP2300) with a charge-coupled-device (CCD) array (Princeton Instruments, Pixis256) was used. According to Kirchhoff’s law (Eq. (3)), where absorptivity equals emissivity at thermal equilibrium, the emissivity spectra can be extracted from the reflectivity measurements (A = 1 – R). Good agreement is found between the measured and the predicted emissivity values (Fig. 3), though a moderate red-shift of the absorptivity maximum is observed for the measured as compared to the predicted response and the drop in absorptivity at longer wavelengths is not as dramatic as in the original simulated multilayer. Importantly though, the absorptivity maximum of the multilayer measured at room temperature approaches unity and is significantly higher when compared to a bare W film.

Fig. 3. (a) Measurements (solid lines) and numerical simulations (dashed lines) of the absorptivity/emissivity of the Al₂O₃/W multilayer (red) compared to a bare W film (blue). The vertical dashed black line represents the InGaAs bandgap at 1.65 µm (0.75 eV).

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3.3 High-temperature performance

To verify the performance of the multilayer under operating conditions, we tested the structure at various elevated temperatures in vacuum (10⁻⁵ mbar), using a heating rate of 20°C/min. Please note that for every high-temperature measurement of the structure’s reflectance, the respective thermal emission at the same temperature was subtracted when determining the absorptivity/emissivity. The resulting emissivity spectra are shown in Fig. 4(a). In heating the structure from room temperature to 900°C, a slight reduction of the emissivity maximum was observed, likely due to thermal annealing of the multilayer. Beyond this temperature, the structure maintained stable performances up to 6 h at 1300°C. Despite the slightly reduced emissivity, the above bandgap emission of the multilayer reached as high as 93% of the black-body limit (see Fig. 4(b)), representing only a small reduction as compared to the predicted value of 96% (Fig. 1(b)) and placing it among the highest emissivities for multilayer structures reported at high temperatures [7]. More dramatic changes were observed for the below-bandgap emission though. Using a polynomial interpolation function to cover spectral regions with increased background noise at longer wavelengths (see Figure S4 for details), we estimated a suppression of below-bandgap emission of 40% of the black-body limit, which is significantly less than the predicted 65%.

Fig. 4. (a) Measured absorptivity spectra for the Al₂O₃/W multilayer deposited on single-crystalline polished SiC and heated up to 1300°C under vacuum and (b) the corresponding emittance at different temperatures (solid lines) compared to the corresponding black-body spectrum (dashed-dotted lines). The vertical dashed black lines represent the InGaAs bandgap at 1.65 µm (0.75 eV).

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The drop in performance as compared to the original design can be attributed to the slight red-shift in the response of the fabricated multilayer, as well as a less steep drop-off in emissivity below the bandgap. The two effects combined placed the emission maximum closer to the bandgap energy of the InGaAs photocell and generates significant below-bandgap emission. Part of the observed changes are reversible, most likely due to temperature dependence of the optical constants in the structure (see figure S5). However, permanent changes in the structure are observed as well, most likely the result of thermally induced changes in the structure of the multilayer. Such changes most likely include annealing of the different layers in the stack and possible oxidation of the W layer, as previously suggested for similar multilayer structures [33]. Our results emphasize the sensitivity of the final performance of the thermal emitter to small changes in the optical performance due to uncertainties in the fabricated geometry and thermally induced changes.

4. Conclusions

In conclusion, we have shown the design, fabrication, and optical characterization of our Al₂O₃/W multilayer for thermophotovoltaic applications. The chosen structure consists of alternating layers of W and Al₂O₃ whose thicknesses have been optimized numerically for operation with an InGaAs photocell. The parameters of fabrication of the emitter are optimized to reduce stresses in the films upon deposition and improve thermal stability under operating conditions. The fabricated structure displays significant enhancement in emissivity when the nanostructure is compared to bulk W films, reaching almost unity emissivity close to the bandgap of the photocell. At high temperatures, modifications of the emissivity spectrum are observed, which can partially be attributed to thermal annealing and possible oxidation of the different layers, as well as the temperature dependence of the optical constants. Importantly though, this initial drop in performance is followed by a stable emission profile at higher temperatures. This suggests that if such thermally-induced changes can be taken into account in the design-phase, further optimized performance with high-temperature stability may be achieved.

Funding

Seventh Framework Programme (309006).

Acknowledgments

We thank Nikolay Komarevskiy for the original development of the evolutionary optimization algorithm and Kevin M. McPeak and Stefan Meyer for technical assistance in thin-film deposition.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Inverse design and realization of an optimized photonic multilayer for thermophotovoltaics

Abstract

1. Introduction

2. Design and fabrication

2.1 Inverse numerical design of an optimized multilayer

2.2 Multilayer fabrication

3. Optical characterization

3.2 Room-temperature reflectivity measurements

3.3 High-temperature performance

4. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (4)

Equations (9)

OSA Continuum