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Abstract
This paper presents a detailed-balance analysis required for the achievement of a high-efficiency spectral selective STPV system utilizing thermodynamic and optical modeling approaches. Key parameters affecting the design and optimization of spectrally selective surfaces that are essential for high-efficiency STPV applications are investigated. A complete GaSb-based planar STPV system utilizing a micro-textured absorber and a nanostructure multilayer metal-dielectric coated selective emitter was fabricated and evaluated. The micro-textured absorber features more than 90% absorbance at visible and near-infrared wavelengths. The selective emitter, consisting of two nanolayer coatings of silicon nitride (Si3N4) and a layer of W in between, exhibits high spectral emissivity at wavelengths matching the spectral response of the GaSb cells. The performance of the STPV system was evaluated using a high-power laser diode as a simulated source of concentrated incident radiation. When operated at 1670 K, an output power density of 1.75 W/cm2 and a system efficiency of 8.6% were recorded. This system efficiency is higher than those of previously reported experimental STPV systems. Optical and thermal losses that occurred at multiple stages of the energy transport process were modeled and quantified. Essential guidelines to mitigate these losses and further enhance the system performance are also provided.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Solar thermophotovoltaic (STPV) systems offer a unique way of converting concentrated solar energy into electricity. They utilize an intermediate element that efficiently absorbs the broad wavelength incoming concentrated solar radiation and thermally re-radiates photons at tailored wavelengths matching with the characteristic bandgap (EBG) of the solar cell. STPV systems aim to achieve efficiencies higher than the Shockley-Queisser (SQ) limit [1] through a spectral modification of the incoming solar radiation with the aid of the intermediate absorber/emitter element. The major contribution to the SQ limit arises from two fundamental losses in the energy conversion process. One is due to the non-absorption of sub-bandgap photons that do not carry sufficient energy to create electron-hole pairs. Second, the excess energy of photons carrying greater energy than EBG of the solar cell is lost as heat during the thermalization process. Spectrally selective absorbers and emitters can greatly enhance the STPV system efficiency by maximizing the absorption of the incident sunlight and suppressing the emission of both sub-bandgap (E < EBG) and excessive energy (E>>EBG) photons, thereby utilizing most of the solar spectrum during energy conversion [2].
A simplified schematic of a typical planar STPV system is shown in Fig. 1(a). A solar absorber is heated by concentrated solar radiation. The absorbed solar energy is reemitted towards a thermophotovoltaic (TPV) cell through the emitter, which is thermally coupled to the absorber. The reemitted energy from the emitter is narrowband thermal radiation matched to the spectral response of the TPV cells. A selective spectral filter placed in between the emitter and the solar cell reflects any sub-bandgap photons back to the emitter for recycling. An infrared (IR) heat shield installed on the absorber side minimizes the thermal radiation loss from the absorbing surface [3]. Effective recycling of the low energy photons greatly improves the system efficiency [3–6]. A thermal management system is utilized in STPV for keeping the TPV cells near the room temperature (300 K) during operation under high thermal stress.
Fig. 1. (a) Schematic of a typical planar STPV system. (b) Maximum ηsol-th, ηth-elec, and ηSTPV as a function of the absorber/emitter temperature under fully concentrated sunlight and a blackbody absorber.
The upper bound for STPV conversion efficiency can be derived by realizing an STPV system as an ideal solar-thermal engine [7]. At the most fundamental level, the solar-thermal engine can be assumed to have two stages of energy conversion: solar-to-thermal conversion by the intermediate element and thermal-to-electric conversion by TPV cells. The ultimate STPV efficiency (ηSTPV) is the product of the efficiencies of the two intermediate stages, solar-to-thermal conversion efficiency (ηsol-th) and thermal-to-electric conversion efficiency (ηth-elec). The theoretical limits of ηsol-th, ηth-elec, and ηSTPV as a function of the steady-state temperature (TA) of the absorber/emitter is shown in Fig. 1(b). Note that high TA provides low ηsol-th but high ηth-elec, and vice-versa. The optimal value of TA that maximizes ηSTPV is 2544 K, and the corresponding system efficiency is 85.4%. Therefore, in theory, the STPV technology has a very similar ultimate solar-to-electricity conversion efficiency limit as that for an infinite number of stacked monochromatic solar cell junctions illuminated by a maximum solar concentration [8]. However, this efficiency can only be achieved for an ideal STPV system with several constraints, such as operating under a full solar concentration of 46000X, monochromatic emission from the emitter, and using the TPV cells with no optical losses and non-radiative recombination, that cannot be achieved in practical STPV systems [9,10]. A realistic STPV system uses TPV cells with finite conversion losses and is required to have a broader bandwidth than a monochromatic emitter to maximize the open-circuit voltage and impedance matching in the TPV cells [2]. In previous simulation studies, conversion efficiencies around 45% were reported for less idealized STPV systems [2,11,12].
In a practical STPV system, there are conversion losses within the TPV cell, reflection and reemission losses from the absorber, cavity losses due to non-unity radiative view factor (VF) between the emitter and the cells, and a loss due to the emission of sub-bandgap photons. Designing a high-efficiency STPV system is a balancing act and requires a comprehensive understanding of all the loss mechanisms within a STPV system. This paper formulates thermodynamic simulations for a comprehensive understanding of energy transport at various components of a planar STPV system as well as to derive optimal parameters for high-efficiency system operation. Based on the knowledge acquired from the simulations, a complete STPV system is designed, fabricated, and tested using Gallium Antimonide (GaSb) cells. Combining the results from simulation and experiment, a necessary framework for further investigation and towards improving the overall system efficiency is also provided.
2. Absorber requirements
When the concentrated solar radiation is incident on the absorber surface, a part of the incident solar energy is lost due to the reflection from the absorber. A near-blackbody absorber, such as an array of vertically aligned multi-walled carbon nanotubes [4], can offer high absorptance over a broad range of the solar spectrum. Because a good absorber is a good emitter too, there will be a significant radiation loss from the absorber as it reaches high temperatures. Therefore, another requirement for an efficient absorber is to have low emittance, especially in near-infrared wavelengths, where the blackbody radiation is higher for STPV operating temperatures. A selective absorber with an extremely high absorbance near the peak of the solar spectrum and low emittance (or absorbance) at infrared wavelengths can greatly enhance the absorber-to-emitter thermal extraction, which is desirable for a high-efficiency STPV system [3,5]. Figure 2(a) shows an example absorbance spectrum (in blue) of an ideal absorber for a STPV system operating at 1700 K along with the blackbody radiation curve (magenta) and the normalized solar spectrum (black) at an air mass (AM) of 1.5. The overlap between solar energy and the thermal emission indicates that a perfect absorber is not feasible. An optimization of absorber-side cut-off wavelength (λabs-cut) is required to maximize the net accumulated spectral flux (Φ), which is the absorbed solar energy minus the reradiated thermal loss [13] from the absorber, and is given by the following equation:
Fig. 2. (a) Normalized values of AM1.5 solar spectra (black), blackbody radiation curve at 1700K (magenta), and the absorptivity of an ideal absorber (blue step function). (b) Net radiation flux collected by the absorber as a function of cut-off wavelength (λabs-cut) for the equilibrium temperatures of 1400 K (solid blue curve) and 1700K (solid red curve), while ${C_x}$ is assumed to be 100. The optimal values of λabs-cut, where $\emptyset $ is maximum, are shown by vertical dashed lines. (c) Same as (b) but for a constant equilibrium temperature of 1700K at ${C_x}$=100 (red) and ${C_x}$=300 (blue).
3. Emitter requirements
EBG of a GaSb cell is ∼0.72 eV (or λBG = 1.72 µm) at room temperature. For a blackbody emitter at 1700 K, only 26% of the emitted spectrum is above the GaSb cell bandgap [14]. Clearly, a blackbody is not an ideal choice for an STPV emitter, unless an effective recycling scheme is incorporated to reflect unconvertible photons back to the emitter. Otherwise, spectral selectivity is required for the emitter to suppress the emission of the longer wavelength photons (λ>λBG) beyond the TPV cell bandgap, while enhancing the emission of photons with energy above the bandgap (λ<λBG). Besides, thermal stability is an important factor to consider when designing a spectral control element. Rare-earth elements like erbium, thulium, and ytterbium, and refractory metals, such as tungsten (W), molybdenum (Mo), and Tantalum (Ta), are promising materials for fabricating a selective absorber/emitter because of their high melting point and good intrinsic selective emission properties suitable for STPV applications [7,15]. Pfiester and Vandervelde [16] provided a detailed review of many different solutions for designing spectrally selective thermal emitters. One key parameter of a STPV emitter is choosing the operating temperature of the emitter, which is governed by the bandgap of the TPV cells. The optimal operating temperature for an emitter is one for which the blackbody emission peak wavelength lies just above the bandgap of the TPV cell. Low bandgap cells (<1 eV) are preferred because they require lower operating temperatures (<1800 K) for the emitter. Silicon (Si), which is commonly used in conventional PV cells, has an indirect bandgap of 1.12 eV or λBG = 1.11 µm and is regarded high for TPV applications. For a Si-cell based STPV system, the optimal operating temperature would be ∼2600 K, which is quite high. For TPV conversion, Germanium (Ge), GaSb, and Indium Gallium Arsenide Antimonide (InGaAsSb) cells are of considerable interest due to their low bandgap. Figure 3(a) shows the optimal emitter temperature required for a STPV device using different bandgap TPV cells. In this study, GaSb TPV cells manufactured by JX Crystals Inc. are used. The desired emitter temperature for GaSb TPV cells is ∼1700 K.
Fig. 3. (a) Optimal STPV operating temperatures (red line) for different bandgap TPV cells. The vertical dashed lines show the bandgap values at 300 K. (b) EQE plot for GaSb TPV cells purchased from JX Crystals along with a varying bandwidth step function. (c) Thermalization loss and ηTPV as a function of emitter bandwidth computed at 1700K emitter temperature. The bandwidth corresponding to the peak ηTPV is shown by a dashed vertical line.
Another key aspect of designing a selective emitter is the bandwidth of thermal emission. One would desire that the selective emitter has adequate bandwidth of thermal emission above the bandgap so that the TPV cells would produce maximum output power. However, increasing the bandwidth far above the bandgap may result in increased thermalization loss that impairs the TPV conversion efficiency (ηTPV). The optimal bandwidth of thermal emission to maximize ηTPV can be derived using the external quantum efficiency (EQE) data of the TPV cells. The GaSb cell EQE is shown in Fig. 3(b) (courtesy of JX Crystals Inc.). The right edge of the EQE plot represents λBG. The simulated values of thermalization loss and ηTPV as a function of the selective emitter bandwidth (Δλ) are shown in Fig. 3(c). The spectral emittance is assumed to have a unit step function response with its right edge being fixed at λBG. Δλ is varied by shifting its left edge towards shorter wavelengths. In the simulation, the emitter temperature is considered to be 1700 K and the GaSb cells are maintained at room temperature. The thermalization loss (red curve) increases with increasing the bandwidth until the bandwidth surpasses the left edge of the EQE curve. The optimal bandwidth of selective thermal emission for maximum ηTPV is estimated to be around 400 nm.
An ideal selective emitter with a unit step response for spectral emittance is not possible to fabricate in practice [13]. So, for a practical selective emitter, there are two figures of merit that are commonly used to assess its performance. They are spectral selectivity (ηsel) and in-band emissivity (εin-band), which are defined by Eq. (2) and Eq. (3), respectively.
4. Photon recycling
In real STPV systems, the practical implementation of any spectral selectivity exhibits non-idealities [13] that prohibit from achieving a zero emittance above λabs-cut for the absorber side and above λBG for the emitting surface. In both cases, the emission of the longer wavelength photons leads to increased thermal radiation loss within the STPV system. A significant improvement in the system efficiency can be achieved via recycling schemes that involve reflecting these unused photons back to the absorber/emitter. On the absorber side, a heat shield made of a material with high infrared reflectivity, such as gold (Au), can be installed to reflect the thermal radiation back to keep the absorber hot. Figure 4(a) shows the emittance of a W surface alone (black curve) and its effective emittance (εEff in green curve) in the presence of a Au reflector placed at 1 mm distance from the absorber surface modeled using Eq. (4) [3,13].
Fig. 4. (a) Effective absorptivity (green) of a W-Au arrangement is significantly lower than that of plain W (black) at shorter wavelengths due to the high infrared reflectivity of Au (red curve). The benefit of using the Au heat shield is larger at higher temperatures due to the blackbody radiation curve (blue for 1000 K and magenta for 1700K) shifting towards shorter wavelengths where the emissivity of W is greater. (b) GaSb cell reflectance (blue) measured using the Varian Cary 5E Spectrophotometer. The reflectance of only the active cell area is shown in green. The dashed vertical line represents the λBG for GaSb.
On the emitter side, one would prefer all low-energy photons below the bandgap are reflected back to the emitter. A selective window filter that is transmissive to in-band radiation and highly reflective at wavelengths >λBG placed in between the emitter and TPV cell can serve this purpose. Several resonance and plasma-interference filter structures based on semiconductors and transparent conducting oxides as potential edge filters have been reported in previous studies for photon recycling in STPV systems [17–19]. Recycling of sub-bandgap photons can also be achieved using metal reflectors at the back interface of TPV cells. A recent study [20] reported achieving a 95% average reflectivity for below-bandgap photons by incorporating a rear gold reflective mirror in a lattice-matched In0.53Ga0.47As TPV cell. The spectral reflectance of the GaSb TPV cells purchased from JX Crystals Inc. is shown in Fig. 4(b). The blue curve represents the area-weighted surface reflectance (due to the active area of the cell and the silver grid bars) measured using the Varian Cary 5E Spectrophotometer. After accounting for the reflectance from the silver grid bars, the active area of cells has maximum absorption (∼5% reflectance) near 1.4 µm (green curve), where the spectral response of the cell is at peak. At sub-bandgap wavelengths (above λBG), these cells can offer an average reflectivity of ∼30% for photon recycling.
5. Geometric optimization
High-efficiency STPV systems require a high absorber-to-emitter heat extraction rate. Thermal extraction efficiency (ηe), which is the ratio of the power emitted by the emitter to the power incident on the absorber side, is governed by both spectral and geometric properties of the absorber and emitter [21]. Suppressing the reflection and emission losses from the absorber surface, and meanwhile, maximizing εin-band of the emitter surface can yield in a high ηe value. High absorbance of the absorber also results in high emission losses from the absorbing surface. Besides spectral selectivity, geometric optimization can also help in reducing the absorber-side emission losses. This is usually done by keeping the absorber area small compared to that of the emitter [14,21,22]. The geometric control of ηe is, therefore, defined by the emitter-to-absorber area ratio (AR). Figure 5(a) illustrates the dependency of ηe on AR for 3 cases: (a) both absorber and emitter are blackbody surfaces (red curve), (b) emitter is blackbody while absorber is spectrally selective with λabs-cut=2.0 µm (blue curve), and (c) both absorber and emitter are blackbody with the inactive area of the absorber being shielded with an Au reflector. In each of these cases, the steady-state temperature of the absorber/emitter surfaces is assumed to be 1700 K. In a planar STPV design, the absorber and emitter share the same substrate. Usually, one side of the planar substrate serves as an absorber and the opposite surface as an emitter. For equal-area (AR=1) blackbody emitter and absorber, ηe=50% (red curve) as both the surfaces emit an equal amount of radiation (assuming the radiation losses from edges are negligible). The radiation loss from the absorber can be lowered by decreasing the absorber surface area or increasing AR. For an AR=10, ηe increases to ∼90%. For a planar STPV configuration, the physical dimensions of the absorber and emitter sides are likely the same as they use the common planar substrate. However, the active absorber area, which receives the concentrated solar radiation, can be limited to a smaller portion of the absorber side. The remaining or inactive area on the absorber side is required to have low emittance (ideally zero) to minimize radiation loss. The red curve in Fig. 5(a) assumes that the radiation loss from the inactive area on the absorber side is zero for AR>1. This is not true in practice. In a real STPV setup, the inactive area is shielded with a heat reflector. This case is illustrated with the dashed black curve in Fig. 5(a), where an Au-based heat reflector is used to shield the radiation loss from the inactive area. The value of ηe is little lower but comparable to the case where the inactive area has zero emittance. Significant improvement in ηe can be achieved at lower AR if the absorber features a spectral selectivity with λabs-cut=2.0 µm. This is because at 1700 K, a blackbody emits a significant fraction of radiation beyond 2.0 µm. The suppression of this radiation results in a greater ηe at lower AR values.
Fig. 5. (a) Effect of Emitter-to-absorber area ratio on thermal extraction for a blackbody absorber and emitter (red), selective absorber (blue), and blackbody absorber with a gold heat shield. (b) Cavity loss as a function of the separation distance between two equal-area square parallel plates.
Owing to a finite spacing between the emitter and TPV cells, not all the radiation leaving the emitter surface is intercepted by the cells. This is referred to as cavity loss. A radiative view factor (VF), which is defined as the fraction of the radiation leaving the emitter that strikes the cells, can be computed based on the geometry and orientation of the two surfaces. Cavity loss is computed as (1-VF). The cavity loss (expressed in %) for two square surfaces as a function of the separation distance (d) between them is shown in Fig. 5(b). The cavity loss increases exponentially with d. For d=1 mm, the cavity loss is ∼8% (VF=0.92). The cavity loss increases to 50% when d=10 mm. VF is a crucial parameter to be considered in the design of a high-efficiency STPV system.
6. Experimental validation
Despite the significant potential of STPV systems, very few experimental demonstrations have been reported so far. Early designs were based on cylindrical configurations utilizing a centered radiator surrounded by a large cavity made of TPV cells [9,23,24]. Their reported efficiencies were poor (<1%), mostly due to high cavity losses, lack of cooling systems to prevent overheating of the TPV cells, high optical concentration losses, inefficient thermal extraction, and low area-ratio of the emitter to TPV cells. In 2014, Lenert et al. [4] built a more robust and efficient STPV system using a vertically aligned multi-walled carbon nanotube blackbody absorber and a 1-D Si/SiO2 photonic crystal as a selective emitter. It was a compact planar design using a narrow-bandgap InGaAsSb TPV cell (0.55 eV) that allowed efficient operation at lower system temperature (1285 K). The system efficiency of 3.2% was reported when tested under simulated solar conditions. Later, Ungaro et al. [25] demonstrated a high-efficiency STPV system utilizing nanostructures-based selective absorber/emitter fabricated on a W substrate. The reported efficiency was 6.2% at ∼1700K using GaSb cells. Another high-efficiency planar STPV system was reported by Kohiyama et al. [3] with a measured system efficiency of 5.1%. They utilized multilayer coatings of Molybdenum (Mo) and Hafnium oxide (HfO2) on a Mo substrate for fabricating spectrally selective absorber and emitter surfaces. An in-depth analysis of the spectrally selective thermal emission from the HfO2-Mo trilayer emitter structure was described by Blandre et al. [26]. Similarly, Bierman et al. [6] fabricated a high-efficiency STPV system by pairing a tandem plasma-interference optical filter with a 1-D Si/SiO2 photonic crystal based selective emitter. The filter was engineered to recycle 80% of the sub-bandgap photons by reflecting them back to the emitter. Using an InGaAsSb cell, the reported system efficiency was 6.8%. Recently, a high-efficiency TPV system employing a Si rod-type photonic crystal thermal emitter and InGaAs cells was reported by Suemitsu et al. [27]. The emitter was heated using an internal electric heater and a TPV conversion efficiency of 11.2% was experimentally measured at a radiating temperature of 1338 K.
Here, we fabricated a planar STPV system using GaSb TPV cells and a spectrally selective emitter. The spectral properties of emitter were optimized to maximize the conversion efficiency. The following sections describe the fabrication details and performance evaluation of the experimental STPV system.
6.1 Fabrication of absorber and emitter
The absorber and emitter were fabricated on the top and bottom surfaces of a 25.4 × 25.4 × 0.5 mm polished W substrate. For absorber, a 0.64 cm2 rectangular area on the top surface was micro-textured to enhance the absorptance by scanning an IPG Photonics YLP-1/30 nanosecond 1064 nm pulsed laser over the absorber surface using Galvo. The whole 6.45 cm2 area on the bottom surface of the W substrate served as emitter and was composed of a multilayer nanostructure to achieve spectral selectivity. The multilayer structure consists of two layers of Si3N4 dielectric and a layer of W sandwiched in between. The optical response of the multilayer emitting surface was modeled using a standard transfer matrix method (TMM). The optical constants for W and Si3N4 required for the TMM simulation were obtained from the literature [28,29]. A parametric sweep allowing the film thicknesses of the three nanolayers to vary with a 5 nm step size was run to derive the optimal thicknesses that would result in high ηsel and εin-band to maximize the GaSb cell output. The spectral absorptivity of 12 such simulation cases is shown in Fig. 6. Case 1 represents the absorptivity of plain W. The values of ηsel and εin-band computed for all these cases are listed in Table 1. Tungsten exhibits an excellent ηsel (69.2%) but poor εin-band (0.33). Based on the simulated reflectance spectra, the multilayer structure consisting of two 120 nm layers of Si3N4 and a 25 nm layer of W in between (Case 9 in Fig. 6 and Table 1) offers the combined optimal values of ηsel (∼71%) and εin-band (0.95).
Fig. 6. Simulated absorptivity of multiple Si3N4/W/Si3N4 thin-film stacks aimed for achieving a high spectral selectivity emitter for GaSb TPV cells.
Table 1. ηsel and εin-band computed for different emitting surfaces.
A selective emitter was fabricated on the W substrate by depositing Si3N4 and W films with thicknesses described in Table 1 for Case 9. The two Si3N4 layers were deposited by plasma-enhanced chemical vapor deposition (PECVD) method in an Oxford Plasmalab System 100 reactor using silane and ammonia gas mixture diluted in argon. The process of mixing high and low-frequency powers was employed to minimize the film stress and, at the same time, to obtain a higher film density. The substrate temperature during the deposition process was maintained at 300°C. The W film was sputtered onto the substrate at room temperature from a high-purity (99.95%) W target at 90W DC power and 0.67 Pa Ar gas pressure. The deposition rate of these films was calibrated using ellipsometry measurements.
6.2 Experimental setup
A complete STPV system was assembled inside a vacuum chamber. Two thin fused silica rods were used to support the W substrate over the GaSb TPV cells (total cell area is 5.92 cm2) with a spacing of ∼1.5 mm. The temperature of the cells and the emitter was monitored using type R thermocouples that were bonded to the substrate and the cell mount using the OB-600 high-temperature chemical set cement purchased from OMEGA. A reflective heat shield constructed of a gold foil mounted on an aluminum frame was installed on the absorber side (separation distance = ∼2 mm) covering the non-textured area of the W substrate. A 9.5 CFM capacity 2-stage vacuum pump was run to achieve vacuum conditions of 80 mTorr. A 300 W continuous-wave line-focus laser diode (λ=808 nm) was set up to simulate the concentrated incident radiation in the lab. The laser was focused on the 0.64 cm2 rectangular micro-textured absorbing surface. The emitter surface and the textured absorber area are shown in Figs. 7(a) and 7(b). The complete STPV system is depicted in Fig. 7(c). The incident laser power is varied to achieve multiple steady-state temperatures. During the experiment, the peak power output from the GaSb cells delivered to a resistive load was recorded using multimeters.
Fig. 7. (a) Picture showing the emitter side of the W substrate. (b) Picture showing the textured absorber area (dark stripe) of the W substrate mounted on silica rods and a thermocouple bonded to it. (c) Experimental setup of the STPV system built for this study. The inset shows the heated absorber/emitter substrate viewed from the top glass window. The absorber-side heat shield was removed in this picture.
6.3 System characterization
Various components of the STPV system were characterized before the full experimental evaluation. The absorptance (1-reflectance) of the micro-textured absorbing surface was measured at visible and near-infrared wavelengths using multiple laser sources (405 nm, 532 nm, 634 nm, 980 nm, 1064 nm, and 1342 nm) and a Labsphere RTC-060-SF integrating sphere (IS). The absorptance was found to be nearly constant (∼92%) across the wavelength of 400-1000 nm. At 1342 nm, the absorptance dropped to 87%. Figure 8 shows these absorptance measurements in green squares. A second-order regression was fitted (green curve) to these data to model the reflection loss from the absorber surface for an incident solar radiation between 0.4 µm to 2 µm. The specular reflectance of the Si3N4/W/Si3N4 emitter surface was measured between 300-3300 nm using a Varian Cary 5E Spectrophotometer. Some differences were observed between the measured and simulated absorption spectra, which is attributed to inadequate control of the deposited film thickness. Ellipsometry measurements of the emitter surface revealed that the three films were under deposited by ∼10% of the aimed thickness. Also, the measured absorptivity was found little higher at longer wavelengths (>λBG), which is attributed to the differences in the optical constants of the materials used during fabrication and the values used in the TMM simulation. Both n and k values of the W and Si3N4 materials used in the emitter coatings were also measured using a J.A. Woollam M2000 Variable Angle Spectroscopic Ellipsometer that has a wavelength range up to 1.6 µm. The ellipsometry measurements mostly match well with the optical constants used in the simulation except for the n value of W at certain wavelengths. For wavelengths below 1 µm, the n values used in the simulation [28] are consistent with the ellipsometry measurements. Near 1.3 µm, the measured n value of W is ∼15% lower than that used in the simulation. Beyond 1.5 µm, the measured n values were found larger than those reported in the literature [28]. This discrepancy in the n values of W resulted in a reduced absorptivity (lower spectral irradiance) of the Si3N4/W/Si3N4 emitter near 1.3 µm, and a much greater absorptivity (greater spectral irradiance) in the sub-bandgap wavelengths. Despite these differences, the fabricated selective emitter exhibits good ηsel and εin-band values of 58% and 91%, respectively.
Fig. 8. (a) Spectral irradiance of the thermal radiation emitted from a blackbody (dashed magenta curve), the Si3N4/W/Si3N4 selective emitter (based on modeled absorptivity is in red and that using the measured absorptivity is in blue), and a W emitter at 1700K. The EQE of the GaSb cell and the measured absorptivity of the micro-textured absorber are also shown.
The spectral irradiance of the thermal radiation emitted from a blackbody, the Si3N4/W/Si3N4 emitter surface, and a W emitter at 1700K are also shown in Fig. 8 along with the EQE of the GaSb cell. For the Si3N4/W/Si3N4 and W emitters, the spectral irradiance was derived by convolving the spectral absorptivity with the blackbody irradiance. Two sets of irradiance curves are shown for the Si3N4/W/Si3N4 emitter. One is based on the modeled absorptivity (case 9, Fig. 6), and is shown by the red curve in Fig. 8. The other set (blue curve) is derived using the measured absorptivity of the fabricated sample. For the fabricated sample, the spectral emission for λ>λBG is higher compared to that for the modeled spectra. This is due to the higher measured absorptivity of the selective emitter at longer wavelengths, as described in the previous paragraph. The increased sub-bandgap emission would not only impair the system conversion efficiency but also adds to the heat load on the TPV cells [30]. An effective thermal management system is essential in STPV systems to maintain the temperature of the TPV cells near the ambient temperature.
A STPV system’s energy balance can be described by the following equation:
The projected thermal-to-photovoltaic conversion efficiency (ηTPV) for the different emitter types shown in Fig. 8 at the radiating temperature of 1700K are listed in Table 2. The radiating temperature is assumed to be 1700K. The photovoltaic conversion efficiency (ηGaSb) of the GaSb cells for the in-band incident radiation (between 0.4 to 1.72 µm) is assumed to be 30% [32]. The total (0.4 to 10 µm), in-band (0.4 to 1.72 µm), and sub-band (1.72 to 10 µm) radiated power densities, which are represented by Prad, Pin-band, and Psub-band, respectively, are also provided in Table 2. The maximum heat load (Pheat-load) on the TPV cells can be computed using the following expression:
where the factor of 0.7 indicates that 30% of Pin-band is transformed into electric power. The expected short-circuit current density (JSC) for the GaSb cell illuminated by these radiators are computed as:Table 2. Performance evaluation parameters for the different emitter types radiating at a steady-state temperature of 1700K.
Similarly, the GaSb cells were also characterized. The reflectance spectra of the cells were already discussed in section 4. The fill factor (FF) of the cells was measured using a quartz tungsten halogen (QTH) lamp source and found to be 0.66. The photovoltaic conversion efficiency (ηGaSb) of the GaSb cells for a spectrally matched narrowband IR spectrum was experimentally computed. The narrowband spectrum was derived from the QTH lamp source and a 200 nm bandwidth optical bandpass filter (center wavelength at 1337 nm) purchased from PIXELTEQ. The QTH lamp output was calibrated using Thorlabs’s PM100D power meter. The maximum ηGaSb was measured to be 26.3%. The measured ηGaSb is slightly lower than the manufacturer-reported value of ∼30% for spectrally matched incident radiation [32,33].
6.4 Results and discussion
The STPV system was evaluated for a varying level of the incident laser power simulating the concentrated solar radiation. The steady-state temperature of the W substrate and the peak output power from the GaSb cells were recorded. The modeled and measured TPV cell output power density, as well as the overall system efficiency (ηSTPV) at different STPV temperatures are shown in Fig. 9. The modeled output power and ηSTPV are based on the measured absorptivity of the selective emitter. The thermal radiation from the emitter has a better spectral matching with the EQE of the GaSb cells at higher temperature that results in an exponential increment in the TPV cell output and improved system efficiency. Both the measured TPV cell output and system efficiency follows the simulation curves closely. A maximum electrical output power density of 1.75 W/cm2 was recorded at a temperature of 1670 K. The required incident laser power was 132 W that is equivalent to a solar concentration factor of ∼2060 (assuming air mass of 1.5), which is readily achievable with Fresnel lens setup.
Fig. 9. (a) Experimental (red crosses) and simulated (black curve for blackbody emitter and blue curve for our selective emitter) TPV cell output power at various absorber/emitter temperatures. (b) Modeled (black curve is for no photon recycling and blue curve is with photon recycling) and experimental (red crosses) STPV system efficiency obtained at various operating temperatures.
The modeled losses computed using thermodynamic simulations at different stages of energy transport in our STPV system operating at 1670 K are shown in Fig. 10. Each loss is expressed in both watts as well as % of total incident power (in the parenthesis). The thermodynamic formulation of these losses is described in more detail in our previous study [14]. The simulated input power (Pin) required to obtain a steady-state temperature of 1670 K is 119.8 W. The modeled ηSTPV value at 1670 K temperature is 10.1%. The experimentally measured ηSTPV is 8.6% after normalizing the TPV cell output power density to the emitting surface area. The difference between the modeled and measured system efficiency is attributable to simplified approximations employed at various stages of the simulation. One such example is the temperature dependence of the selective emitter absorptivity, which is not accounted for in the simulation. The deviation of optical properties at TPV operating temperature can have a direct impact on the surface spectral characteristics of the design and hence affect the overall conversion efficiency. Previous studies have illustrated that the optical properties and the surface absorptivity of W are temperature-dependent [34–37]. One experimental study [35] showed that the n value of W significantly increases with temperature at near-infrared wavelengths, and nearly doubles at 2 µm when the temperature is raised from 300 K to 1500 K. Compared to W, Si3N4 has a much lesser dependence of surface absorptivity with temperature, especially below wavelengths less than 8 µm [38]. Bhatt et al. [39] investigated the temperature-dependency of the spectral absorptivity of the Si3N4/W/Si3N4 selective emitter using both simulation and experimental methods. For wavelengths less than 1.4 µm, the absorptivity was found to have minimal dependence on temperature. As such, ${\varepsilon _{in - band}}$ remains fairly stable between 300 K and the STPV temperatures. At longer wavelengths, the absorptivity was found to increase noticeably with temperature. At 1500 K, the increased absorptivity beyond 1.7 µm lowered the modeled ηsel value from 71% to 60%. This suggests that the actual sub-bandgap loss in our system is larger than the modeled value shown in Fig. 9. Considering the modeled absorptivity spectra at 1500 K, the simulated system efficiency for the experimental setup in this study reduces to ∼9% at 1670 K, which is in a better agreement with the experimentally measured ηSTPV = 8.6%.
Fig. 10. Power flow diagram showing losses at different stages of the STPV system operating at T=1670 K.
The combined reflection (Pref) and emission losses (Prad, abs) from the absorber side is ∼20% of the input power. In the current setup using the high-power laser for heating the absorber/emitter substrate, Pref is 8% of the incident power. If the STPV system were tested with a realistic solar simulator, such as a conventional xenon arc light source, Pref would increase to 9.5% due to the increased reflectivity of the micro-textured absorber at longer wavelengths (Fig. 8). Owing to this increased Pref, ηSTPV would reduce to 8.4% under concentrated broadband solar radiation. In a real environment, the efficiency of the solar concentrator setup should also be considered. The emission from the 4 sides (Prad, side), convective (Pconv), and conduction (Pcond) heat losses is less than 5% of the incident power. The modeled ηe is ∼79%. The installation of the Au heat shield is key for achieving such a high ηe. The values of AR and VF in our STPV setup are 10 and 0.91, respectively. Approximately 24 W of thermal power radiated from the emitter is reflected back to the emitter by TPV cells. The simulated output power density for the GaSb cells at the 1670 K emitter temperature is ∼2 W/cm2, which is ∼14% greater than the experimentally measured value. Note that the simulation assumes the TPV cells are maintained at room temperature. During the experiment, the TPV cell temperature was measured to be 321 K that resulted in a ∼6% drop in the open-circuit voltage of the GaSb cells.
STPV systems are versatile and can utilize alternative sources of heat, such as radioisotope heaters, thermal storage systems, combustible materials, industrial waste heat, etc., as inputs. The integration with other heat sources allows a STPV system to produce continuous electrical power 24 hours a day, thereby making STPV very appealing for many residential [40–42], industrial [32,43], automotive [44,45], and space applications [46]. The 8.6% system conversion efficiency demonstrated in this study may appear low compared to other photovoltaic technologies. However, the lower ηSTPV is compensated by the system’s ability of continuous operation without the presence of the sun and producing high electric power density. A 1 m2 conventional solar cell panel with a conversion efficiency of 25% produces 1 kWhr electricity in approximately 7 days by operating for ∼6 hours a day. With the illustrated output power density of 1.75 W/cm2, the proposed STPV system with a 1 m2 cell area can produce the same amount of electricity in less than 4 minutes. Therefore, the STPV system can be made cost-effective by optimizing the design to produce high electric power density at a reasonable conversion efficiency.
6.5 Thermal management of TPV cells
Thermal management of the TPV cells is an important aspect of STPV design. During STPV operation, ${P_{heat - load}}$ must be effectively dissipated to maintain the TPV cells at near ambient temperature. TPV cells operating at high temperatures are less performing. EBG, and hence VOC, of GaSb decreases with increasing cell temperature [33]. The optimization of the emitter bandwidth discussed in section 3 assumed the cell temperature to be 300 K. A reduction in EBG of GaSb due to increased cell temperature shifts λBG to longer wavelengths and can potentially affect the emitter design metrics. As such, a more precise design of a selective emitter requires consideration of the thermal effects in the PV cells. For instance, an STPV system implementing a less efficient thermal management would require an emitter bandwidth lower than that reported in section 2 to suppress ${P_{heat - load}}$. Similarly, a 21% reduction in the maximum output power density was reported for the JX Crystals GaSb cell when the cell temperature was increased from 303 K to 373 K [47]. In order to maximize ηSTPV, it is important to employ energetically economic approaches for thermal management. Because STPV systems operate in vacuum conditions, convection cooling is not feasible. Recently, radiative sky cooling has attracted increased attention for its potential application for thermal management in TPV systems [48–50]. Radiative cooling is a passive approach of dissipating excess heat into the cold deep space via thermal radiation using a selective cooling surface with a very high emissivity within the Earth’s atmospheric window (8-13 µm) [51,52]. Zhou et al. [48] performed realistic simulations of radiative cooling for TPV applications and reported that a cooling emitter made of a low-iron soda-lime glass surface with 2D-periodic photonics crystal structures can potentially cool the TPV cells to ambient temperature given that the area of the cooling emitter is ∼70 times that of the TPV cell. Their simulation study also assumed a narrowband selective emitter at 1500 K with no sub-bandgap radiation.
Due to high ${P_{heat - load}}$ in our STPV design, the required radiative cooling structure would be impractical in size or perhaps inadequate on its own for cooling the GaSb cells unless the heat sources inside the cells are reduced. Blandre et al. [49] showed decreasing the TPV emitter radiation by reducing the absorptivity or lowering the emitter temperature are suitable solutions to mitigate the heating effects in the cells. ${P_{heat - load}}$ can also be reduced by implementing a highly reflective metal surface as the back contact of the TPV cells to reflect the sub-bandgap photons back to the emitter. The overall system efficiency can still be the same (or even higher due to a lower cell temperature) because decreasing the thermal emission from the emitter also reduces the amount of incident power required to achieve a steady-state temperature of the emitter [49]. The feasibility of using radiative cooling in our STPV system requires comprehensive design study and radiative transfer modeling of a cooling structure, which is beyond the scope of this paper. Here, a water-cooling system comprising of a 5 cm x 5 cm x 0.5 cm copper fin heat sink was employed for the thermal management of the GaSb cells. Because an active water-cooling setup is a closed-loop system, the pump power is only required to overcome dynamic friction losses caused by the pipe walls. The pumping power must be subtracted from the TPV system output power to estimate the system efficiency. This prototypic study did not consider the power consumption of the cooling pump because the TPV cell modules producing power were only 5.92 cm2 in area. The cooling cost per unit area of the TPV cells is largely diluted in a large-scale STPV system. Seyf and Henry [53] showed that the required pumping power for the thermal management of a 1 m2 size of TPV cell arrays is insignificant compared to the net power generated by the TPV cells.
6.6 Thermal stability of emitter
Both W and Si3N4 were selected for this study due to their high melting point and near-similar thermal expansivity [54–58]. The surface morphology of the micro-textured absorbing surface and the Si3N4/W/Si3N4 coated emitter surface was examined using a FEI Quanta 650 scanning electron microscope (SEM). No noticeable change was observed in the surface morphology of the absorber surface after annealing at 1670 K for ∼1 hour. However, the emitter surface developed random cracks (Fig. 11(a)) after ∼ 15 minutes of operation at 1670 K, indicating the presence of in-plane tensile stresses [59–61]. Over some cracked areas, the top Si3N4 film was found to be peeled off from the W layer. The tensile stress built up in the Si3N4 film is attributed to a slight mismatch in the coefficient of thermal expansion (CTE) between the adjacent layers of Si3N4 and W. The CTE of W is 4.4 × 10−6 K−1 at 300 K and can rise to 5.7 × 4x10−6 K−1 at 1600 K [54,57,62]. Fang et al. [63] measured the CTE of bulk Si3N4 as 3.3 × 10−6 K−1 at 300 K, and ∼6.4 × 10−6 K−1 at 1000 K. Based on the experimentally derived CTE values for Si3N4 and W from the literature, an in-plane compressive stress is likely to occur in the Si3N4 film at annealing temperatures below 800 K. The compressive stress can impair the adhesion and possibly cause partial delamination between the Si3N4 and W films. A stress reversal occurs at higher annealing temperatures (>800 K), resulting in an in-plane tensile stress that increases with temperature. The occurrence of the random cracks is, therefore, attributed to this in-plane tensile stress developed at higher annealing temperatures. A similar thermally-induced structural damage to PECVD Si3N4 films at elevated temperatures was also reported by Liu et al. [60].
Fig. 11. (a) SEM image of the Si3N4/W/Si3N4 selective emitter after annealing at 1670 K for ∼15 minutes. (b) Zygo NewView 7300 surface profile depth measurements of two consecutive craters (shown in the inset) of the Si3N4 film after annealing. The penetration depth profile (right) showed that the crack penetrated through the entire thicknesses of the top Si3N4 film and delaminated from the W film. (c) Measured (black) and fitted (red) Raman spectra of the emitter sample annealed at 1670 K for ∼1 hour.
The cracked areas, where peeling occurred, were also examined with a Zygo NewView 7300 optical profilometer. The surface profile depth measurements of two consecutive craters (Fig. 11(b)) showed that the crack penetrated through the entire thicknesses of the top Si3N4 film. The depth of the craters closely matches the thickness of the top Si3N4 film. This indicates that only the top Si3N4 film has peeled off. After operating at 1670 K for ∼15 minutes, ηSTPV dropped to ∼7%. The spectrophotometer data of the annealed sample revealed that the εin-band value was lowered to 0.78 due to the reduction in the spectral emissivity of the emitter surface over the EQE wavelengths of the GaSb cells. A continuous one hour of operation at 1670 K resulted in a complete failure of the Si3N4/W/Si3N4 structure. The annealed emitter surface now exhibits visible granular features, and the reflectance of the structure is no more specular in nature.
To understand the failure of the structure after the prolonged heating at 1670 K, a Raman spectroscopy of the annealed sample was performed using a Renishaw inVia Confocal Raman Microscope and a 405 nm laser excitation. The resulting Raman spectra were analyzed using Bio-Rad’s KnowItAll Informatics System Software, and the results are shown in Fig. 11(c). The black curve is the measured Raman spectra, whereas the red curve is the best-fit spectra from Bio-Rad’s database. The measured Raman spectra matches very well with that of tungsten trioxide (WO3) with three intense peaks occurring at 806.62, 715.73, and 271.84 cm−1, which correspond to the stretching vibrations of O-W-O and W-O bonds, and the bending vibration of O-W-O, respectively [64,65]. The occurrence of fractures and the delamination in certain areas of the top Si3N4 film exposed the underneath W layer to the residual O2 inside the vacuum chamber, thereby causing the oxidation of W. The formation of WO3 is believed to be the primary cause of the structural damage of the multilayer metal-dielectric structure. The melting point of bulk W is 3695 K. However, the melting point for WO3 drops to ∼1740K [66,67] (or even lower for nanostructures due to the melting point depression), which is close to the operating temperature of the emitter. The melting of the oxidized W areas further damaged the underlying Si3N4 film, thereby degrading the overall structure. Raman spectroscopy performed at multiple locations of the annealed surface show no sign of the crystallization of the amorphous Si3N4 film.
The proposed Si3N4/W/Si3N4 selective emitter structure was found stable for operating temperatures up to 1173 K for 1 hour. Based on spectrophotometer measurements, annealing the emitter at 1173 K for ∼1 hour showed no change in the spectral surface absorptivity. This temperature threshold may not be the most optimal operating range for GaSb-based STPV systems. However, there are other low bandgap TPV cells, such as InGaAsSb (bandgap between 0.29-0.72 eV), for which a selective thermal radiator at 1173 K provides a peak emission near the bandgap wavelength. Therefore, the Si3N4/W/Si3N4 selective emitter can still be useful for STPV systems using lower bandgap (<0.5 eV) TPV cells. Lowering the radiator temperature can simplify the design of the incident concentration setup as the required input power to achieve the thermal equilibrium is now lesser. Also, the thermal load on the cells is reduced and passive cooling methods become more feasible for TPV cells [49]. The thermal stability of the proposed emitter can be further enhanced by improving the vacuum conditions (suppress residual O2) within the STPV chamber [68].
6.7 Future improvements
Considering only the in-band portion (λ<λBG) of the thermal emission from the emitter, a ηGaSb of 19.5% was achieved at 1670 K. This is lower than ηGaSb = 26% measured during the cell characterization using the narrowband emission from the QTH lamp and filter setup. This significant reduction in ηPV is due to increased thermalization loss in the actual experiment. As discussed earlier, the optimal emitter bandwidth for maximal system efficiency is 0.4 µm right above the edge of the bandgap. The bandwidth of the fabricated emitter is much larger (∼0.8 µm), thereby causing much larger thermalization loss at shorter wavelengths. Lowering the thermalization loss by reducing the emitter bandwidth can help to improve the system efficiency. The highest system loss (29%) in our design is caused by the high sub-bandgap emission, which can be suppressed by improving ηsel, or employing a better photon recycling scheme, such as installing a selective window filter between the cells and the emitter. Alternatively, the re-utilization of sub-bandgap photons can also be achieved using TPV cells that have metal reflectors at the back interface [20]. A 75% reduction in the sub-bandgap loss in our current design would boost the ηSTPV value to 10.9%.
Another major loss factor is TPV cell conversion loss (26%) within GaSb cells that comprises of thermalization loss and losses due to poor FF and EQE values. Significant differences were found between the theoretical (reported in datasheet and literature) and the practical values of FF and EQE for the GaSb cells [33,69]. ηSTPV would rise by ∼3% if the FF and EQE values had matched the specification. The reflection loss from the absorber surface is 8%. Reducing it to 1% can add 0.6% gain in the system efficiency. Cavity loss is also 8.5% of the total incident power. Therefore, future works should be focused on improving the selectivity of the emitter surface, suppressing the sub-bandgap loss, utilizing more advanced TPV cells with highly reflective metal back surfaces, implementing better thermal management for the cells, and reducing the reflection loss from the absorber surface. The combination of these improvements would lead to an improved system efficiency of 16% or higher.
Long-term stability at high temperatures is a major issue with the proposed metal-dielectric planar emitter. Previous studies [60,70–72] have shown that the elastic modulus, hardness, film density, and in-plane stress of Si3N4 films deposited using PECVD are significantly influenced by deposition conditions. An increase in deposition temperature results in the enhancement of the mass density of the film due to the possible reduction of the elemental composition of hydrogen and excess nitrogen [72]. Similarly, the elastic modulus and hardness were found to increase with the increase in substrate temperature, and with an increase in plasma power and decrease in chamber pressure [71]. Denser Si3N4 films deposited at higher substrate temperatures during the PECVD process exhibited a higher mechanical strength [59,71]. The PECVD procedure, therefore, must be fine-tuned to improve the structural stability of the planar selective emitter at higher temperatures. The thermal stability of the proposed emitter can also be enhanced by improving the vacuum conditions within the STPV chamber. Furthermore, the applicability of other dielectric materials must also be explored for fabricating spectrally selective surfaces. Shimizu et al. [73] illustrated the usage of HfO2/Mo/HfO2 nanolayer structures over a Mo substrate for constructing spectrally selective absorber and emitter surfaces. The selective surface was demonstrated to be fairly stable up to 1423 K for ∼ 1 hour at a vacuum condition of 0.4 mTorr. Another study [74] reported a tungsten-based layered metamaterial selective emitter with a thermal stability up to 1473 K for 3 hours when tested under a high-vacuum environment (3 × 10−5 Torr). Recently, Chirumamilla et al. [68] investigated the impact of residual O2 partial pressure on the thermal stability of 1D refractory W-HfO2 based multilayered metamaterial emitter structures under medium vacuum conditions (∼15 mTorr). Their study showed excellent spectral and structural stability up to 1573 K when the residual O2 in the annealing chamber is minimized by encapsulating the chamber with Ar atmosphere.
7. Conclusion
STPV is a promising technology to fulfill our future energy needs, given their potential to exceed the SQ limit. In this study, a combination of thermodynamic modeling and TMM simulation was used for a detailed-balance analysis of a practical STPV system comprising a planar design using GaSb TPV cells. The study involved comprehensive analysis required for the design and optimization of spectrally selective surfaces that are essential components of high-efficiency STPV systems. Significance of determining the optimal emitter temperature, λabs-cut, AR, and emitter bandwidth for global system optimization was discussed. The relevance of photon recycling on both the absorbing and emitting sides for achieving high ηe and ηSTPV was investigated. Utilizing the knowledge gained from the simulation, a high-efficiency planar STPV system was designed and tested. A micro-textured absorber and a Si3N4-W-Si3N4 coated selective emitter were fabricated on a W substrate. The absorptivity of 0.92 was measured for the textured absorber for wavelengths below 1 µm. εin-band for the selective emitter was measured nearly 3 times greater than that of a W emitter. Owing to a high VF in our setup, the cavity loss was limited to 8% of the radiated power from the emitter. The implementation of the Au heat shield significantly suppressed the thermal emission from the non-active region of the absorber. The performance of the STPV system was evaluated using a 300 W continuous-wave laser as a simulated source for incident radiation. A high output power density of 1.75 W/cm2 and a system efficiency of 8.6% was recorded at the operating system temperature of 1670K. The required incident solar concentration to achieve this efficiency is 2060X at an air mass of 1.5. This experimental efficiency is higher than those of previously reported STPV systems. Various optical and thermal losses occurred at multiple stages of the energy conversion process were quantified. Combining the simulation and experimental results, essential guidelines to further improve the system efficiency and long-term thermal stability were also provided.
Acknowledgments
We thank the NASA Langley Professor program and NSF IUCRC Center for financial support. GaSb TPV cells were purchased from JX Crystals, Inc. and we thank them for providing the EQE data for the cells.
Disclosures
The authors declare no conflicts of interest.
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