Efficiency optimization of quantum dot photovoltaic cell by solar thermophotovoltaic system

1 Introduction

The ever-growing demand for energy has led humanity to search for renewable energy resources to cope with ever-growing power demand [1,2]. The renewable resources are clean and have no adverse effects on the environment [3]. Solar energy is one of the best renewable sources of energy in terms of availability. It can be converted into electricity by semiconductor photovoltaic (PV) cells [4,5,6]. When conversion of solar energy through PV cells is considered, the efficiency of a single junction PV cell is low as it is limited by the Shockley–Queisser limit [7]. Shockley and Queisser calculated maximum theoretical efficiencies for various bandgap energies corresponding to various semiconductor PV cells. For a single junction silicon PV cell, Shockley–Queisser limit for efficiency came out to be 30% under sun’s full illumination [8]. If all losses are considered, the actual efficiency further drops down to 24% [9]. Some of the incident radiations are reflected from the cell’s surface. Some of the energy is lost at the junction of the cell due to electrical contacts that carry current out of the cell. Other losses are due to added impurities during manufacturing process. Mainly, the low efficiency of PV cell according to Shockley–Queisser limit is due to the energy losses by two types of incident photons; those photons which have energy below the bandgap of PV cell as they do not contribute to the electron–hole pair generation and secondly, those photons which have extra high energy above the bandgap of PV cell. They create electron–hole pairs with the loss of some energy. These photons create heat energy which further reduces the efficiency.

To overcome Shockley–Queisser limit, a number of techniques have been employed. In this regard, solar concentrator is used with PV module to focus more solar energy on to the PV module to increase the efficiency of the system. Thermophotovoltaic (TPV) generators are also in use in which a spectrally selective thermal emitter is directly heated with a heat source and then the emitter emits a spectrum on to the PV module based on its bandgap energy [10,11]. Solar thermophotovoltaic (STPV) system has been proposed in this research which is a modified form of TPV generators. In STPV system, the broadband absorber first absorbs the solar radiations and then transfers its captured energy to the emitter by conduction [6] as shown in Figure 1. The emitter is spectrally selective, so it emits radiations whose energy is just above the bandgap energy of targeted PV cell. In this way, PV cell acquires its required spectrum which increases the efficiency of the PV cell. STPV also reduces thermal losses significantly inside the PV cell because a minimum amount of high-energy photons fall on the PV cell. STPV acts as an intermediate structure between incoming solar radiations and the PV cell. Hence, it works at very high temperatures due to the continuous absorption of sunlight. STPV works on thermal equilibrium principle, according to which the absorptance of energy is equal to the emission of energy [12,13]. In the proposed STPV system, we implement nanostructures for making absorbers and emitters. Both require vital design considerations like polarization insensitivity, angle insensitivity, high-temperature durability, oxidation (corrosion) resistance, and high absorptance in their respective emitted spectrum. Except for temperature durability, all other design considerations can be achieved by the type of design like disk shape, rod shape, square shape, gratings, etc., especially for the top nano-resonator part of the absorber and emitter. For this purpose, metasurfaces and metamaterials are an ideal candidate. Metamaterial is an array of sub-wavelength nanostructures made from conventional materials while metasurfaces have sub-wavelength thickness. Metamaterials are employed because their optical behavior can be manipulated by changing the design. The refractive index of metamaterial can be varied by changing its geometry [14]. Therefore, they are used in phase manipulation of electromagnetic waves [15–18]. We can change the refractive index and hence, can change the overall absorptance of the metamaterial by varying their geometry. Due to this outstanding property, they have wide applications in solar energy harvesting, optical sensing, holography, etc. However, high temperature durability is totally dependent upon the type of material and, therefore, needs a careful selection of material to be employed for absorber and emitter.

Figure 1

A depiction of STPV system.

Refractory materials are usually highly heat resistant because they have sufficiently high melting points. Some of the best-known examples of refractory materials include tungsten (W), rhenium (Re), and tantalum (Ta) with melting points of 3,422, 3,185, and 3,017°C, respectively [19]. In this regard, extensive research on broadband and narrowband absorbers employing refractory materials has been conducted [20]. Although they have high melting points, refractory materials suffer from oxidation at elevated temperatures [21]. An example of tungsten can be taken, which starts to oxidize at 25°C to form tungsten trioxide (WO₃) that has a melting point below 1,500°C [22,23]. Therefore, to avoid oxidation, metal nitrides such as zirconium nitride (ZrN) and titanium nitride (TiN), having melting points of 2,980 and 2,930°C, respectively, have also been employed in order to develop absorbers and emitters [24,25].

Similarly, alkali metals, when employed as metal layers in absorbers, gave apsorptance above 90% in visible regime [26,27]. Similarly, plasmonic materials including gold (Au) [28], silver (Ag) [29], aluminum (Al) [30], and nickel (Ni) [31] have also been employed for absorber designs as they are fairly lossy materials, especially in the visible spectrum. However, the melting points of these materials are low (<1,500°C), so they are not suitable for STPV applications.

Keeping these design requirements in perspective, the family of metal carbides are a very suitable candidate for STPV applications due to their high melting points. The melting points of metal-carbides lie between 2,000 and 4,000°C. They are highly non-malleable [32–34], and most important, they also possess oxidation-resistant characteristics [35,36]. Amongst these carbides, we employed boron carbide, vanadium carbide, silicon carbide, and titanium carbide for our absorber design. However, on the basis of higher absorptance efficiency, we have chosen titanium carbide (TiC) [37,38]. TiC displayed better results for the proposed broadband solar absorber when top TiC nanostructure was made into a pyramid shape. Moreover, TiC has a melting point of 3,067°C, and shows fair thermal and electrical conductivity along with reasonable resistance to corrosion and oxidation [39]. For the absorber design, the spacer used mostly to date is silicon dioxide having melting point of 1,710°C. However, we employed hafnium oxide (HfO₂) as a spacer, whose melting point is 2,758°C.

We designed the selective emitter from platinum (Pt), which also has a reasonably high melting point of 1,768°C. Since the radiation spectrum is to be absorbed primarily by absorber, emitter layer having a somewhat lower temperature will not affect the overall STPV design considerably. In order to further complement this situation, dielectric coatings are also proposed for the absorber and emitter to increase their thermal stability. The emitter implements gratings as a top layer having metal-insulator-metal (MIM) configuration as that of absorber. The spacer layer is same for absorber and emitter since they both employ Hafnium oxide.

Independent studies on absorbers and emitters can be found in the literature, but studies having complete STPV system designs are limited. This leaves room for improvement in overall efficiency of the STPV systems or their designs that could withstand detrimental environmental conditions. For complete STPV designs, PV cell efficiency of 41.8% has been reported for indium–gallium–arsenide–antimonide (InGaAsSb, bandgap = 0.55 eV) PV cell with tantalum-based absorber and emitter [7]. By employing a chromium-based absorber and emitter, 21% efficiency has been achieved for the same InGaAsSb PV cell [40]. An efficiency of 43.2% have been achieved for the same PV cell of InGaAsSb by employing chromium in the metasurface design [41]. Another design, made up of Tungsten with alternating layers of Si/SiO₂ in the emitter, a PV cell efficiency of 50.8% has been reported for silicon PV cell (bandgap = 1.1 eV) [42]. In another design, made up of gold stripped emitter, 41% efficiency was achieved for germanium PV cell [43], having a bandgap of 0.6 eV. Most of the emitters designed to date have been optimized for conventional crystalline PV cells as mentioned above. However, we have optimized our emitter for lead sulfide (PbS)-based colloidal quantum dot (CQD) PV cell having extremely low energy bandgap of 0.41 eV [44] and achieved a comparable PV cell efficiency of 35.2%. The quantum dots in PVs are an emerging technology which has several advantages over conventional crystalline PV cells. These advantages include tunable bandgap, less weight, mass area saving, low manufacturing cost, and versatile to use in micro to macro applications. In this work, we provide a complete numerical investigation of an STPV system developed to enhance the efficiency of these CQD PV cells.

2 Absorber design and efficiency

We propose MIM configuration for the design of broadband absorber in which top layer implements the shape of a pyramid. The bottom and top layers are made of titanium carbide whereas spacer layer is made up of hafnium oxide. The 3D and 2D models of absorber are shown in Figure 2. The design parameters shown in Figure 2(a) and (b) are Period (p) = 300 nm, ground height (hg) = 155 nm, spacer height (hs) = 40 nm, Pyramid: top x span = 110 nm, top y-span = 110 nm, bottom x-span = 240 nm, bottom y-span = 240 nm, and thickness of pyramid = 160 nm. These design parameters were chosen after complete optimization of the design by employing sweeps over design dimensions and particle swarm optimization technique. The finite difference time domain algorithm was employed to calculate absorptance of the absorber by equation (1).

where R is the reflection and T is the transmittance at the corresponding wavelength λ, angle of incidence θ, and polarization angle φ. The proposed absorber has an average absorptance of 0.92 in 300–2,000 nm range. The absorptance remains near unity from 400 to 700 nm where respective solar irradiance is sufficiently high as shown in Figure 3(a).

Figure 2

(a) 3D model of absorber and (b) 2D model of absorber.

Figure 3

(a) Absorption profile of absorber. (b) Layer wise absorption.

Transmittance is near zero throughout the span of wavelengths because transmission is totally blocked by the ground layer. The spacer layer between two metal layers forms a Fabry–Pérot cavity, trapping most of the energy in spacer layer. The reflection remains negligible till 700 nm, after which it slightly increases but remains below 0.2. The actual efficiency of the absorber is found by equation (2) [7].

where ε abs is the absorptance of the absorber at a given wavelength, angle of incidence θ, and polarization angle φ. I sol ( BB ) is the spectral irradiance of the blackbody at 5,778 K. Practically it is the total absorbed spectrum by the absorber to the total incident spectrum. It comes out to be 96% when the wavelengths are taken from 300 to 2,000 nm. It means that the absorber absorbs 96% of the total incident energy in the said range.

Figure 3(b) shows layer wise absorption contribution of the absorber which shows that front layer, in fact the top pyramid layer, contributes mainly in absorption from 300 to 1,500 nm, beyond this both the layers contribute equally.

2.1 Polarization and incidence angle independence

The proposed design of the broadband absorber is independent of angle of incidence for s- and p-polarizations as shown in Figure 4(a) and (b). The results shown resemble very nearly with the actual pattern of absorptance curve shown in Figure 3(a). For p-polarization (whose polarization angle is 0°), absorptance remains near unity from 300 to 700 nm when incidence angle goes from 0° to 25°. Further increase in incidence angle also gives near unity absorptance for 700–900 nm span of wavelengths. For s-polarization, absorptance remains near unity from 300 to 800 nm for almost all the incidence angles. For higher incidence angles (above 40°), we get again near unity absorptance from 1,200 to 2,000 nm. We also vary polarization angle from 0° to 90° and examine the polarization insensitivity behavior of the absorber. The absorber is perfectly polarization angle insensitive as shown in Figure 4(c). Absorption remains near unity from 300 to 750 nm for all the polarization angles, then decreases slightly till 1,600 nm, and then again increases. The absorptance, however, remains constant for all polarization angles.

Figure 4

(a) Variation in absorptance for the change in incidence angle with respect to p-polarization, (b) variation in absorptance for the change in incidence angle with respect to s-polarization, (c) polarization angle vs absorptance, (d) 3D model of emitter, and (e) 2D model of emitter.

3 Emitter design

The efficiency of PV cell is dependent upon the emittance of the emitter, which should be narrowband and spectrally matched with the response of PV cell. The emitter must emit the electromagnetic (EM) spectrum having energy just above the bandgap energy of targeted PV cell. If EM spectrum below bandgap is emitted, the efficiency of PV cell reduces significantly as this spectrum does not take part in electron hole pair creation and also produces waste heat. The emitted spectrum by the emitter from 300 to 700 nm (approximately beyond 2 eV) does not alter the efficiency significantly; therefore, we emphasize more on the emitted spectrum whose energy is below 2 eV during design optimization. We designed selective emitter having gratings structure on the top as shown in Figure 4(d) and (e). Emitter design also has MIM configuration with platinum on the top and bottom, while hafnia in the middle layer as a spacer. The optimized design parameters shown in Figure 4(d) and (e) are ground period (P) = 650 nm, ground height (hg) = 150 nm, and spacer height (hs) = 70 nm.

Top gratings: length (lg) = 610 nm, duty cycle (ds) = 62.5% of grating period, grating period (Pg) = 216 nm, grating height (gh) = 300 nm, tooth angle = 90°, no. of grating periods (n) = 3. The emittance curve is shown in Figure 5(a). The emittance is plotted vs electron volt scale starting from 0.3 eV. The emittance increases sharply after the bandgap energy of 0.41 eV and reaches to near unity and then decreases sharply. The main part of emitted spectrum which significantly takes part in PV cell efficiency, spans from 0.3 to 1.4 eV. The emittance curve is narrowband, having high value of emittance which is the basis for good efficiency. After 1.5 eV, the emittance again increases till higher energies but this part of the emitted spectrum beyond 1.5 eV does not contribute significantly toward efficiency. Figure 5(b) shows emittance curve of the emitter at wavelength scale. The top layer of the emitter peaks at 1,800 nm with the emittance of 0.7 and the bottom layer peaks at 2,300 nm with the emittance of 0.3. As a result, the emitter as a whole gives near unity absorption just above the bandgap which spans from 1,800 to 2,400 nm.

Figure 5

(a) Emittance curve of emitter on energy scale, (b) emittance curve on wavelength scale, (c) electric field profile of emitter at 1,900 nm, and (d) magnetic field profile of emitter at 1,900 nm.

The resonating wavelength for overall structure is 1,900 nm on which there is maximum emission. Figure 5(c) and (d) shows the electric and magnetic field profiles at resonating wavelength of 1,900 nm. It is clear from the figure that high intensity electric and magnetic field exists around all three grating slits meaning that all three gratings on the top are resonating at 1,900 nm. These intensity plots, therefore, further support the result that gratings are main contribution toward selective emittance of the emitter design. The emittance is solely responsible for the PV cell efficiency, which is discussed in the next section.

3.1 PV cell efficiency

According to Shockley–Queisser analysis, we find ultimate efficiency U eff ( E g , T ) of PV cell by equation (3) [7,40–43].

(3) U eff ( E g , T ) = ∫ 0 2 π d φ ∫ 0 π 2 sin 2 θ d θ ∫ E g ∞ ε emit ( E , θ , φ ) I ( BB ) ( E , T ) E g E d E ∫ 0 2 π d φ ∫ 0 π 2 sin 2 θ d θ ∫ 0 ∞ ε emit ( E , θ , φ ) I ( BB ) ( E , T ) d E ,

where wavelength has been taken on electron volt (eV) scale. E _g is the bandgap energy for which the emitter is optimized and T is the equilibrium temperature in Kelvin of the emitter. Range of wavelengths taken here in calculations are from 400 to 4,000 nm. Ultimate efficiency from equation (3) is further depreciated by a voltage mismatch factor V eff ( E g , T ) . This factor is also in form of efficiency, which is given by equation (4) [7,40–43].

(4) V eff ( E g , T ) = V c V g ln f 2 π h 3 c 2 ∫ 0 2 π d φ ∫ 0 π 2 sin 2 θ d θ ∫ E g ∞ ε emit ( E , θ , φ ) E 2 e E k b T − 1 d E 2 π h 3 c 2 ∫ E g ∞ E 2 e E k b Tc − 1 d E .

Another simplest form of equation (4) is equation (5) given below.

(5) V eff ( E g , T ) = V op V g ,

where V c = K b T c q , V _g is the bandgap voltage which is equal to E g q , q is the charge on an electron, V _op is the open-circuit voltage, h is the plank’s constant, c is the speed of light, T _c is the operating temperature of PV cell which is taken as 300 K (room temperature), and f is the non-ideality factor taken as 0.5. The third factor to calculate overall PV cell efficiency is impedance matching factor which is given by equation (6) [7,40–43].

(6) im ( V op ) = Z m 2 ( 1 + Z m − e − z m ) ( Z m + ln ( 1 + Z m ) ) ,

where Z m can be calculated by the equation. Z op = Z m + ln ( 1 + Z m ) , and Z op = V op V c , where V op can be determined using equation (5). Finally, the overall efficiency of PV cell is determined using equation (7) [7].

(7) η pvc = U eff ( E g , T ) V eff ( E g , T ) im ( V op ) .

The main factors to optimize on design basis are U eff and V eff . The ultimate efficiency U eff reduces significantly for photons below bandgap while increases for photons above bandgap up to a limited range of emitted spectrum. The main spectrum which must be optimized (for our case) is from 0.41 eV (3,024 nm) to the bandgap energy (0.65 eV) which corresponds to 1,900 nm. The emittance should be maximum in this range to obtain highest value of U eff while keeping below bandgap emittance at minimum level. For our designed emitter, the ultimate efficiency U eff peaks at the temperature of 900 K and is equal to 62%. V eff increases from 19 to 94% at the temperature ranging from 400 to 2,000 K, respectively. im(V _op) increases slowly from 44 to 76% over the span of given temperatures. The practical trends for our design are shown in Figure 6(a). From these efficiencies, the optimum temperature is 1,350 K, which yields the final efficiency of PV cell η pvc to be 35.2%. The achieved efficiency of presented design in this study is comparable with other designed emitters as shown in Table 1.

Figure 6

(a) Efficiencies of PV cell vs temperature. (b) Effect of protective coatings on absorber. (c) Effect of protective coatings on emitter.

Table 1

Comparison of different efficiencies associated with the PV cell

Design	Temperature (K)	PV cell bandgap (eV)	U eff (%)	V eff (%)	im(V op) (%)	η pvc (%)
Ta photonic crystal (ex) [45]	1,200	0.54	54.6	74.2	77	39.5
Tungsten circles, r = 360 nm (ex) [46]	1,380	0.55	55.9	81	78.7	35.6
Tungsten circles, r = 400 nm (ex) [46]	1,380	0.55	55.7	81.6	78.8	35.8
Chromium disks [40]	1,573	0.54	25	90	82	21
Ta photonic crystal (ex) [47]	1,500	0.54	59.5	83.9	78.9	39.5
Tungsten photonic crystals Design 1 (ex) [48]	1,500	0.55	56.6	81.8	78.8	36.5
Design 2 (ex) [48]	1,500	0.55	59.8	83.4	79.1	39.4
Tungsten multilayer design 1 [49]	1,273	0.55	64.5	—	—	—
Tantalum cross [7]	1,535	0.55	67.8	78.8	78.2	41.8
Platinum gratings (this design)	1,350	0.41	57	83	74.5	35.2

Note: Here (ex) means extracted values from graphs.

We also apply additional dielectric layers on the top layers of absorber and the emitter to protect them from corrosion and also make them more thermally stable at elevated temperatures. As STPV works at sufficiently high temperatures, these stability requirements became vital part of the design. We apply protective coatings of such thicknesses on the absorber and emitter which do not alter their efficiencies significantly. We use hafnia (HfO₂), alumina (Al₂O₃), and silicon nitride (Si₃N₄) as protective materials having melting points of 2,758, 2,072, and 1,900°C, respectively, as shown in Figure 6(b) and (c), respectively. We apply 25 nm thick protective coatings of hafnia, alumina, and silicon nitride on the absorber to give efficiency of 98.4, 98.2, and 98.5%, respectively. For emitter, we apply hafnia 10 nm, alumina 20 nm, and silicon nitride 20 nm to give η pvc equal to 34, 35.2, and 34.7%, respectively. Now we discuss about some challenges in this scope of work. There are several kinds of challenges come in the development of STPV systems. It includes material selection and the design of nano structure to meet the requirements. We have to choose such metamaterial which must be thermally stable, compatible with the fabrication process, and must be angle of incidence and polarization insensitive. It should give high absorptance in the respective electromagnetic spectrum. The design of thermal emitter is another big challenge. We have to match its spectral response with the targeted bandgap. On the implementation side, there is a big challenge of fabrication of nano structure. We have to strictly maintain the precision and resolution as small changes may alter the optical properties of metasurface. Sometimes techniques that work on small scale production may not be suitable to implement on the large industrial scale. Integration of solar absorber and emitter with the PV cell can also be a challenge in maintaining proper functionality. On the other hand, to measure and examine the optical and physical properties of metasurfaces/metamaterials require advanced and complex methods which are costly and time consuming. Moreover, the design of metasurfaces is often complex. So, they need complex simulations to carry in iterative fashion which require advance simulation and modelling tools and expertise with a lot of time.

4 Conclusion

In this work, a nanostructure-based STPV system is designed to improve CQD PV cell efficiency. A titanium carbide-based solar absorber and platinum-based selective thermal emitter is designed. Both the materials have reasonable high melting points for them to be employed for STPV systems. The proposed broadband absorber achieves high absorptance efficiency of 96% from 300 nm to 2,000 nm. The broadband absorber also achieves excellent insensitivity against the change in incidence angle as well as in polarization angle. The selective emitter has been optimized for PbS quantum dot PV cell having low bandgap of 0.41 eV. To get maximum PV cell efficiency, ultimate efficiency U eff and voltage mismatch factor V eff for the PV cell are to be optimized mainly. These factors depend upon emittance curve of the emitter. U eff increases for slightly above bandgap photons and reduces for below bandgap photons. V eff increases with above bandgap narrowband emittance and decreases for non-ideal emittance of the emitter. The emitter achieves the highest possible PV cell efficiency of 35.2% at the temperature of 1,350 K. Finally, protective dielectric coatings have been proposed to be deployed on absorber and emitter designs to further provide anticorrosion resistance and thermal stability characteristics. After employing these coatings, it is observed that no significant change occurs in the efficiency profiles of absorber and emitter designs. The novelty and significance of the work presented is given below.

• Use of comparatively new and thermally stable materials

• Emitter optimization for quantum dot PV technology

• Emitter optimization for very less energy bandgap

• Achieved theoretically a reasonable PV cell efficiency of 35.2%

For the future perspective, more stable and suitable materials can be employed to design broadband absorber and narrowband thermal emitter. The thickness of the structure of absorber and emitter can be further reduced to make them more compact and cost effective. Emitter can further be optimized to achieve an increased efficiency of targeted PV cell. It can also be optimized for other bandgaps corresponding to various PV cells to improve their cell efficiencies. One of the most advanced ideas is that the emitter should be designed so that it gives narrowband high emittance in two different regions of corresponding blackbody spectrum. In this way it will be applicable to optimize the efficiency of tandem PV cells which have multiple junctions (corresponding to various bandgaps) in them.