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Abstract
We investigate photon recycling at the top subcell in mechanically stacked multi-junction solar cells with nanometer air gaps between the subcells. We determine the incident-angle-dependence of the reflectivity from the rear surface of the top subcell. The results show that more than 30% of the luminescence at the top subcell is reflected at the air gap even for an air gap thickness of 10 nm. In addition, we demonstrate enhanced luminescence extraction in GaAs//InGaAsP dual-junction devices with nanometer air gaps compared to a device with no gap between the subcells. Our findings indicate that an efficient photon recycling can be realized even for air gaps of a few tens of nanometers.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Light management for designing the optical properties of solar cells has gained much attention with the objective of obtaining high conversion efficiency [1–7]. In devices with high-quality materials, the radiative recombination exhibits a primary recombination channels, which significantly affects the performance of photovoltaic devices [8–15]. The luminescent coupling between the subcells in stacked multi-junction devices has been extensively studied [4,10,16–19]. Photon recycling originates from the re-absorption of the luminescence (i.e., photons generated by radiative recombination) in the same subcell. In contrast, in luminescent coupling, the luminescence in the higher-bandgap sub-cells can be re-absorbed by the lower-bandgap subcells located below [Fig. 1]. The re-absorption of the luminescence leads to an increase in the photocurrent in the subcell.
Fig. 1 Schematic of photon recycling and luminescent coupling in multijunction solar cells with nanometer air gaps.
An accurate assessment of light management for photon recycling can help significantly increase the conversion efficiency of thin-film solar cells through photon recycling [13,20]. In addition to single-junction solar cells, the design of optical coupling between the subcells in multi-junction solar cells has received increased attention to further boost the performance. Monolithic devices with no gaps between the subcells exhibit strong optical coupling between the subcells [21]. In contrast, when a gap, such as an air gaps [10,22], exists between the subcells, light with a large incident angle is reflected because of total internal reflection. More than 90% of the luminescence is reflected from the semiconductor/air interface because of total internal reflection. Moreover, the adhesive bonding used in mechanically stacked solar cells causes a significant reflection loss of over 15% for normally incident long-wavelength light transmitted through the top subcell and absorbed by the bottom subcell [23]. Furthermore, eliminating the substrate leads to enhanced photon recycling in single-junction devices, resulting in enhanced open-circuit voltages compared to devices with substrates [20].
In mechanically stacked multijunction solar cells bonded using metal nanoparticle (MNP) arrays [24–26], nanometer air gaps exist between the subcells and can affect the optical properties. So far, even though the coverage of MNP is ~10%, a normally incident light can transmit even for an air gap width of only 10 nm [27]. In addition, this bonding technique using MNP arrays leads to a low contact resistance (≲ 1 Ωcm2). Overall, the effects of nanometer air gaps on photon recycling and luminescent coupling have not been well understood.
In this paper, we investigated the effects of the thickness of the air gap between stacked subcells on photon recycling at the top subcell to understand the optical properties of mechanically stacked multijunction solar cells bonded using MNP arrays. We determine the incident-angle dependence of the reflectance at the interface between the top and bottom subcells. Accordingly, the efficiency of photon recycling at the top subcell and luminescent coupling from the top subcell to the bottom subcell are obtained. In addition, we fabricate devices with no gap and with nanometer air gaps and compare their solar cell characteristics. Furthermore, using photoluminescence spectroscopy, we demonstrate enhanced luminescence extraction using the devices with nanometer air gaps compared to the device with no gap between the subcells.
2. Calculated photon recycling efficiency
We calculated the photon recycling efficiency. The transmittance and reflectance of light with a large incident angle are sensitive to the nanometer air gaps between dielectrics of high refractive indices [28]. The wave vector k makes an angle θ with the normal incidence to the dielectric/air interface [Fig. 1] and has components k‖ and k┴ parallel and perpendicular to the interface, respectively, i.e., k‖ = nk0 sinθ and k┴ = nk0 cosθ, where the wave number k is given by n(2π/λ0) with the refractive index of the dielectric media being n and wavelength of light in air being λ0. When θ is sufficiently large, k‖ exceeds k0 and gives rise to an evanescent wave on the air side with the relationship . The transmissivities of transverse electric (TE) and transverse magnetic (TM) waves can be expressed as follows [28]:
andwhere a is the air gap thickness.As a test structure, we consider stacked multi-junction solar cells with an air gap between the top GaAs subcell and the bottom subcell layers. Here, we initially ignore the MNP arrays between the top GaAs and the bottom subcell layers. For luminescence, the reflectance of light with a large incident angle is more important, because the direction of the luminescence exhibits a random distribution. To investigate the luminescence of the GaAs subcell at a wavelength of 800 nm, we calculate the reflectance R ( = 1 - T) of light with an incident angle θ using the refractive index of GaAs (n = 3.7) for an 800-nm wavelength light. For simplicity, we use the same refractive index (of 3.7) for the bottom subcell, which corresponds to the case of c-Si subcell. In addition, we ignore the optical absorption.
Figure 2 shows the incident angle dependence of the reflectance for different air gap thicknesses. Above the critical angle of 15.7°, the reflectance increases with the increase in the incident angle. The reflectance above the critical angle increases with the increase in the air gap thickness. Note that the interface with no air gap and zero refractive index difference does not undergo reflectance even for a large incident angle. Because of the enhanced reflectance, the reflection of the luminescence on the rear surface of the top GaAs subcell increases. This implies that even a nanometer air gap is sufficient to improve photon recycling. Consequently, the enhanced photon recycling efficiency leads to an increase in the minority carrier density in the top GaAs subcell, resulting in an enhanced open-circuit voltage.
Fig. 2 Reflectance at the air gap of the top GaAs//bottom subcell structure with 10, 20, and 100 nm gap thicknesses for light with different incident angles.
Based on the angle-dependent reflectance, we discuss the photon recycling efficiency of the GaAs subcell. Note that in single-junction solar cells, the probability densities associated with escaping from the front are determined from the angle-dependent Fresnel coefficients for specular reflection and transmission at the front and back interfaces [13]. To evaluate the reflection efficiency of the luminescence from the rear surface of the top subcell, we calculated the reflection efficiency on the rear surface of the top GaAs subcell for incident light with a random distribution R, as follows.
From Eq. (3), we obtained the total reflection efficiency of the top GaAs//bottom subcell structure with air gaps [solid markers in Fig. 3]. The reflectance values are the averages of the TE and TM modes. For a gap thickness of 10 nm, more than 10% of the luminescence is reflected from the rear surface of the top GaAs subcell. The reflection efficiency increases with gap thickness. In contrast, in the case of zero gap thickness, there is no reflection of the luminescence because of the zero refractive index difference. For comparison, the reflection efficiency for thin film GaAs top subcell is calculated using the equationand plotted by open markers. For an infinite gap thickness, only 3.7% of the luminescence is transmitted, with more than 95% reflected at the GaAs/air interface. For a gap thickness of 10 nm, more than 30% of the luminescence is reflected from the rear surface of the top GaAs subcell. Note that for the realistic devices, the reflection efficiency depends on reabsorption in the GaAs top subcell because a part of the luminescence is reabsorbed by the GaAs subcell before it reaches to the rear surface of the top GaAs subcell. Thus, a part of the reflected luminescence is reabsorbed at the GaAs subcell, resulting in enhanced minority carrier density and open-circuit voltage.Fig. 3 Reflection efficiency for luminescence on the rear surface of the thick (solid) and thin (open) GaAs top subcells as a function of the air gap thickness. Squares: TE wave. Triangles: TM wave. Circles: average.
3. Solar cell characteristics and luminescence extraction
3.1 Fabrication of mechanically stacked dual-junction devices
We investigated the effects of air gaps on solar cell characteristics and luminescence extraction. Mechanically stacked dual-junction devices were fabricated using a bonding technique with MNPs [24]. Multi-junction solar cells composed of semiconductors with diffferent lattice constans have been realized using this technique [24–26,29–31]. We used a simple GaAs//InGaAsP double-junction solar cell bonded using MNP arrays to investigate its fundamental properties. The combination of elements used in this solar cell is commonly used in solar cells of highest efficiency, namely InGaP/GaAs//InGaAsP/InGaAs [13]. The p-n junctions are bonded using Pd NP arrays to form a two-terminal double-junction solar cell comprising a GaAs top cell and an InGaAsP bottom cell (1.15 eV) grown on an InP wafer [Fig. 4]. The fabrication processes follow the methods described in previous papers [16,17]. An Au electrode is formed in advance on the GaAs top cell with a thin GaAs contact layer. Both the GaAs and InGaAsP p-n junctions have a sub-cell thicknesses of 2.5 μm. The sizes of the GaAs top and InGaAsP bottom cells are ~3.5 × 3.5 mm2 and ~7 × 7 mm2, respectively. To fabricate the Pd NP arrays, a diluted solution of polystyrene-block-poly-2-vinylpyridine (PS-b-P2VP) was spin-coated on the surface of the bottom cell to form a nanometer-scale pattern. This patterned bottom-cell was immersed in an aqueous solution containing Pd ions because of which the Pd ions formed a patterned Pd template on the bottom cell. Next, a plasma treatment was performed to remove the polymer and reduce the Pd ions to form the Pd MNP arrays. The typical height of the Pd NPs and period of the arrays are ~20 nm and 100 nm, respectively. Next, the GaAs top cell, which was grown on a GaAs wafer, was exfoliated using the epitaxial lift-off (ELO) technique [1,20]. In this technique, a thin GaAs top cell placed in water is scooped up and transferred to the bottom cell, which is covered with Pd NP arrays. The stacked sample is pressed down by a weight at room temperature for 2 h [17]. We prepared three test devices. The first one is a device stacked using Pd NPs and pressed using a weight, namely Pd-1. The second device is stacked using Pd NPs but without using any weight, namely Pd-2. The third device is stacked without using Pd NPs, namely No-Pd. As discussed below, the Pd-1 and Pd-2 devices have nanometer gaps in the ranges of 10–20 and 20–40 nm, respectively, whereas, the No-Pd device has no gap.
Fig. 4 Schematic of the semiconductor wafer bonding using Pd NP arrays. Pd-1: Devices stacked by Pd NPs using weight. Pd-2: Devices stacked by Pd NPs without using weight. No Pd: Devices stacked without using Pd NPs.
3.2 Fundamental solar cell characteristics
Figure 5(a) shows the external quantum efficiency (EQE) curves for the GaAs and InGaAsP subcells of the device with no Pd NPs. The EQE of the multi-junction solar cells was determined by following advanced procedures in order to minimize the artifacts due to tuning the bias light and voltage [32,33]. Note that a normally incident light was used for the EQE measurements. In contrast, the devices with Pd NPs show an interference pattern for the InGaAsP subcells compared to the device with no gap [Figs. 5(b) and 5(c)], indicating that a part of the light transmitted through the GaAs subcells is reflected at the airgap. Although the free spectral range remains largely unchanged between the Pd-1 and Pd-2 devices, the fringe height increases in the Pd-2 device, indicating an increase in its reflectance.
Fig. 5 (a) EQE curves for the GaAs and InGaAsP subcells of the device with no Pd NPs, (b) device with Pd NPs (Pd-1), and (c) device with Pd NPs (Pd-2). (d) Reflectance spectra for normally incident light of the device with no Pd NPs, (e) device with Pd NPs (Pd-1), and (f) device with Pd NPs (Pd-2). (g) Current–voltage curves for the device with no Pd NPs, (h) device with Pd NPs (Pd-1), and (i) device with Pd NPs (Pd-2).
Figures 5(d)–5(f) show the reflectance spectra for the normally incident light. The height of the interference below 850 nm increases for the Pd-1 and Pd-2 devices. A previous study has shown that the nanometer gaps between the subcells cause reflectance at the interface and that the reflectance increases with the increase in the gap thickness. Based on the calculation of the reflectance in the previous paper [27], the gap thicknesses for the Pd-1 and Pd-2 devices were found to be in the range of 10–20 and 20–40 nm, respectively. The thicknesses correspond well to the gap thickness observed by transmission electron microscopy in the devices fabricated by using a weight and the height of a nanometer-scale pattern that is not pressed by a weight, respectively [25].
Although the device with no gap between the subcells (No-Pd) shows low reflection loss, it has poor solar cell properties. Figure 5(g) shows the current–voltage curves for the device with no Pd NPs. Here, we used a Xe/halogen two-light-source solar simulator. The slope under the open-circuit condition is gradual compared to the curves shown in Figs. 5(h) and 5(i), indicating a high contact resistance. We obtained a contact resistance (Rs) of ~2000 Ω cm2 from the slope, which is as high as the bonding resistance of GaAs/GaAs devices reported in a previous study [25]. Even though a better conductance was not achieved, the device with no Pd NPs form zero gap between the subcells. In contrast, the device with Pd NPs shows a good contact resistance, which is three orders lower than that of the device with no Pd NPs. The air gap is formed between the subcells because of the Pd NPs. In addition, the Pd-2 device shows higher open-circuit voltage by ~15mV compared to the Pd-1 device, indicating an increased voltage due to photon recycling. The short-circuit current decreases in the Pd-2 device, in which the air gaps causes the reflection of the indent light and luminescence. These results suggest that the Pd-1 device has good optical and electrical properties. As a result, it exhibits the highest solar cell efficiency among the devices developed in this work.
3.3 Photoluminescence measurements
We performed photoluminescence (PL) measurements using a 785-nm laser illumination to investigate the luminescence recycling. The GaAs subcell consists of a 2.5-μm thick base, absorbing >99% of the 785-nm laser light. Figures 6(a)–6(c) show the PL spectra for the devices with no Pd NPs, with Pd NPs (Pd-1), and with Pd NPs (Pd-2). The PL intensity increases with the increase in the excitation intensity; however, the spectral shape remains largely unchanged with respect to varying excitation intensities. The device with nanometer gaps has a better PL intensity than the device with no gap. In addition, the Pd-2 device with larger airgaps exhibits a higher PL intensity than the Pd-1 device. This indicates that a larger airgap leads to enhanced reflectance of PL at the interface between the subcells. Furthermore, on a log scale [Figs. 6(d)–(f)], the PL spectra show interference patterns for the device with airgaps [Arrows in Fig. 6(f)]. This also supports the fact that the enhanced luminescence extraction originates from the luminescence reflected from the rear surface of the GaAs subcells. The free spectral range of the interference patterns shows similar characteristics and can be explained well by considering a GaAs subcell thickness of 2 μm and a refractive index of ~3.7 at ~800 nm [34].
Fig. 6 (a) PL spectra for different excitation intensities of the device with no Pd NPs, (b) device with Pd NPs (Pd-1), and (c) device with Pd NPs (Pd-2). (d)–(f) PL spectra on log scale. (g) PL intensity for different excitation intensities of the device with no Pd NPs (triangle), with Pd NPs (Pd-1) (square), and with Pd NPs (Pd-2). (h) Normalized PL intensity for an excitation intensity of 83 mW/cm2.
Figure 6(g) shows the spectrally integrated PL intensity obtained from the PL spectra for different excitation intensities of the devices with no Pd NPs, with Pd NPs (Pd-1), and with Pd NPs (Pd-2). The PL intensities are evaluated for wavelengths ranging from 820 to 900 nm. The radiative efficiency may depend on the quality of the materials and the density of the (photoexcited) carriers. Figure 6(h) shows the normalized PL intensities for an excitation intensity of 83 mW/cm2 and are compared for the devices with no gap and with nanometer gaps. With the increase in the gap width between the subcells, the luminescence extraction increases. Even for the device with a gap width of ~10 nm, the luminescence extraction doubles, indicating an increase in the photon recycling. Such an enhanced luminescence extraction leads to an increase in the photocarrier density, resulting in an enhanced open-circuit voltage in the top GaAs subcell, which can be expressed as
where ηext is the external luminescence efficiency [2]. Our results show that the PL intensity increases for the device with larger airgaps. This implies that as expected in Fig. 3, the reflection efficiency of the luminescence can be modified by varying the gap width between the subcells. In fact, the Pd-2 device shows an increase in PL intensity by a factor of ~1.5, which corresponds to an increase in open-circuit voltage by 10 mV according to Eq. (5). In the experimental results in Figs. 5(i) and 5(h), the open-circuit voltage increases by 15 mV in the Pd-2 device, compared to the Pd-1 device, which is consistent with the above calculation based on PL intensities. In contrast, the current is reduced in the Pd-2 device, which is primarily caused by reduced current in InGaAsP subcell that is limiting the current in the series-connected GaAs/InGaAsP device. This is explained by the enhanced reflection at the interface between the GaAs and InGaAsP subcells. According to the tradeoff between the enhanced voltage of GaAs subcell and the reduced current of InGaAsP subcell, the Pd-1 device with a gap shows the better efficiency.Finally, we discuss the effect of nanometer air gaps on the solar cell characteristics. From the current–voltage curves, it can be seen that the bonding without using Pd NPs leads to a high contact resistance. In the device with no Pd, however, the short-circuit current increases compared to the devices with Pd NPs, which originates probably from the enhanced luminescence coupling and reduced reflection loss at the interface due to no air gap thickness. This increases the current in InGaAsP subcell that limits the current in the series-connected GaAs/InGaAsP devices, resulting in the enhanced short circuit current in the no-Pd device. In the device with Pd NPs, the use of Pd NPs results in a significant reduction in the contact resistance between the subcells. While the reflectance of PL increases significantly with the air gap thickness, indicating enhanced photon recycling effect, the reflectance loss for the normally incident light slightly increases with the increase in the air gap width for nanometer airgaps as well as the reduced luminescent coupling. As a result, the current in the series-connected GaAs/InGAsP device would decrease because the current in the GaAs/InGaAsP device is limited by that in the bottom InGaAsP subcell. Therefore, our findings indicate that tuning the gap width is critical for matching the subcell current and using photon recycling for enhancing the voltages.
4. Conclusions
We investigated the effect of nanometer air gaps between subcells on the photon recycling effect in mechanically stacked multijunction solar cells. The calculation results show that the photon recycling and luminescent coupling efficiencies depend strongly on the air gap thickness, which is a key parameter for tuning the luminescent effects in multijunction solar cells. In addition, we demonstrated the enhanced luminescent extraction using mechanically stacked multi-junction solar cells with nanometer air gaps compared to a device with no air gap.
Funding
New Energy and Industrial Technology Development Organization (NEDO); Ministry of Economy, Trade and Industry (METI); Japan Society for the Promotion of Science (JSPS) (17K07037, 18K07987).
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