1. Introduction

Since Shockley and Queisser proposed the limiting efficiency of solar cells in 1961 [1], gallium arsenide (GaAs) solar cells have reached their state-of-the-art power conversion efficiency (PCE) of 29.1% [2,3]. It has been agreed that the nearly-perfect material quality and control of photogenerated carrier losses are the two most important requisites to approach their theoretical limit of 33% [4,5]. For GaAs, the loss of photogenerated carriers to the non-radiative recombination may be suppressed by cascaded events of photon emission and re-absorption, also known as photon recycling [6–10]. Photon recycling benefits the device performance as it increases the probability of the re-absorbed and re-emitted photons escaping the solar cell, and thus increase the external radiation efficiency. However, the effect is only significant when the non-radiative recombination rate of the active material is small [4]. It has been theoretically and experimentally demonstrated that optical enhancement of the open-circuit voltage (V_oc) via photon recycling plays a significant role in approaching the Shockley and Queisser limit [4,11]. Over the past decade, various light management approaches have been proposed, including surface texturing, thin-film type Fabry-Pérot resonators with a rear gold mirror, monolithically grown distributed Bragg reflectors (DBRs), as well as angularly and spectrally selective filters (SSFs) [12–19]. The V_oc enhancement in these devices has been reported, although the net increases are small and dependent on the epitaxial material qualities and processing techniques. Meanwhile, the monolithic growth of strain-balanced multiple quantum wells (MQWs) in GaAs-based single- [20–23] and triple-junction solar cells (TJSCs) [24,25] have also been widely exploited to extend the absorption edge for maximized photocurrent generation and to fine-tune the current-match condition of TJSCs. The weak and incomplete optical absorption of long wavelength components in these GaAs-based MQW devices are compensated by light trapping techniques such as rear reflectors and textures [26–29]. Because of the strain-balanced nature, the In_0.1Ga_0.9As/ GaAs_0.85P_0.15 MQWs exhibit relatively high material qualities and thus a very low non-radiative recombination rate. The proposed light-trapping structures could further increase the photon re-absorption and escaping probabilities, leading to strong photon recycling. Over the past decade, the photon recycling effects in GaAs-based MQW-DBR devices have been shown to contribute to the dark current reduction via fitting the two-diode model [27,28]. Nevertheless, the use of MQWs exhibits a reduced V_oc in GaAs-based solar cells, such that the PCE does not surpass the single-junction bulk device. Since the radiative recombination rate of InGaAs/GaAsP MQWs is at least an order of magnitude larger than that of the GaAs bulk, it is worthwhile to investigate the photon recycling effects of MQW solar cells in order to maximize the voltage output while keeping the photocurrent gain. As a result, in this work, we investigate the correlation between photon confinement and photovoltaic properties of single-junction, strain-balanced MQW incorporating a frontal SSF and/or a rear monolithically-grown DBR. The SSFs with three different cutoff wavelengths: 880, 910, or 940 nm are designed and fabricated to be partially or fully overlapped with the spontaneous emission spectrum of the MQWs. We further study the device characteristics under dark, one-sun, and concentrated illumination conditions.

2. Experimental methods

Figure 1 show the schematic structures of the two SJ MQW solar cells employed in this work for (a) without a rear DBR and (b) with a 12-pair, monolithically-grown DBR, which hereafter are referred as the MQW and MQW-DBR solar cells, respectively. These samples were grown on n-type GaAs wafers with a nominal doping concentration of 10¹⁷ cm⁻³ using metal-organic vapor phase epitaxy (MOVPE). The growth sequence began with an n+ GaAs buffer layer, n++/p++ GaAs tunnel diode (TD) layers for connection, a p+ Ga_0.5In_0.5P back surface field (BSF) layer, followed by a p-type GaAs base, intrinsic MQW region, n-type GaAs emitter, an Al_0.6In_0.4P window, and a n++ GaAs contact layer. The 1000 nm-thick intrinsic region is composed of 50 pairs strain-balanced In_0.1Ga_0.9As/ GaAs_0.85P_0.15 MQWs with a well and barrier thickness of 7 and 13 nm, respectively. For devices incorporated with a rear DBR, as seen in Fig. 1(b), 12 pairs of p-type AlAs (75 nm)/GaAs(63 nm) layers are alternately deposited between the tunnel diode and BSF layers. The complete epitaxial structures are provided in the supporting information, and detailed device characteristics can be found in a previous report [30].

 

Fig. 1. The schematic epitaxial structure of the two solar cells used in this work: (a) an MQW solar cell grown on the GaAs substrate and (b) an MQW-DBR solar cell with a 12-pair, monolithically-grown DBR.

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The epitaxial wafers were then processed into devices using standard fabrication procedures: 1) photolithographic definition of the frontal electrode with a metallic shield ratio of 10%, followed by the metal deposition and lift-off, 2) self-aligned wet chemical etch of the ohmic layer to expose the window layer, 3) electron-beam evaporation of the rear electrode, and 4) dissection of devices with an area of 1 × 1 cm². The conventional anti-reflective coating is not employed in the process. Instead, a frontal SSF composed of alternative TiO₂ and SiO₂ dielectric layers is designed and implemented to achieve a minimal optical reflection loss from 400 nm to a specified cutoff wavelength and maximize the reflectivity from the cutoff wavelength and beyond.

The implementation of the SSF is similar to that of a DBR by using alternative depositions of dielectric layers with a high- and low- index of refraction [31]. The difference between the SSF and DBR lies on the top and bottom phase-matching layers. The deposition sequence of an SSF follows the order of ${\left( {\frac{\textrm{L}}{2}\;\textrm{ H}\;\frac{\textrm{L}}{2}} \right)^\textrm{S}}$, where S denotes the number of periods; L/2 denotes the low-refractive-index layer (SiO₂) with a thickness of one-eighth of the target wavelength, and H denotes the high-refractive-index layer (TiO₂) with a thickness of one-quarter wavelength. Moreover, an additional buffer SiN_x layer is introduced between the optical filter and the solar cell window layer for phase matching. The refractive index and extinction coefficient of SiN_x, SiO₂, and TiO₂ under specific deposition conditions are extracted from their reflectance spectrum (n&k 1500-D) and incorporated into the optical model to calculate the spectral response of the SSF on the MQW solar cell. In this work, we employ a commercial implementation of the three-dimensional rigorous coupled-wave analysis (DiffractMod, Synopsys Corp.) to assist the optical design. The thickness of the SiN_x layer plays a crucial role in the performance of SSFs. Figure 2(a) shows the calculated reflectance spectra of an SSF placed on the MQW solar cell with various SiN_x thicknesses: 0, 40, 70, 100 nm. We further define a solar-spectrum-weighted reflectance, <R > as in Eq. (1):

 

Fig. 2. (a) The calculated reflectance spectra of SSFs on an MQW cell with various SiN_x thicknesses: 0, 40, 70, 100 nm. (b) The AM1.5G spectrum- weighted reflectance, <R > of SSFs for λ=400-870 nm is plotted as a function of the SiN_x thickness. The inset shows the schematic layer structure for optical simulation and the deposition sequence of the SiN_x, and 12 pairs of SiO₂ and TiO₂ layers.

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We began the fabrication process of SSFs on MQW solar cells by partially covering the bus bars of the metallic contact with a vacuum tape for subsequent electric probing. Subsequently, a 70 nm-thick SiN_x layer was deposited via plasma-enhanced chemical vapor deposition (PECVD), followed by the deposition of 12-pair alternative SiO₂/TiO₂ thin film stacks at 100°C via electron beam evaporation. Finally, the vacuum tape was removed for subsequent optical and electrical characterizations. The SSFs with three different cutoff wavelengths: 880, 910, and 940 nm are designed and simultaneously fabricated on the MQW, and MQW-DBR solar cells, as well as on a silicon wafer for model calibration.

Next, the optical reflectance was measured by a UV-VIS-NIR spectrophotometer (Hitachi U-4100). The electroluminescence (EL) was measured at room temperature in a home-built system which includes a probe station (2 probes), Keithley 2400 source meter, Ocean Optics Maya 2000 pro spectrometer (wavelength range 165 - 1100 nm), and an integrating sphere with the barium sulfate coating. The current density- voltage (J-V) characteristics of fabricated solar cells were performed under dark, simulated AM1.5G one-sun, and concentrated illuminated conditions. For the one-sun characterization, the system was composed of a power supply (Newport 69920), a 1000W Class A solar simulator (Newport 91192A) with a Xe-lamp and an AM1.5G filter, a probe stage, a source-meter (Keithley 2400) with a 4-wire mode, and an active temperature control system to control the cell temperature at 25.0 ± 0.1°C. A mono-crystalline silicon reference cell (VLSI Standards, Inc.) was used for solar simulator calibration before measurement. For concentration photovoltaic characterization, the solar cells were measured by using a pulsed solar simulator with conformed international standards IEC 60904-9, including the class AAA, 1000 W/m² irradiance, a 2 m x 2 m irradiation area, and 10 ms exposure time. A 30 × 30 cm² Fresnel lens and an automatically controlled Z-axis displacement platform, where the device under test is mounted, were used to vary the irradiance on the device by controlling the distance of the platform to the Fresnel lens. The temperature was maintained at 25.9 ± 0.1°C during the concentration measurement. Finally, the concentration ratio was determined by the short-circuit current of a solar cell to that obtained under the one-sun standard testing conditions.

3. Results and discussion

3.1 Optical reflectance and electroluminescence

We first examine the optical characteristics of the fabricated SSFs. Figure 3 plots the measured and calculated reflectance spectra of the designed SSFs deposited on the Si wafer for the normally incident light. Here, we define the cutoff wavelength to be at the 50% reflectance point, where three cutoff wavelengths can be determined: 880 nm, 910 nm, and 940 nm in Figs. 3(a)–3(c). We can see that the design and experiment show reasonable agreement with each other. The deposited SSFs provide a low-reflectance region for the visible and near-infrared wavelengths and high reflectance from the cutoff band edge to beyond. The slight discrepancies in the reflectance spectra arise from the thickness variation of deposited thin films, which is limited by the low responsivity of the silicon photodetector for in-situ reflectance monitoring. Nevertheless, in all cases, the maximal reflectance at the stopband is still over 90%, which shall block most of the photon emission in this spectral range. By referring to the EL spectra shown in Fig. 4, we can see that the spectral response of the SSF is indeed partially or fully overlapped with the spontaneous emission spectrum of the MQWs.

 

Fig. 3. The simulated and measured reflectance spectra of spectrum selective filters with three different cut-off wavelengths: (a) 880 nm, (b) 910 nm, (c) 940 nm deposited on Si wafers.

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The EL of the MQW and MQW-DBR solar cells incorporating the designed SSF is measured at a constant current injection level of 20 mA/cm². The devices are denoted as SSF-MQW and SSF-MQW-DBR hereafter. As shown in Figs. 4(a) and 4(b), the EL emission peak of the referenced MQW and MQW-DBR devices without SSFs are located at 932 nm and 935 nm, respectively. The MQW-DBR device exhibits distinct Fabry-Pérot resonance peaks due to photon confinement provided by the rear DBR and flat air- Al_0.6In_0.4P window layer interface. The integrated photon counts of the EL from the MQW-DBR device are enhanced by approximately 24% compared to that of the MQW device. After the deposition of SSFs, we observe the suppression of EL spectra from both the SSF-MQW and the SSF-MQW-DBR devices. The shorter the cutoff wavelength, the more suppression of the total photon emission. The effect of SSFs on the EL can be evaluated through the integrated EL intensity and normalized to their reference counterpart, as shown in Fig. 4(c). The photon emission from the 880 nm SSF-MQW and SSF-MQW-DBR devices are reduced most to 11.6% and 16.9% from their original value, respectively, while the 940 nm SSF-MQW and SSF-MQW-DBR devices still maintain 57.1% and 68.4% of the total photon emission.

 

Fig. 4. The electroluminescence spectra of (a) SSF-MQW solar cells and (b) SSF-MQW-DBR solar cells with 880 nm, 910 nm, 940 nm cutoffs. (c) The normalized electro-luminescence intensity of the above devices.

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It is found that the normalized EL intensity of the SSF-MQW solar cells appears to be proportional to the cutoff wavelength. However, those of the 910 nm and 940 nm SSF-MQW-DBR solar cells only show a small difference. As revealed by the spectra in Fig. 4(b), the EL peaks of the SSF-MQW-DBR device are dictated by the optical cavity resonance between the SSF and DBR. As the 910 nm SSF restricts the photon emission from the ground state of MQWs, the injected carriers can still radiatively recombine from the excited states of MQW, leading to enhanced photon emission near the 910 nm wavelength, as seen in the blue dotted line of Fig. 4(b). As a result, the integrated EL intensity of the 910 nm SSF-MQW-DBR device is not significantly smaller than that of the 940 nm device. The dependence of the normalized EL intensity on the cutoff wavelengths is a result of the spectral response overlap between the SSF and MQWs. Therefore, the decrease of the EL intensity with the decreased cutoff wavelength shows that light emission from the cell is inhibited by the SSF, which in turn can result in stronger internal photon recycling.

3.2 Dark current density-voltage analysis

The photon confinement of MQW solar cells incorporating a rear DBR has been previously investigated via the two-diode model and shown to reduce the saturation current of the radiative component in the dark J-V curve through curve fitting [28]. In this work, we use an alternative method including the series resistance to analyze the dark J-V characteristics of the MQW and MQW-DBR devices before and after the deposition of SSFs [32]. The J-V characteristics of a solar cell taking into account the series resistance can be modeled by Eq. (2):

 

Fig. 5. The fitted (a) ideality factor, and (b) saturation current density for the SSF-MQW and SSF-MQW-DBR solar cells under a 20 mA/cm² injection current. The Dot and Dashed lines represent the reference counterpart before the deposition of SSFs.

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First, as shown in Figs. 5(a) and 5(b), we see that the referenced MQW solar cells (blue dotted line) exhibit a lower ideality factor and saturation current than those of the referenced MQW-DBR solar cells (red dashed line). The result seems counterintuitive, as the photon recycling effect should be more prominent for solar cells with a rear DBR. However, our previous study on the two device structures using an accurate EL analysis has revealed that the material quality of the MQW solar cells is better than that of the MQW-DBR, where the crystallinity of the active region may be affected by the monolithic growth of 12-pair DBR [30]. Here, the fitting results support the conclusion drawn in our previous study. As a result, it is only reasonable to compare the fitting values of the devices concerning their reference counterpart instead of cross-referencing the devices with and without the rear DBR. Nevertheless, after the introduction of SSFs, we observe a similar dependence of the ideality factor and saturation current on the cutoff wavelength for both sets of SSF-MQW and SSF-MQW-DBR solar cells. As the cutoff wavelength decreases, that is, more of the emitted photons from MQWs are reflected back to the active region, both the ideality factor and saturation current are reduced. In other words, the photon recycling of MQWs enhances the radiative recombination, such that the ideality factor of the J-V curve becomes close to unity (radiative limit). Moreover, the saturation current density is reduced by nearly 26 times and 3 times for the 880 nm SSF-MQW and SSF-MQW-DBR solar cells respectively, compared to the 940 nm devices. The amount of saturation current reduction between the two sets of SSF devices is likely dominated by their material quality. Finally, we note that both the SSF-MQW and SSF-MQW-DBR solar cells have a slightly higher ideality factor and saturation current than their reference, indicating that slight device degradation might have occurred during the lengthy deposition process of SSFs (10-15 hours). The increased saturation current could be explained by the front surface damage after the deposition of the SSF. Indeed, we have previously verified that the deposition of the SiN_x and SSF layers on the single-junction GaAs solar cell degrades the surface property by inspecting the internal quantum efficiency (IQE) spectrum [13]. The IQE only shows degradation for wavelengths below 400 nm, which is a signature for the front surface damage. The degradation should explain the increase of J₀ after the SSF deposition and should occur for all devices. However, the 880 nm SSF does not show a significant increase of J₀, but a slightly lower value than that of the reference device. Here, we think that maybe the increment of J₀ due to the surface damage cancels with the reduction of J₀ due to the optical confinement of which the effect is more profound with the 880 nm SSF than that with the 910 nm and 940 nm SSFs. However, the hypothesis requires further work for verification.

3.3 Photovoltaic characteristics

We next discuss the photovoltaic characteristics of the fabricated SSF-MQW and SSF-MQW-DBR solar cells under a simulated AM1.5G one-sun illumination condition, as shown in Table 1 and 2. We compare the solar cell performance before and after the deposition of SSFs. The three baseline MQW and MQW-DBR solar cells have an average PCE of 18.1 ± 0.2% and 19.0 ± 0.4%, respectively. After the deposition of SSFs, The net PCE of the SSF-MQW and SSF-MQW-DBR solar cells have increased by more than 2% due to the antireflective properties provided by the SSFs which enhance the short-circuit current density (J_sc). We further plot the net differences of J_sc, V_oc, fill factor (FF), and PCE, labeled as ΔJ_sc, ΔV_oc, ΔFF, and ΔPCE versus the cutoff wavelength in Figs. 6(a)–6(d), respectively. As shown in Fig. 6, the J-V characteristics of the SSF-MQW and SSF-MQW-DBR devices after the deposition of SSF exhibit similar dependences on the cutoff wavelength. The ΔJ_sc increases monotonically with the cutoff wavelength. However, the improvement for the 940 nm and the 910 nm devices are comparable due to weak optical absorption in the MQW region which contributes to little photocurrent enhancement. The observation is also supported by the external quantum efficiency (EQE) measurement shown in Fig. 7. Next, the ΔV_oc exhibits a maximum at the 910 nm cutoff, as seen in Fig. 6(b). From Eq. (2), we can see that the change of V_oc is dictated by the logarithmic ratio of J_sc / J₀. With the presence of photon recycling, the V_oc is also enhanced through the suppressed saturation current, J₀. As a result, the ΔV_oc exhibits a maximal enhancement at the 910 nm cutoff wavelength, where the net increase approaches 4.4 mV and 3.3 mV for the SSF-MQW and SSF-MQW-DBR solar cells, respectively. The enhancement of V_oc with the 910 nm SSF compared to that with the 940 nm SSF is attributed to the reduced J₀ shown in Fig. 5(b), while that compared to the 880 nm SSF is dominated by the J_sc enhancement. On the contrary, as shown in Fig. 6(c), the FFs of all SSF devices are slightly deteriorated after the lengthy deposition of SSFs, which is also consistent with the R_s analysis from Eq. (2). Overall, we observe in Fig. 6(d) that the PCE of SSF-MQW and SSF-MQW-DBR solar cells is mostly dominated by the change of J_sc under the one-sun irradiance.

 

Fig. 6. The net differences of (a) J_sc, (b) V_oc, (c) FF (d) PCE before and after the deposition of SSFs are plotted versus the cutoff wavelength under a simulated AM1.5 g one-sun illumination condition.

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Table 1. Photovoltaic Characteristics of MQW Solar Cells Before and After the Deposition of Spectrally Selective Filters (SSFs)

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Table 2. Photovoltaic Characteristics of MQW-DBR Before and After the Deposition of Spectrally Selective Filters (SSFs)

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The measured EQE of the SSF-MQW and SSF-MQW-DBR solar cells with the three cutoff wavelengths are respectively shown in Figs. 7(a) and 7(b), where the dot-dashed lines represent the reference devices without the SSF. As shown in Fig. 7, the MQWs in the reference devices extend the optical absorption edge to the 950 nm wavelength, where the rear DBR enhances the photocurrent response as seen by the multiple Fabry-Pérot resonance peaks, as seen in Fig. 7(b). Nevertheless, the introduction of a frontal SSF in both sets of devices suppresses the near-infrared photocurrent response of the MQWs according to the specified cutoff wavelength, which is also identified by the reflectance and EL measurement.

 

Fig. 7. The measured external quantum efficiency spectra of the fabricated devices: (a) SSF-MQW and (b) SSF-MQW-DBR solar cells with cutoff wave-lengths of 880, 910, and 940 nm.

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Next, we investigate the photovoltaic characteristics of SSF-MQW and SSF-MQW-DBR solar cells under concentrated irradiance, up to 150 suns, as shown in Fig. 8 and Fig. 9, respectively. First, the J_sc in Figs. 8(a) and 9(a) varies linearly with the concentration ratio by definition. According to the surface reflective properties, the 940 nm SSF devices produce the most photocurrent and the 880 nm produce the least at any given concentration ratio. As the J_sc increases, the V_oc increases logarithmically. However, we see that in Fig. 8(b), the V_oc of the 880 nm SSF-MQW solar cell has surpassed that of the 910 nm at high concentration ratios. We think that because the J_sc difference between the 880 nm and 910 nm SSF-MQW devices under high concentration is small, the enhancement of V_oc for the 880 nm device could arise from the photon recycling effect provided by the frontal SSF. However, since the spontaneous emission of MQWs could still leak to the GaAs substrate, the capability of photon confinement in SSF-MQW solar cells is relatively weak. As a result, the V_oc of the 910 nm cannot approach that of the 940 nm for the SSF-MQW solar cells. On the other hand, the V_oc of the 910 nm SSF-MQW-DBR solar cell virtually overlaps with that of the 940 nm device under high concentration in Fig. 9(b). Since the 940 nm SSF-MQW-DBR solar cell has a larger J_sc than the 910 nm, the boost of V_oc for the 910 nm SSF-MQW-DBR solar cell is a clear signature of photon recycling. However, here the V_oc difference between the 910 nm SSF-MQW-DBR and the reference solar cell without the SSF is relatively small, ∼5 mV under 150 suns. Next, as shown in Figs. 8(c) and 9(c), the FFs of the SSF-MQW and SSF-MQW-DBR devices exhibit a similar dependence on the concentration ratio: first increase and then decrease rapidly due to the current crowding effect. This is because these devices are not designed for the concentrated illumination based on the grid pitch. However, the FF of the 910 nm SSF-MQW solar cell degrades the most compared to other devices under concentrated irradiance. The large series resistance observed in the 910 nm SSF-MQW device possibly results from non-ideal material growth or cell fabrication. As the series resistance is increased with the concentration ratio, the cell characteristics influenced by a series resistance under concentrated illumination shows a fast degraded FF. However, the V_oc is not be affected [33]. As a result, while the PCE of the SSF-MQW and SSF-MQW solar cells are mostly dominated by the values of J_sc, as respectively seen in Figs. 8(d) and 9(d), the 880 nm SSF-MQW device performs better than the 910 nm counterpart at high concentration ratio.

 

Fig. 8. The photovoltaic characteristics: (a) J_sc, (b) V_oc, (c) FF (d) PCE of the SSF-MQW solar cells with the 880, 910, and 940 nm cutoff wavelength are plotted as a function of the concentration ratio. An MQW solar cell without an SSF is used as the reference. The V_oc under medium concentration ratios (20-50) is enlarged from the dashed box in (b) to show the relative magnitudes of the devices.

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Fig. 9. The photovoltaic characteristics: (a) J_sc, (b) V_oc, (c) FF (d) PCE of the SSF-MQW-DBR solar cells with the 880, 910, and 940 nm cutoff wavelength are plotted as a function of the concentration ratio. An MQW-DBR solar cell without an SSF is used as the reference. The V_oc under medium concentration ratios (20-50) is enlarged from the dashed box in (b) to show the relative magnitudes of the devices.

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4. Conclusion

In summary, we investigate the photon recycling characteristics of single-junction, strain-balanced MQW and MQW-DBR solar cells incorporating a frontal spectrally selective filter. The filters are designed with the empirical optical constants and directly deposited on the MQW and MQW-DBR solar cells. By systematically comparing the SSF-MQW and SSF-MQW-DBR solar cells with 880 nm, 910 nm, and 940 nm cutoff wavelengths, we show that the photon confinement enhances the radiative recombination of MQW solar cells such that the ideality factor approaches unity. The saturation current density is also reduced by 26 times and 3 times for the 880 nm SSF-MQW and SSF-MQW-DBR solar cells, respectively, compared to the 940 nm devices. Photon recycling further contributes to the enhancement of the open-circuit voltage. While the magnitude of enhancement is relatively small, ∼3-5 mV net increase under one-sun and concentrated illumination conditions, the performance of SSF-MQW and SSF-MQW-DBR solar cells may further benefit from the improved epitaxial material quality and implementation of optical filters. These learnings and results also point to future directions for versatile optical engineering approaches for the attainment of highly efficient III-V MQW photovoltaics.