1. Introduction

III-V compound multi-junction solar cells dominate the niche market of concentrator photovoltaics and space applications due to their direct-bandgap absorption, high temperature resistance, and wide material selectivity [1,2]. Currently, monolithically-grown Ga_0.5In_0.5P/ GaAs/Ge cell structures are reported solar cells with the highest certified power conversion efficiency ~32% under AM1.5G one-sun illumination [3]. Mature epitaxial technology can also make multi-junction solar cells very competitive for the terrestrial market. By incorporating a low-cost concentrator, the cell area can potentially be minimized, and the material cost increase can be amortized by the increase of power conversion efficiency. As a consequence, III-V multi-junction solar cells appear to be a promising candidate to satisfy the requirement of third-generation photovoltaics [4].

In high-performance triple-junction solar cells, the antireflective coating (ARC) that accounts for saving more than 30% optical loss is often realized by multi-layer dielectric stacking. However, issues such as polarization dependency, limited angular and spectral responses, mechanical instability due to thermal strain, etc. preclude multi-junction solar cells with a conventional ARC from fully exploiting their broadband optical absorption. Recently, the introduction of sub-wavelength structures (SWSs) as the antireflective layer has offered a new possibility in the suppression of the Fresnel reflection [5,6]. Due to the spatially graded structural profile in a single layer, the SWS ARC exhibits not only broadband and omnidirectional antireflective characteristics, but also polarization insensitivity [7–12]. Moreover, the SWS ARC is also robust and mechanically durable, making it particularly desirable for concentrator and space photovoltaics. However, presently proposed nano-fabrication techniques for SWS ARCs could result in severe front surface recombination, which is a major obstacle in the application of III-V solar cells due to the high absorption coefficients of III-V materials [13,14]. In this paper, we demonstrate the implementation of antireflective nanostructures in a Ga_0.5In_0.5P/GaAs/Ge triple-junction solar cell. The structures are fabricated on the silicon nitride (SiN_x) passivation layer using polystyrene nanosphere lithography followed by dry etching [15]. The technique provides a relatively simple, scalable, and cost-effective process to control the structural profile [10, 16-22], while minimizing the surface recombination resulting from etching. Under one-sun illumination, the short-circuit current of a cell with the SWS ARC is enhanced by 46.1% and 3.4% due to much improved optical transmission and current matching, compared to cells without an ARC and with a conventional single-layer (SL) ARC, respectively. The improvement of photocurrent is also investigated by the external quantum efficiency (EQE) characterization of fabricated cells, which matches the analysis of reflectance spectroscopy. The corresponding power conversion efficiency is only comparable with the SL ARC cell due to a slightly degraded open-circuit voltage resulting from process imperfections. Further optimizations of the SWS ARC, including the periodicity and etching depth, are made possible by performing comprehensive calculations based on a rigorous couple-wave analysis (RCWA) method. The optimization technique allows an increase in the cell performance via improved optical transmission and current mismatch issues commonly seen in multi-junction solar cells.

2. Experimental

Polystyrene (PS) nanosphere lithography is employed to fabricate SiN_x-based SWSs on a triple-junction solar cell. First, the Ga_0.5In_0.5P/GaAs/Ge cell structure was monolithically grown by metal-organic chemical vapor deposition (MOCVD) on a p-type germanium substrate. In the epi-structure, individual sub-cells were interconnected by highly-doped tunneling diodes, allowing band-to-band tunneling for the series output. At the beginning of the cell processes, the GaAs ohmic layer was first lithographically defined by selective etching of ammonia between the cap GaAs and Al_0.5In_0.5P window layer. A 1-µm-thick silicon nitride (SiN_x) was then deposited using plasma-enhanced chemical vapor deposition (PECVD). The SiNx has a refractive index of around 1.8 and a nearly-zero extinction coefficient characterized by an n&k analyzer (n&k Technology 1200). The SiN_x film was subsequently treated with oxygen plasma to achieve a hydrophilic surface on which a mixture of ethanol and polystyrene microspheres was spin-coated. By tuning the degree of hydrophilicity, spinning speed, and the mixture concentration, a large area of nearly-close-packed, nanosphere monolayer arrays was obtained on a 4-inch wafer, as shown in Fig. 1 (a) . Here, the PS spheres with a diameter of 600 nm serve as the etching mask for SiN_x. After steady air-drying for 15 min., the samples with a 1-µm-thick SiN_x layer were etched by an inductively-coupled-plasma reactive-ion-etching (ICP-RIE) system (Oxford Instrument, Plasmalab System 100) operated at 13.56 MHz under a gas mixture of CHF₃ and O₂ through individual electronic mass flow controllers. The ratio of gas flow, chamber pressure, and etching time collectively control the sidewall profile, allowing the profile tuning of nanostructures. Figure 1(b) and 1(c) display two different etching profiles with an approximate etching depth of 900 nm using spheres with the same diameter of 600 nm. The structure shown in Fig. 1(b) results from a two-step etching process and therefore shows an evident slope discontinuity. On the other hand, the side wall profile of Fig. 1(c) shows a smooth gradient which resembles moth-eye structures. Hence, the RIE conditions for the structure shown Fig. 1(c) were employed in the cell fabrication. We note that in both Fig. 1(b) and 1(c), a thin layer of SiN_x, ~100 nm thick was kept for surface passivation. After the fabrication of SiN_x SWSs, an additional lithography step was applied to expose the ohmic GaAs layer by selectively etching the undesired SWSs. The front and back metal contacts were deposited by electron beam evaporation and annealed at 400°C for 35 sec for ohmic contacts. Finally, the cutting of cells was performed using a mechanical scriber with a precise control/alignment system and a diamond tip. The fabricated SWS solar cells have a cell area of 0.5x0.5 cm² with a 10% metallic shadow ratio [23]. Furthermore, cells without any AR treatment and with a conventional SL ARC, which contains a layer of 85-nm-thick SiN_x, were also fabricated for comparison.

 

Fig. 1 (a) A large-area scanning electron micrograph of nearly-close-packed polystyrene nanospheres with a 600 nm diameter deposited on SiN_x; (b) the cross-sectional view of SiN_x sub-wavelength structures resulting from two-step and (c) from one-step etching processes. A thin layer of SiN_x ~100 nm thick is kept for passivation.

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3. Characterization and RCWA simulation

3.1 Photovoltaic characterization

The reflectance spectra of cells with the SiN_x SWSs and the SL ARC were measured using an UV/Visible/NIR spectrophotometer (Hitachi U4100) with an integrating sphere. The measured results are plotted in Fig. 2(a) . Compared to the conventional ARC, the SWS ARC improves the optical transmission for ultraviolet/blue wavelengths, showing a relatively flat response. Although the reflectance of the SWS ARC around the 600 nm wavelength is relatively high, the AM1.5G-weighted reflectance of SWSs is approximately 7.15% for the wavelength range of 300 nm to 1700 nm, which is still ~2.50% lower than that of the SL ARC, ~9.65%. The suppression of the Fresnel reflection contributes to the enhanced optical absorption, which has also been verified in the external quantum efficiency (EQE) characteristics of fabricated cells, as shown in Fig. 2(b). Figure 2(b) shows the measured EQE results for the top and middle junctions for cells with the SWS, SL ARC and without any ARC, respectively. As shown in Fig. 2(b), the EQE of the Ga_0.5In_0.5P top cell is indeed improved for λ< 500 nm with SWSs, which agrees well with the reflectance spectroscopy. The transmission enhancement boosts the short-circuit current of the top junction. Therefore, the current limiting junction is switched from the top junction to the middle one for the cell with the SWS ARC due to the transmission improvement. However, although the cell with the SL ARC shows a better EQE response for the 500-700 nm wavelength range, the total output photocurrent of the SL ARC cell is still limited by the top junction, due to strong reflection in the UV wavelength range. As a result, the cell with the SWS ARC exhibits a higher short-circuit current, Jsc ~10.24 mA/cm² than that of the SL ARC, ~9.90 mA/cm². Table 1 summarizes the device current-voltage characteristics under simulated AM1.5G irradiation (Oriel Class A solar simulator, calibrated to an NREL-certified polycrystalline silicon solar cell). Overall, the short-circuit current of the SWS cell is enhanced by 46.1% and 3.4%, compared to cells without an ARC and with a SL ARC respectively, due to improved optical transmission and current matching. However, as indicated in Table 1, the power conversion efficiency of the cell with SWSs is only comparable to the cell with the SL ARC due to a slightly degraded open-circuit voltage. The reason for the voltage degradation is still under investigation, possibly arising from the mesa isolation by scribing. It is also noted that the overall open-circuit voltage and power-conversion efficiency of the fabricated triple junction solar cells are smaller than those seen in commercialized cells due to the existence of reversely connected p-n junctions on both sides of the Ge wafer, arising from the diffusion process. The parasitic Ge junction should have been removed during the fabrication process either by etching or mechanical polishing before back metallization [24]. As a consequence, the reversely connected p-n junctions reduce the overall output voltage significantly. However, this process imperfection does not affect the analysis of antireflective characteristics of the SWS cell, as the Ge sub-cell absorbs photons from a wide range of near-infrared wavelengths and thus is never the current-limiting junction.

 

Fig. 2 (a) The measured reflectance spectra are plotted for cells with sub-wavelength structures (SWSs) and a conventional single-layer antireflective coating (SL ARC). The green symbol-line represents the calculated reflectance spectra according to the inset 7x7 array model. (b) The measured external quantum efficiency (EQE) of the Ga_0.5In_0.5P top cell and the GaAs middle cell with SWS, SL ARC and without ARC. The SWS cell shows higher EQEs for λ< 500 nm than the SL ARC cell, consistent with the observation in (a).

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Table 1. AM 1.5G Current-Voltage Characteristics of Solar Cells with Various Antireflective Coatings (ARCs)

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3.2 RCWA simulation

The rigorous couple wave analysis (RCWA) approach has been employed to investigate the diffraction and transmission properties of nanoscale structures before [25]. In the present work, a commercial implementation of the three-dimensional RCWA (DiffractMod, Rsoft Corp.) is employed to first examine the consistency between simulation and experiment, and to further optimize the SWSs. As shown in the inset of Fig. 2(a), the simulated structural profile of a unit cell consists of 7x7 SiN_x SWSs in a hexagonal array. The sidewall profile is approximated with a parabolic function to match the structures seen Fig. 1(c). Moreover, a variation of 10% in the structural height was introduced to account for the fluctuation in the etching depth. Below the SiN_x SWS layer there are a thin SiN_x passivation layer, ~100 nm thick, the Al_0.5In_0.5P window layer, and the Ga_0.5In_0.5P top junction. The material dispersion of each layer was taken into account for wavelengths between 300 nm and 1000 nm. The electric field is set to be 45-degree linearly polarized to account for the un-polarized solar radiation. As shown in the green symbol-line of Fig. 2(a), the simulated reflectance agrees well with the experimental data measured by the integrating sphere for wavelengths larger than 450 nm. A slight discrepancy occurs at short wavelengths, possibly arising from the mismatched material dispersion. Further characterizations of the complex refractive indices of the Ga_0.5In_0.5P and Al_0.5In_0.5P layers are required to improve the accuracy in the UV spectral range.

After confirming the validity of our simulation model for wavelengths larger than 450 nm, the optical reflectance is optimized as a function of the periodicity and the etching depth, which correspond to the nanosphere diameter and the average height of SiN_x SWSs, respectively. The diameters of PS spheres vary between 300 nm and 1800 nm, given a SWS height of 900 nm. As shown in Fig. 3(a) , the diameters between 600nm and 1000nm exhibit relatively low reflectance for the near-infrared wavelengths. For reference, the dashed line in Fig. 3(a) represents the data shown in Fig. 2(a). Additionally, the dependence of reflection on the structural height up to 900 nm is considered in Fig. 3(b) with a fixed diameter of 600 nm. The optimized heights are near the 500 nm to 600 nm range. For larger structural heights, the reflectance at long wavelengths also becomes larger. To further examine the impact of structural dimensions on cell performance, we also calculate the short-circuit current density under the AM1.5G irradiance with an assumption of 100% charge conversion and collection, using the same method for Fig. 3(a) and 3(b), expressed as

 

Fig. 3 The calculated reflectance spectra for the wavelength range of λ = 300 nm-1000 nm as a function of (a) the nanosphere diameter, and (b) the structural height. (c) The calculated short circuit current densities as a function of the diameter and height.

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4. Conclusion

In conclusion, we have successfully fabricated SiN_x-based sub-wavelength antireflective structures for a Ga_0.5In_0.5P/GaAs/Ge triple-junction solar cell employing polystyrene nanosphere lithography. The side-wall profiles of these structures can be controlled by adjusting the etching conditions. Further, the reflectance spectroscopy and external quantum efficiency measurements confirm the improved optical absorption in the ultraviolet/blue wavelengths. Under one-sun AM1.5G illumination, the short-circuit current of a cell with sub-wavelength structures is enhanced due to much improved current-matching. Calculations based on a rigorous coupled-wave analysis not only verify the broadband antireflection consistent with the measured data, but could also serve as an optimization tool for the implementation of sub-wavelength antireflective structures in multi-junction solar cells.