1. Introduction

The photon to electron conversion efficiency of photovoltaic devices [1], which include photo sensors and solar cells, must be improved, for especially ultrathin-film devices (several hundred nanometers to several micrometers) that have such attractive characteristics as enhanced carrier extraction, reduced material usage, and simplified fabrication processing. However, one of their drawbacks is lower photon absorption efficiency. For example, silicon (Si)-based photovoltaic devices with thicknesses less than several micrometers cannot completely absorb photons with wavelengths that exceed 600 nm; this problem reduces the photo-electron conversion efficiency. To boost it, an effective method must be found that traps and ultimately absorbs photons within the ultrathin active layer for a longer interaction time. Over the years, various methods have been demonstrated that precisely manipulate the properties of photons. Currently, textured structures [2,3], which have randomly corrugated surfaces, are widely used for photon trapping. However, the obtained characteristics are non-uniform, and realizing perfect scattering is difficult in textured structures.

Recently, using photonic crystals (PCs) for enhancing photon trap efficiency in photovoltaic devices has been investigated. Various unique characteristics of photonic crystals have been shown [4–13], including large area in-plane optical resonance at the photonic band-edge modes of a two-dimensional (2D) PC, which can be applied to lasers and light-emitting diodes [9–13]. If the incident light from the free space is coupled to the photonic band-edge modes, we expect longer interaction time to the photovoltaic material and enhancement of the optical absorption.

Several investigations have improved the light-absorption efficiency in photovoltaic devices using PCs [14–18]. However, few reports have addressed their concrete design rules, especially analyses of photonic band structure in photovoltaic devices. We recently reported a 50-nm-thick Si photovoltaic device with a photonic crystal and enhanced the light’s optical absorption 20 times with a PC’s band-edge wavelength, which showed an optical absorption enhancement effect at the photonic band-edge [18]. However, this work only showed optical absorption enhancement for a single wavelength; this is insufficient for the wide wavelength operations that are required for solar cells.

In this paper, we investigate the photonic band structure of photovoltaic devices with photonic crystals and methods for optical absorption enhancement for multiple wavelengths. We focus on the generation of multiple photonic band-edge modes by higher order modes in the vertical direction of photovoltaic layers and by the band folding effect due to the photonic superlattice structure and numerically show optical absorption enhancement.

2. Enhancement of optical absorption by higher order modes for vertical direction

Figure 1 shows a schematic image of the devices discussed in this paper. We consider a superstrate type solar cell and introduce a PC into the thin microcrystalline Si (µc-Si) photovoltaic layer, which is widely used as a material for thin film solar cells. In this structure, large area photonic resonant modes can be formed by photonic band-edges. When light is introduced from the free space, absorption enhancement can be realized if the frequency of the incident light is identical with the band-edge frequency.

 

Fig. 1 (a) Schematic image of devices discussed in this paper. A PC is introduced into the photovoltaic layer. Calculation parameters are also described here. (b) Absorption coefficient of µc-Si used in the calculations.

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To realize absorption enhancement on multiple wavelengths, multiple photonic band-edge modes have to be formed. We first discuss higher order modes for the thickness direction (Fig. 2(a)). If a 400-nm-thick µc-Si photovoltaic layer is assumed, at least three modes are formed in the thickness directions in the 600-1000-nm wavelength range. We carried out numerical calculations using the three-dimensional (3D) finite difference time domain (FDTD) method. The detailed parameters are shown in Fig. 1. A 400-nm-thick µc-Si photovoltaic layer was bounded by two transparent conductive films (optical absorption of the transparent conductive films is ignored). Even though the typical thickness of a μc-Si layer is one or more micrometers, we employed this thickness to reduce material usage and production cost and for easier carrier extraction. We set a semi-infinite glass layer and a perfect conductor on the forward and back sides of the structure and placed 140-nm high SiO₂ rods with a 110-nm radius on a square lattice with a period (a) of 275 nm. 70-nm-high Si rods formed on the other side. This is because in the fabrication process, SiO₂ rods are formed on the glass substrate and then the µc-Si photovoltaic layer is deposited. Therefore, Si rods protrude from the other side. The absorption coefficient of the µc-Si used in the following calculations is shown in Fig. 1(b) [19].

 

Fig. 2 (a) Schematic image of higher order modes for thickness direction in devices discussed in this paper. (b) Photonic band diagram for structure calculated using 3D FDTD methods. We used the material characteristics for a 900-nm wavelength. (c) Calculated optical absorption spectrum of the structure by 3D FDTD method.

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Using 3D FDTD, we calculated the photonic band diagram for the structure shown in Fig. 1 with the material characteristics for a 900-nm wavelength (Fig. 2(b)). The black lines indicate the 0th order (fundamental) modes for the vertical direction, and the red and blue lines represent the 1st and 2nd order modes. From Fig. 2(b), multiple photonic band-edges are formed at the Γ point in this structure.

We calculated the optical absorption spectrum of the structure by the 3D FDTD method. To consider the influence of the material dispersions, we carried out multiple calculations for different wavelength continuous wave (CW) light sources (every 2 nm) with corresponding material characteristics. The results are shown in Fig. 2(c). In the no-PC structure, the optical absorptivity in the wavelength range between 600 and 950 nm is as small as 10-70%, but by introducing PC, we enhanced the absorption at multiple wavelengths between 600 and 930 nm. Compared with the band diagram in Fig. 2(b), the peaks at 930, 820, and 750 nm correspond to the 0th (fundamental), 1st, and 2nd order modes for the vertical direction, respectively. The peak around 730 nm corresponds to the higher order band-edge for the 0th (fundamental) order mode for the vertical direction, which means that higher order band-edges also work for optical absorption enhancement. There is some frequency discrepancy between Figs. 2(b) and 2(c), because the band diagram calculations in Fig. 2(b) do not include the material dispersions.

To quantitatively evaluate the amount of optical absorption, we averaged the optical absorption in the wavelength range from 500 to 1000 nm weighted by the solar spectrum (air mass (AM) 1.5), defined as:

The enhancement of optical absorptivity by PC can be applied not only to µc-Si but also to other materials, including amorphous Si (a-Si) and GaAs, where strong optical absorption can be obtained just above their electrical bandgap energy. We carried out similar calculations for the a-Si based solar cells shown in Fig. 3(a). The equivalent thickness of a-Si was set to 250 nm, which is the typical thickness of a-Si-based solar cells due to their electrical characteristics. The absorption coefficient of the a-Si used in the following calculations is shown in Fig. 3(b) [19]. The obtained absorption spectra for this structure and one with no-PC are shown in Fig. 3(c). Optical absorption enhancement can clearly be seen in the wavelength range between 600 and 750 nm, where little absorptivity is obtained in the no PC structure; this result shows the benefit of PC for optical absorption enhancement. For the a-Si structure, since strong optical absorption can be obtained just above its electrical bandgap energy (1.6-1.8 eV), the wavelength range is relatively small where the optical absorption must be enhanced. On the other hand, µc-Si has smaller absorptivity even above its electrical bandgap, as shown in the dashed line in Fig. 2(c). Further investigations are required for more broadband optical absorption enhancement.

 

Fig. 3 (a) Schematic image of calculation model for a-Si based photovoltaic device. (b) Absorption coefficient of a-Si used in calculations. (c) Calculated absorption spectrum of structure by 3D FDTD method.

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3. Further optical absorption enhancement by photonic superlattice structure

We showed the broadband optical absorption enhancement for both the µc-Si and a-Si structures. However, in the µc-Si solar cell (Fig. 2), since the intervals among these peaks are as wide as 100 nm, the next issue is creating them with higher density. Here, we adopt a photonic superlattice structure. We first consider the structure shown in Fig. 4(a) as a reference (the reference structure) with a lattice constant of a. This structure can be expressed as Fig. 4(b) in the reciprocal lattice space, where a square lattice structure appears with a lattice constant of 2π/a. The schematic of its band diagram is shown in Fig. 4(c). Next we consider the photonic superlattice structure shown in Fig. 4(d), where multiple lattice points (2 × 2 periods) are included in the period while maintaining the periodicity of the reference structure. This structure can be expressed as Fig. 4(e) in the reciprocal lattice space, where additional reciprocal lattice points appear. The size of the fundamental Brillouin zone is reduced, and the band diagram becomes Fig. 4(e), where the photonic bands are folded in the Γ point directions, and the number of the Γ point photonic band-edge modes increased. Therefore, optical absorption enhancements are expected on more wavelengths.

 

Fig. 4 (a) Real space image of PC (reference structure) with a lattice constant of a. (b) Higher order modes for thickness direction in devices discussed in this paper. (b) Expression of reference PC structure (shown in Fig. 4(a)) in the reciprocal lattice space, where a square lattice structure appears with a lattice constant of 2π/a. (c) Schematic of band diagram for structure shown in Fig. 4(a). (d) Real space image of photonic superlattice structure, where multiple lattice points (2 × 2 periods) are included in the period while maintaining periodicity of reference structure. (e) Expression of photonic superlattice structure (shown in Fig. 4(d)) in reciprocal lattice space, where additional reciprocal lattice points appear compared with Fig. 4(b). (f) Schematic of band diagram for structure shown in Fig. 4(d). Since the fundamental Brillouin zone is reduced, photonic bands are folded in Γ point directions, and the Γ point photonic band-edge modes increased.

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We calculated the optical absorption in the photonic superlattice structure using 3D FDTD methods. The structure for this calculation (Fig. 5(a)) consists of a 2 × 2 period superlattice of one circle with a radius of 0.55 a and three circles with radii of 0.335 a. This structure’s filling factor is equivalent to the reference structure. Other than the photonic crystal structure, the parameters are the same as those shown in Fig. 1(a). The shapes of the PC structures on the glass substrate side and the metal side are changed simultaneously. The calculated absorption spectrum for this structure is shown in Fig. 5(b) by a solid blue line, and the spectrum for the structure with no-PC is shown by a dotted line. The number of absorption enhancement peaks increases by introducing a superlattice structure while maintaining the original absorption peak characteristics in the fundamental structure, which enhance the absorption for a wide wavelength range.

 

Fig. 5 (a) Schematic image of PC structure for this calculation, which consists of a 2 × 2 period superlattice. (b) Calculated optical absorption spectrum of structure shown in Fig. 4(a) by 3D FDTD method. (c) Schematic image of PC structure for this calculation, which consists of a 4 × 4 period superlattice. (d) Calculated optical absorption spectrum of structure shown in Fig. 4(c) by 3D FDTD method.

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We also investigated a larger superlattice structure with 4 × 4 periods. The fundamental Brilloun zone size was reduced further, and more bands were folded into the Γ point directions. Thus, further enhancement of the number of optical absorption peaks is expected. We considered the structure shown in Fig. 5(c) and carried out FDTD calculations. The results are shown in Fig. 5(d); the number of peaks increased, and absorption enhancement was realized. We also investigated the absorption for the incline angle incidences for the superlattice structure with 4 × 4 periods shown in Fig. 5(c). We calculated the absorption spectra for various angles for both the Γ-X and Γ-X directions and both polarizations. Figure 6 shows the summarized average optical absorption for various angle incidents in a wavelength range from 500 to 1000 nm weighted by the solar spectrum (AM1.5), defined as Eq. (1). This result indicates that the averaged optical absorption does not have strong dependence on the incident angles and the directions.

 

Fig. 6 Average optical absorption for various angle incidents for both Γ-X and Γ-X directions and both polarizations in wavelength range from 500 to 1000 nm weighted by solar spectrum (AM1.5), defined as Eq. (1), for superlattice structure with 4 × 4 periods shown in Fig. 5(c).

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We calculated and summarized the average optical absorption for the normal incidence in the wavelength range from 500 to 1000 nm weighted by the solar spectrum (AM1.5) in Fig. 7 for the structure in this paper. Introducing the photonic superlattice structure clearly enhanced the optical absorptions, and the averaged absorption for a superlattice with 4 × 4 periods is almost twice as large as that with no-PC. These results clearly show the effectiveness of PC and its superlattice structures. In addition, we calculated the optical absorption for the Lambertian textured structure (4n² curve) [3] with a µc-Si thickness of 400 nm, and the result is included in Fig. 7. Since the optical absorption in our superlattice structure with 4 × 4 periods exceeds the 4n² curve, this structure is expected to provide better absorption than textured structures.

 

Fig. 7 Average optical absorption in wavelength range from 500 to 1000 nm weighted by solar spectrum (AM1.5), defined as Eq. (1), for this paper’s structure. Dashed red line indicates average optical absorption for Lambertian textured structures.

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4. Conclusion

We investigated optical absorption enhancement by photonic crystals in µc-Si-based photovoltaic devices that were as thin as 400 nm and realized it on the photonic band-edge wavelength by comparisons between the absorption spectrum and the band structure. Enhancement occurs on multiple wavelengths due to the higher order modes for the vertical direction. We also investigated the structure with photonic superlattices and further increased the number of absorption peaks due to the increase of band-edges. The average optical absorption weighted by the solar spectrum was enhanced from 33% with no-PC to 58% with a 4 × 4 period superlattice PC, and the value for the 4 × 4 period superlattice PC exceeds the Lambertian textured structure.