1. Introduction

A Light management in photovoltaic cells is of great importance because it allows for increased efficiency and reduced materials cost [1–8]. Texturing of solar cell surfaces allows for absorption enhancement owing to the ability of incident light rays to couple to modes that are totally internally reflected within the cell. In research so far, the surface texture in crystalline Si (c-Si) solar cells has been formed by a wet chemical process utilizing the anisotropic etching rate of c-Si [9], and the dimensions of the surface texture and cell thickness are much larger than the wavelength of the photons. In the ray-optics regime, the maximum enhancement of the optical path length in a weakly absorbing medium is 4n² times the single pass absorption, where n is the refractive index of the material [10]. However, this limit only holds when the thickness of the solar cell is much greater than the wavelength of light.

In recent years, the problem of light trapping in the subwavelength regime has received renewed interest because it enables simultaneous improvements in optical absorption and photocarrier collection [1–8, 11–13]. With the reduced optical thickness of the absorber material, electromagnetic phenomena such as propagating surface plasmons, nano-optic cavities, and photonic crystals have been pursued to enhance the absorption [2, 4, 14–19]. The spatial distribution of the electromagnetic field plays a role in determining the optical absorption efficiency and carrier generation rates: near-field optics is critical for light-trapping conditions to be achieved in low-dimensional structures [16]. In addition, enhanced optical absorption beyond the 4n² limit has been theoretically predicted for designed surface textures in the subwavelength regime [20].

Although there is a wealth of theoretical work, there have been few experimental demonstrations of photonic nanostructure applications. To realize such optical enhancement in practical solar devices, large-scale photonic nanostructures need to be formed without lithographic techniques. Various techniques have been investigated in an attempt to fabricate micro- or nanoscale textures [12], but most are limited to a relatively small spatial area and are not practical for large-scale implementation. We recently proposed one way of realizing large-scale subwavelength photonic structures based on a wet chemical process of these self-organized nanostructures [21, 22]. With an insertion of photonic nanostructures based on vertically aligned QDs into the c-Si solar cells, the power conversion efficiency was found to increase [21]. In such proposed solar cells, incorporated Ge dots exhibit an increase in absorption of low-energy photons below the band gap energy of Si-based solar cells [23–25]. However, the impact of the photonic nanostructures to enhanced power conversion is still not well understood.

In this paper, we report the investigation of the optical properties of surface photonic nanostructures fabricated by a wet etching technique with QD crystallizations. By using photoluminescence excitation (PLE) spectroscopy, we demonstrate enhanced carrier generation as a result of the photonic nanostructures. Simulations using the finite-difference time domain (FDTD) method of the spatial distribution of the electric field reveal that the photonic structure with a subwavelength size can enhance the electric-field density close to the incident surface, which is available for achieving enhanced photocarrier generation in QDs.

2. Fabrication and characterization of photonic nanostructures

We fabricated the surface photonic nanostructures using selective wet etching with HF/HNO₃ and KOH solution without the use of any mask patterns [21, 22]. QDs consisting of 50 layers of Ge with Si spacer layers were grown on Si (100) substrates by a gas source molecular beam epitaxy system [26]. The Ge QD layers with a coverage of 8 monolayers (MLs) were grown in the Stranski-Krastanov mode and separated by 5-nm Si spacer layers. By wet etching the vertically aligned QDs as illustrated in Fig. 1(a) [27], photonic nanostructures were formed on the top of the QD multi-stacked layers because the etching rate depends on the strain and Ge composition [22, 28]. The wet etching with HF/HNO₃ forms the dip photonic structures on the Ge QDs due to larger wet etching rate of Ge QDs and strained Si [22] while the wet etching with KOH forms the convex photonic structures due to lower etching rate of Ge QDs [29]. The shape of the photonic nanostructures was observed using atomic force microscopy. Figure 1(b) shows top views of the samples formed by HF/HNO₃ and KOH, in which dips and convex structures are formed, respectively. In the horizontal direction, the QDs are not ordered but randomly distributed.

 

Fig. 1 (a) Schematic illustration of the side view of the surface photonic structures formed by selective wet etching using HF/HNO₃ and KOH. (b) Atomic force microscope images of the photonic structures formed by HF/HNO₃ (left) and KOH (right) etching. Images are ~1 × 1 μm in size. (c) Distribution of the width (left) and depth (right) of the dip formed by HF/HNO₃ etching. (d) Distribution of the width (left) and depth (right) of the convex formed by KOH etching. Error bars show the FWHM of the distributions.

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In the HF/HNO₃-etched samples [Fig. 1(c)], the dip depth and width increase monotonically with increasing wet etching time up to 30 s. Note that the inhomogeneous size distribution of the dip depth also increased with increasing etching time. In contrast, the KOH-etched samples [Fig. 1(d)] show that the convex height increased but then dropped as the etching time was increased. The convex width remained relatively constant even though the width distribution was large. From these results, we found that while samples etched with KOH had structures with a width that was always larger than the height, the depth of the structures in the samples etched with HF/HNO₃ were larger than the width, meaning that the photonic nanostructures fabricated by HF/HNO₃ have surface textures with a larger roughness than those in the samples formed by KOH.

3. Fundamental optical properties

Figure 2 shows the fundamental optical spectra of the photonic structures formed with HF/HNO₃ and KOH etching, respectively. For reflection and transmission spectra measurements, the integrated sphere was use to collect the diffused light scattering. In the HF/HNO₃-etched sample, the optical extinction in the near-infrared region increases significantly with increasing etching time, and there is also a reduction in the transmitted component, indicating that the optical extinction is enhanced owing to light trapping, which is probably related to the larger roughness. In the reflection spectra, even though the reflection is not as low as that in c-Si with surface texture [9] or with an antireflection coating using the graded index method [30], the reflection in the sample with a longer etching time is reduced to around 0.2. Note that at longer wavelengths (>950 nm) the reflection increases because the extinction decreases and the reflection from the rear surface increases with increasing wavelength. For comparison, in the KOH-etched sample, even though there is a reduction in the reflection component, the extinction component exhibits a small change at longer wavelength. The insets in Fig. 2 show the extinction at 1100 nm as a function of the etching time and reveal that the extinction increases with increasing etching time. These results indicate that enhanced optical extinction in the near-infrared region does not primarily originate from reduced reflection at the incident surface but from light trapping due to the surface photonic nanostructures, implying enhanced photocarrier generation in the photonic nanostructures.

 

Fig. 2 Transmission, reflection, and extinction spectra of photonic structures formed by (a) HF/HNO₃ and (b) KOH etching. Inset: Extinction at 1100 nm for different etching times.

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4. Photoluminescence excitation spectroscopy

To demonstrate enhanced photocarrier generation owing to the insertion of photonic nanostructures, we performed PLE spectroscopy over a range of 850–1200 nm. We can expect to eliminate the influence of the extraction efficiency of PL signals in the PLE measurements, in which the PL detection efficiency is independent of the excitation wavelength and the PLE signal reflects the optical absorption efficiency. For PLE measurements, wavelength-tunable picosecond laser pulses, obtained from an optical parametric oscillator system based on a Ti:sapphire laser, were used as the excitation source. The samples are attached to the cold finger in the cryostat using silver pastes. The sample temperature was kept at 20 K during PLE measurements. The emitted light was collected without using integrated spheres and by using the optical lens with a 100-mm focal length and 25-mm diameter. The PL spectra were recorded by InGaAs array detectors.

From the PL intensity of the Ge QDs, we can evaluate the optical absorption of the Ge QDs and c-Si close to the surface because the Ge QDs are positioned at a distance from the surface of less than ~250 nm. Note that photocarriers generated close to the Ge QDs are collected by the Ge QDs and result in PL signals. Figure 3(a) shows typical PL and PLE spectra of the Ge/Si QDs. A broad PL spectrum appeared at ~1500–1600 nm, and we note that the PL intensity and spectral shape depend on the excitation light intensity. We observed the same power-law dependence of the PL intensity as a function of the excitation intensity that has been reported in type-II QDs [31]. We used the spectrally integrated PL intensity at 1500–1550 nm for the following PLE measurements, in which the intensity reflects the carrier generation rate under different photoexcitation wavelengths. In PLE spectra, PL intensity was normalized by the excitation intensity. A strong PLE signal appeared at a wavelength of <1000 nm, indicating that the photocarriers generated in the c-Si close to the surface are collected by the Ge QDs. A part of non-systematic large changes in the PLE signals may be caused by some spatial inhomogenuity of the samples, as we have seen in AFM images in Figs. 1, because the ambiguity of the PL signal in our experimental setup is less than 30% even without using integrated spheres.

 

Fig. 3 (a) PL and PLE spectra of the Ge/Si QDs without etching measured at 20 K. Inset: Schematic of the PLE measurements. Normalized PL intensity of Ge/Si QDs in the samples etched for different etching times with (b) HF/HNO₃ and (c) KOH. Excitation wavelength dependence of the normalized PL intensity of Ge/Si QDs in the sample etched with (d) HNO₃ and (e) KOH. Curves show the results for different optical thickness d = 20 (solid), 40 (dotted), and 60 nm (broken), calculated using Eq. (1).

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Figures 3(b) and 3(c) show the normalized PL intensity as a function of the etching time in the samples formed by HF/HNO₃ and KOH, respectively. The PL intensities were normalized by that of a nonetched sample. We found that with increasing etching time, the PL intensity increases by approximately twice that in the nonetched samples: in the sample etched with HF/HNO₃ for 30 s, more than twice the number of photocarriers are generated. This enhancement cannot be explained simply by a reduction in the reflection at the front surface because the intensity of the incident light increases by 20%. In addition, the modification of the extraction efficiency of the PL is also too small to explain the enhancement because the PL intensity under short-wavelength excitation conditions (~850 nm) remains almost unchanged or exhibits only a very small change, as discussed later. These results demonstrate that the optical absorbance near the surface is enhanced by the presence of the photonic surface nanostructures.

Figures 3(d) and 3(e) show the increase in the normalized PL intensity with increasing photoexcitation wavelength, which indicates that the enhancement primarily originates from the enhancement of the optical absorption efficiency rather than the photoluminescence efficiency. Note that in the latter case, the enhancement of the PL intensity would be independent of the photoexcitation wavelength. The magnitude of the enhanced PL intensity is described as

5. Electromagnetic wave simulation

To understand the impact of the photonic nanostructure on the optical properties, the electric field distributions across the photonic nanostructures were investigated using FDTD simulations [33]. Since we are interested in a qualitative understanding of the light trapping effects, a two-dimensional rather than three-dimensional analysis was adopted to limit the complexities of the simulation. We use dips, as shown in Fig. 4(a), to model the photonic nanostructure formed by HF/HNO₃. For simplicity, a photonic structure without Ge QDs was used for the calculation because of the small refractive index difference between Si and Ge. Figure 4(a) shows a schematic illustration of the photonic nanostructure used in the simulation, in which the wavelength, corrugation period, and the maximum dip depth are set at 1000 nm, 400 nm, and 200 nm, respectively. We used thin Si substrate with a ~2-μm thickness for simplicity. The rear side of the Si substrate is covered with perfect electric conductor (PEC).

 

Fig. 4 (a) Schematic illustration of the photonic nanostructure used in the simulation. (b) Dip depth dependence of the electric-field density at a 1000 nm wavelength (TE and TM polarization). (c) Typical electric-field distribution for the photonic structures with a 200 nm depth. The calculation was performed for the sample without PEC reflector at the rear surface.

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Figure 4(b) shows the time- and spatial-averaged electric-field density, |E|², in the Si substrate at a range between 600 and 1100 nm from the surface, as a function of hole depths, which was changed by tuning the curvature of the holes. The electric-field density was normalized by that around the zero depth. The electric-field density is enhanced superlinearly by increasing the dip depth. The electric-field density for the 200-nm-deep photonic structures increases by a factor of more than two, for both the transverse magnetic (TM) and transverse electric (TE) polarizations compared with the Si substrate without photonic structure. We also found that the lateral spatial modulation of the electromagnetic wave, as shown in Fig. 4(c), appeared even in the subwavelength sized photonic nanostructures. Therefore, we concluded that the photonic nanostructures with a subwavelength size would be available for enhanced photocarrier generation.

Finally, we discuss the optimum design of having photonic nanostructures aligned with the QDs for further enhanced carrier generation. From Fig. 4(b), we found that the electric-field density would increase superlinearly with increasing dip depth. This calculation results indicate that enhanced depth in the photonic nanostructures is a promising way for an increase in the optical absorption. This approach may be analogous to nanowire solar cells [3, 7, 8]. In the photonic nanostructures fabricated by using the wet chemical process with self-organized nanostructures, we have obtained strong light trapping, which results in the enhanced electric field density by a factor of more than two at 1000 nm wavelength. Therefore, we can expect the designed photonic nanostructure formed by vertically aligned QDs to exhibit a strong light trapping effect, leading to enhanced optical absorption particularly in near-infrared region. Further optimizations of photonic nanostructure would lead to the enhanced current density in actual solar cell devices, which also contributes to an increase in open-circuit voltage. Furthermore, the enhanced optical absorption in the near-infrared region would be benefit to thinner c-Si solar cells, which fits to a promising direction of c-Si solar cell development.

6. Conclusions

We have demonstrated enhanced photocarrier generation using photonic nanostructures formed from vertically aligned wet-etched QDs. The surface photonic nanostructures exhibit both reduced reflection and enhanced optical absorption. The FDTD calculation indicates that the photonic nanostructure with a subwavelength size would be available to light trapping for efficient photocarrier generation in solar cells.