Light absorption by metal nanoparticle (MNP) and quantum dot (QD) coated nanostructures is theoretically investigated for crystalline silicon (Si) solar cells. Despite light trapping by bare Si nanostructures, the near infrared region (NIR) of the solar spectrum remains unharvested owing to the indirect bandgap (1.1 eV) and low absorption coefficient of Si beyond visible wavelengths. In this work, periodic Si nanostructures, in the form of vertical nanowires (NWs), nanopyramids, and flat-topped nanocones, have been modeled, with their sidewalls decorated with spherical gold (Au) NPs. MNPs scatter light into neighboring Si and introduce localized plasmonic effects, thereby, offering strong broadband absorption and high conversion efficiency. Finite-difference time-domain (FDTD) analysis shows enhanced absorption beyond visible wavelengths, in the presence of Au NPs, for varying NP size and nanostructure periodicity. For 700 nm < λ < 1600 nm, the average absorption by Au NP coated Si nanopyramids and flat-topped nanocones is 5× higher than their bare counterparts. Moreover, Si QD/Si NW hybrid structures display better absorption characteristics than the Au NP/Si NW combination. The findings can be used to design and optimize highly efficient Si solar cells that combine light trapping nanostructures with broader, size tunable absorption profiles of plasmonic NPs and QDs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Crystalline silicon (Si) is the primary material of choice for commercial solar cells due to its high abundance, low cost, non-toxic nature, and well-established processing techniques [1,2]. However, Si, having a high refractive index (n = 3.52 at λ = 1200 nm and T = 293 K), suffers from major reflection losses . Texturing has been known to improve Si solar cell performance by employing sub-wavelength nanostructures to reduce front-surface reflection and trap weakly absorbed photons [4–8]. Light trapping, in these nanostructures, is achieved by increasing the optical path length through scattering and multiple internal reflections, over a large angular range, as the incident light bounces back and forth between neighboring nanostructures. The maximum path length enhancement for a randomly textured surface is given by the Lambertian limit , that amounts to 4n2, with n being the refractive index of Si. By tailoring the shape and structural parameters (diameter, pitch, height etc.) of the nanostructures and implementing more efficient light trapping strategies, Si solar cells could be made to operate close to the Lambertian limit or even overcome it . Silicon nanostructures of various geometrical shapes have been explored for enhanced light trapping and absorption [11–13]. However, increasing light absorption over a broad range of the solar spectrum remains a challenge because Si, with its indirect band gap (1.1 eV), suffers from low absorption coefficient at wavelengths beyond the visible. In fact, the absorption coefficient of Si drops below 1000 cm−1 for wavelengths above 800 nm, thereby, reducing the efficiency of the solar cell device [14,15]. Enhancing light absorption throughout the entire solar spectrum, in addition to reducing reflection losses, is therefore critical in achieving high conversion efficiency in Si solar cells.
Plasmonic effects from MNPs offer a potential solution to extend and enhance photon absorption over a wide range of wavelengths for photovoltaic applications [16,17]. Recently, several studies [18–20] have reported various designs of plasmonic Si solar cells with excellent light trapping and broadband absorption capabilities that lead to high power conversion efficiency (PCE). Electromagnetic radiation, incident on a metal surface, causes the delocalized conduction band electrons to oscillate in coherence, resulting in surface waves, known as surface plasmons. The surface plasmons propagate at the interface of the metal and the surrounding dielectric medium. For MNPs, the resulting electromagnetic wave is strongly confined around the MNPs, adding to the incident field, and giving rise to near-field enhancements through localized surface plasmon resonance (LSPR). Plasmonic enhancements can also be achieved through far-field scattering, where the MNPs act as sub-wavelength scattering elements, enabling multiple scattering events, and increasing the optical path length of incident photons in the absorbing medium. In addition, plasmonic effects can generate free electron-hole pairs that are either directly injected into neighboring Si or may transfer their energy via resonant energy transfer process [21,22]. The optical properties and the plasmonic enhancements provided by the MNP/nanostructure hybrid setup can be precisely tuned by controlling the size, shape, distribution, and dielectric environment of the MNP. Decorating the Si nanostructures with MNPs can combine the benefits of light trapping and anti-reflection properties of the nanostructures with tunable, plasmon enhanced, broader absorption spectrum of the MNPs . Simulations by Zhou et al.  demonstrated enhanced absorption characteristics in the near-infrared (NIR) region for vertical Si nanowires (NWs) coated with gold (Au) and silver (Ag) NPs. Zhang et al.  fabricated Si micropillar array, coated with copper (Cu) NPs, that yielded higher short-circuit current density (Jsc) than the Si micropillars alone. Recently, Banerjee et al.  proposed a hybrid organic–inorganic photovoltaic device with Ag NP decorated Si NW array, where plasmonic enhancements gave 52% higher PCE.
Apart from MNPs, semiconducting NPs or quantum dots (QDs), offering size tunable bandgaps and multiple exciton generation (MEG), are also being considered as promising candidates to boost the efficiency of next generation solar cells . Extended hot carrier lifetimes and MEG in QDs enable photons, with energy higher than the semiconductor band gap, to be absorbed. These photons would otherwise be wasted as heat through phonon emission. Extended absorption in the NIR range can be obtained by conveniently tuning the QD size. It is well established that larger QDs yield smaller bandgaps . The use of zero dimensional QDs, with discrete energy levels, also offers additional photon absorption through an intermediate band, within the bandgap of the absorbing material, leading to higher photocurrents. Intermediate band transitions can absorb the unharvested photons and potentially exceed the Shockley-Queisser limit, reaching a theoretical efficiency of 63% [29,30]. The optimal size and bandgap of the QDs, for best performance, depend on a multitude of factors that are governed by the architecture of the solar cell devices. For example, QDs with different sizes can be stacked into multi-layers to construct tandem (two junctions) or multijunction solar cells, that enable near-complete absorption of the solar spectrum. Hybrid nanostructures, with QDs grown on the sidewalls of Si NWs, have also been proposed to leverage the advantages of light trapping and broadband optical absorption. Compared to bare Si NWs, Jung et al.  demonstrated ∼13% enhancement in PCE for the ZnSe QD/ Si NW combination, while, Ji et al. , Cao et al.  and Dutta et. al  implemented different Si QD/ Si NW heterostructures with excellent optical performance.
Despite many reported results on MNP and QD coated Si nanostructures, the efforts have mostly been limited to vertically aligned NW or nanopillar arrays. In this work, we used finite-difference time-domain (FDTD) simulations to study light absorption characteristics of MNP coated Si nanostructures with different geometries. Three types of nanostructures have been considered in this study: vertical NWs , nanopyramids [4,36] and flat-topped nanocones , based on their excellent light trapping properties and well-established fabrication process. Although Joseph et al.  and Khan et al.  have demonstrated superior light trapping by optimized parabolic nanostructures, the structures, chosen for this study, are more commonly found in literatures that deal with light trapping surface textures. A two-dimensional (2D) scheme of Au NPs, coated on the sidewalls of the Si nanostructures, has been carefully modeled. The absorption properties of the Au NP coated Si nanostructures are then investigated, theoretically, with respect to the periodicity of the nanostructures and the size of the Au NPs. Finally, the absorption enhancement in Si QD/Si NW hybrid structure is explored, and its performance is compared with the Au NP/Si NW counterpart.
2. Simulation setup
Figures 1(a)-(c) show the schematics of Au NP coated Si nanostructures, patterned on top of a 2 µm thick Si slab. Au NPs are commonly preferred in plasmonic studies owing to their long-term stability and strong plasmonic effects. The Au NP coating is such that it forms a monolayer film surrounding the entire nanostructure, where the thickness of the film equals the diameter (dAu) of the Au NP. The hybrid MNP/nanostructure setups are illuminated by a plane wave source from the top, at normal incidence. The electric field of the incident light is TM polarized along the x direction and spans a wide range of wavelengths from 300 nm to 1600 nm. Localized surface plasmons are generated around the spherical Au NPs, with plasmonic oscillations coupling light into the nanostructures. For each structure, the absorption spectrum is obtained using finite-difference time-domain (FDTD) simulations through the Lumerical software package.
The nanostructures are placed in an array with square symmetry. The height (h) and period (p) of the nanostructures are decided based on the optimized light trapping structures reported in earlier studies [35–37], [40,41]. A 2D simulation scheme is employed in this study, which simplifies the simulation process and reduces computation time without considerable loss in accuracy when compared to the more realistic 3D models . A unit cell of Au NP coated Si NW, used in the FDTD simulation, is shown in Fig. 1(d). Periodic boundary conditions are applied in the x direction to replicate the array structures. Perfectly matched layer (PML) is used along the z propagation direction to absorb any reflected and transmitted fields. Light absorption by the nanostructures is studied by varying dAu and p. Refractive index (n) and extinction coefficient (k) values, for Si and Au, are obtained from Palik  and Johnson et al. , respectively. The dielectric functions are modeled using a combination of Drude and Lorentz models , which convert discrete values into continuous functions over the desired wavelength range. Total absorption depends on both reflection and transmission. Absorption spectrum, A(λ), is extracted using the relation A(λ) = 1-T(λ)-R(λ), where, λ is the wavelength of the incident light and T(λ) and R(λ) denote the corresponding transmittance and reflectance spectra, respectively, as obtained from the FDTD simulations.
To evaluate the performance of the MNP coated nanostructures, their ultimate efficiencies (η) are calculated using the following equation, as described by Zhou et al. :
3. Results and discussion
3.1 Si nanostructures coated with Au NPs
The absorption spectra of the Si nanostructures, with and without the Au NPs, are shown in Figs. 2(a)-(c), in comparison with the absorption from a 2 µm thick bare Si slab. Here, h and p for all nanostructures are taken as 500 nm and 160 nm, respectively, while dAu is fixed at 20 nm. As illustrated in Figs. 1(a)-(d), the diameter of the nanowire (dNW), the base width of the nanopyramid (bNPYR) and the flat-topped nanocone (Db), are all set at 120 nm. The top diameter (Dt) of the flat-topped nanocone is equal to half the bottom diameter (Db). The Lambertian limit (black curve), for the corresponding equivalent Si film thickness, is also calculated  and plotted in Figs. 2(a)-(c). For the bare Si slab (blue curves), Fabry-Perot modes, arising from the resonances between the top and bottom surfaces of the Si thin film, give rise to periodic oscillations between λ = 500 nm and 800 nm. In general, even without the use of Au NPs, light trapping nanostructures (red curves) alone can increase absorption when compared to the bare Si slab (blue curves). However, despite the light-trapping properties, absorption by the bare nanostructures (red curves) falls sharply when λ > 600 nm, owing to the inherently low absorption coefficient of Si at longer wavelengths. Decorating the nanostructures with Au NPs significantly improves absorption and extends the absorption spectrum (green curves) beyond the visible range. For, 300 nm < λ < 700 nm, Si dominates the absorption and therefore, there is little difference in the absorption profiles between bare Si nanostructures and their Au NP coated counterparts. Au NP/Si NW and Au NP/Si flat-topped nanocone structures experience short-wavelength absorption losses , as observed in Figs. 2(a) and (c). These losses are attributed to weak forward scattering, whereby, most of the incident light is reflected back into the air. When λ > 700 nm, LSPR from the Au NPs couples more incident light into the active Si region. Typically, LSPR for Au NPs occurs when λ∼1000 nm, where transmission and reflection are minimum. Incident light is, therefore, either coupled or forward scattered into neighboring Si. When λ > 1000 nm, the absorption from the Au NP coated nanostructures exceeds the Lambertian limit. In fact, several peaks are observed in the long wavelength regions of the absorption spectra that correspond to the LSPR modes, excited at different wavelengths. The confinement of the electric field at multiple wavelengths results in enhanced broadband absorption. Beyond λ = 1127 nm, corresponding to the bandgap of Si, absorption decreases as most of the incident light is transmitted through air in between the nanostructures.
Although Si NWs enable light trapping, they also suffer from increased surface recombination losses that can degrade device performance. Tapered nanostructures, in the form of pyramids or flat-topped cones, have been considered as promising alternatives to vertically aligned NWs for textured Si solar cells. It is clear from Figs. 2(a)-(c) that, in comparison to their NW counterpart, Au NP coated Si nanopyramid and flat-topped nanocone arrays demonstrate better light trapping characteristics, contributing to stronger absorption over a broader range of the solar spectrum. Enhanced broadband absorption in tapered nanostructures has been attributed to reduced reflection from smaller tip and reduced transmission from the broader base. Moreover, as the nanostructures become tapered, the diameter increases with depth and offers a gradual change in refractive index between air and Si. This graded morphology helps to reduce the refractive index mismatch between air and bulk Si, leading to reduced reflection. In contrast, vertical and uniform Si NWs, without any tapering, act more like a single step converter with a fixed index value, offering mismatch in refractive indexes. The average absorption, between λ = 300 nm and 1600 nm, for both bare and Au NP coated nanostructures, is illustrated in Fig. 3(a). Within the wavelength range of 300-1600 nm, the average absorption by Au NP/Si NW combination is 46.21%, while that of the bare Si NW is 55.11%. This behavior can be explained in terms of the short-wavelength absorption losses in NWs, as described earlier. For 300 nm < λ < 1600 nm, the average absorptions for Au NP coated Si nanopyramids and flat-topped nanocones are 80.64% and 75.04%, respectively, compared to 67.26% and 68.76%, for their bare counterparts. The contribution of plasmonic enhancements, in the long wavelength regions, are shown in the inset of Fig. 3(a). The average absorption between λ = 700 nm and 1600 nm, are 22.49%, 43.46% and 46.46% for Au NP/Si NW, Au NP/Si nanopyramid, and Au NP/Si flat- topped nanocone structures, respectively. The corresponding values for the bare nanostructures are 7.84%, 8.98% and 9.46%, respectively. For Si nanopyramids and flat-topped nanocones, there is clearly 5× more absorption in presence of Au NPs for 700 nm < λ < 1600 nm. The ultimate efficiency values, as plotted in Fig. 3(b), are calculated from Eq. (1) for 300 nm < λ < 1600 nm.
The electric field intensity profiles of the nanostructures, with and without the Au NPs, are investigated for three representative wavelengths, 500 nm, 800 nm, and 1100 nm, as displayed in Fig. 4. The electric field profiles clearly illustrate light distribution in and around the NPs and into the surrounding Si. At shorter wavelengths, like λ = 500 nm, there is weak forward scattering and incident light is mostly reflected back into air by the Au NPs. However, without the NPs, the reflection is suppressed by the nanostructures, leading to enhanced light trapping. This is most obvious for the Si NWs, where the absorption in presence of nanoparticles is reduced for shorter wavelengths. Si nanopyramids, in general, show superior light trapping and absorption enhancements when compared to NWs and flat-topped nanocones. At longer wavelengths, near-field enhancements arise from the excitation of the localized plasmons around Au NPs which increase the scattering cross-sections of the Au NPs. A larger scattering cross-section enables more light, over a wider spectrum, to be scattered back from the Au NP and coupled into neighboring Si, thereby, boosting PCE of the solar cell device. Therefore, at λ = 800 nm and 1100 nm, electric field penetrates the Si, as clearly visible in (a6-c6) and (a9-c9) of Fig. 4. Moreover, variable diameter profile of nanopyramid and flat-topped nanocone provides a graded index from air to Si, and results in stronger electric fields, which penetrate deep and distribute around the base, giving rise to stronger resonance of absorbed light in these tapered structures.
3.2 Effect of Au NP size
The influence of NP size on the optical properties of the nanostructures has been investigated. For all nanostructures, h = 500 nm, p = 160 nm, and Au NPs with varying diameters (dAu = 20, 30, 40 and 50 nm) have been considered. The resulting absorption profiles are shown in Figs. 5(a)-(c), while the average absorption for 700 nm < λ < 1600 nm is displayed in Fig. 5(d). In general, the average absorption by the Si nanostructures, in the long wavelength region, shows a decreasing trend when the size of the Au NP exceeds 30 nm.
Depending on their sizes, NPs can contribute to near-field enhancements through LSPR effect or they can act as light scattering centers, increasing the optical path length of incident light through multiple scattering events. For particles, smaller than the wavelength of the incident light, the scattering (Csca) and absorption (Cabs) cross-sections are given by :47] demonstrated that absorption dominates for small particles, having diameters in the range of 5-20 nm. The small NPs act as sub-wavelength antennas due to LSPR excitation and couple the plasmonic near-fields to the adjacent Si. Larger MNPs (> 50 nm), having large scattering cross-sections at LSPR, can act as sub-wavelength scattering elements, directing more of the incident light into the surrounding Si. However, the resulting absorption enhancements caused by the larger MNPs are accompanied by significant Ohmic losses in the metal itself, making near field effects impractical. Therefore, as discussed by Enrichi et al ., plasmonic NPs, which are embedded into or in direct contact with the semiconductor active layer, are normally limited to 10-20 nm in diameter. This is in agreement with the study by Zhou et al.  where the size of the Au NPs, incorporated into Si NWs, is limited to 30 nm. Also, Zhang et al.  used Si micropillars coated with Cu NPs that have a diameter of 26 nm.
3.3 Effect of nanostructure periodicity
Periodicity of the nanostructures play a crucial role in their anti-reflection properties. Figures 6(a)-(c) illustrate the absorption spectra of the nanostructures decorated with Au NPs, with dAu = 20 nm. The periodicity of the Au NP coated nanostructures is varied as, p = 100, 160, 280 and 400 nm, with h = 500 nm. Bare nanostructures, with p = 100 nm, are used as a reference.
Figure 6(d) illustrates the average absorption by bare and Au NP coated nanostructures with different periods, for 700 nm < λ < 1600 nm. With the exception of p = 280 nm, the average absorption in the long wavelength region decreases with increasing periodicity. This could be attributed to multiple strong LSPR peaks, observed between λ = 700 and 1600 nm, for all the nanostructures at p = 280 nm. Typically, light is better coupled to a grating structure when the period of the grating is slightly less than the incident wavelength. If the period is too small, light becomes insensitive to the structural details and suffers from weak diffraction. On the other hand, for periods larger than the wavelength, higher order reflections lead to reduced absorption . Periodicity is also directly related to the filling ratio (f) which is defined as :6(d) are consistent with the study by Hu et al. , which demonstrated that bare Si NW array, with smaller filling ratio, absorbs less light in the longer wavelength region.
3.4 Si NW coated with Si QDs
Silicon QDs absorb light over a wide range of the solar spectrum and are, therefore, being considered for next generation photovoltaics, for high efficiency and low-cost solar cells. Moreover, Si QDs are non-toxic in nature when compared to QDs that contain heavy metal. Typically, quantum confinement of electrons and holes occurs in Si nanocrystals when their sizes are below the exciton Bohr diameter of 8.6 nm . The bandgap in Si QDs can be tuned, from visible to NIR spectral region, simply by varying the diameter (dSiQD) of the QDs, leading to broadband optical absorption. Here, we investigate the wavelength dependent absorption characteristics of Si QD/Si NW heterostructures for different QD sizes. Figure 7(a) shows light absorption by bare Si NW and Si QD/Si NW hybrid for varying diameter of the QDs. Clearly, incorporation of Si QDs increases absorption beyond the visible range, which further enhances with increasing QD size, as displayed in Fig. 7(b), for 700 nm < λ < 1600 nm. Average absorption between λ = 700-1600 nm increases from 42.59% at dSiQD = 2.8 nm to 85.19% at dSiQD = 5.2 nm. Figure 7(c) compares the absorption profiles of Au NP and Si QD coated Si NW array, where dAu = 20 nm, dSiQD = 5.2 nm, h = 500 nm, and p = 280 nm. It is obvious that, beyond the visible range, the Si QDs offer broader and stronger absorption enhancements than the Au NPs. The average absorption, for 300 nm < λ < 1600 nm, is illustrated in Fig. 7(d), revealing 58.10%, 69.67% and 82.27% absorption by bare Si NW, Si NW+ Au NP and Si NW+ Si QD, respectively. In terms of ultimate efficiency, as given by Eq. (1), Si QD coated Si NWs (dSiQD = 5.2 nm, η = 52.89%) are ∼11% more efficient than Au NP coated Si NWs (dAu = 20 nm, η = 41.97%).
To summarize, light absorption by Au NP coated Si nanostructures of various geometries, has been explored using FDTD simulations. Vertical NW, nanopyramid and flat-topped nanocone have been considered and the absorption properties are investigated with respect to Au NP size and nanostructure periodicity. Long wavelength absorptions are significantly enhanced for Au NP coated Si nanostructures, in contrast to bare nanostructures. Near-field plasmonic enhancements and far field scattering from the NPs extend the absorption spectrum to NIR regions. For Si nanopyramid array (h = 500 nm and p = 160 nm) coated with 20 nm Au NPs, an average absorption of 80.64% is achieved for 300 nm < λ <1600 nm. This translates to η = 41.85%, making the nanopyramid texture, a primary choice for plasmon enhanced solar cells. Larger NPs (> 30 nm) show reduced absorption, in the long wavelength region for h = 500 nm and p = 160 nm. Moreover, Ohmic losses in larger MNPs lead to degraded device performance. Hence, when embedded directly into the nanostructures, smaller MNPs are preferred. In terms of periodicity of the nanostructures, for p > 280 nm, absorption between λ = 700 nm and 1600 nm is reduced due to higher order reflection modes. Si QD decorated Si NWs have also been modeled at various QD sizes, below the Bohr exciton diameter. Si NW array (h = 500 nm and p = 280 nm) coated with Si QDs (dSiQD = 5. 2 nm) provides ∼11% higher η than Au NP (dAu = 20 nm) coated Si NWs. However, the choice of Si QDs over Au NPs will depend on the tradeoff between cost, process complexity and desired device performance. Nanostructures, presented here, may require further optimization through experimental studies to combine the inherent benefits of light trapping with enhanced broadband absorption from plasmonic NPs or QDs, in next generation, cost-effective Si solar cells.
The authors thankfully acknowledge the support from Fab Lab DU, at University of Dhaka, for providing the necessary computational resources for this simulation study.
The authors declare no conflicts of interest.
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