Lambertian Limit Research Articles

Lithography‐Free Method to Synthesize Quasiperiodic Silicon Inverted‐Pyramid Arrays: A Broadband Light Trapper for High‐Efficiency Thin Silicon Solar Cells

Thin silicon solar cells can be a low‐cost effective photo‐conversion device, if the device can efficiently absorb the solar spectrum. Herein, a new lithography‐free technique is developed for the fabrication of quasiperiodic silicon inverted‐pyramids arrays (SiIPAs), which show a high‐light‐trapping phenomenon in the ultraviolet–visible—near‐infrared (300–2000 nm). Fabricated SiIPA samples show a significant reduction of reflectance (3%) in the silicon absorption band (300–1000 nm). A unique additional absorption of 33–44% compared to the planar silicon is observed in the sub‐bandgap region of silicon (1100–2000 nm) for these samples. Photocurrent response measurement confirms the generation of additional electron–hole pairs in the sub‐bandgap region of silicon for the SiIPA samples in comparison with planar sample. In these results, the effect of field confinement and the creation of optical resonance modes within these structures, qualitatively supported by numerical simulation, are signified. The estimated short‐circuit current density using the experimental absorption spectrum of SiIPAs is 55.46 mA cm−2, which is far higher than the Lambertian limit of ≈43 mA cm−2. The theoretical efficiency of the solar cell can be achieved up to 35.22%, which surpasses the Shockley–Queisser limit of 33.7%.

Diameter and gap controlled fabrication of periodic SiMW/SiNW arrays: A broadband absorber for high efficiency silicon solar cell

Vertically aligned and periodic silicon micro/nano-wire (SiMW/SiNW) arrays of different diameters were synthesized by combining lithography-free silica particle patterning, reactive ion etching (RIE), and modified metal-assisted chemical etching (MACE) methods. All required silica particles were synthesized, and process parameters were optimized to fabricate sub 50 nm SiNW to large size SiMW with the controlled inter-wire gap. Fabricated SiMW/SiNW array samples show a significant reduction of reflectance (7–9 %) in the silicon absorption band (300 nm–1000 nm). Additional absorption of 25–33 % compared to the planar silicon is observed in the sub-bandgap region of silicon (1100–2000 nm) for these samples, which signifies the effect of field confinement within these structures. The estimated short circuit current density (JSC) using the experimental absorption spectrum of SiMW is 49.96 mA/cm2, which is 16 % higher than the Lambertian limit of ∼43 mA/cm2. This result can lead to the theoretical efficiency of the solar cell up to 28.73 % without the inclusion of the surface passivation effect.

Designing limiting-efficiency BaSi[formula omitted] solar cells by device simulation and computational material screening

A double heterojunction solar cell consisting of a solar absorber and electron/hole transport layers (ETL/HTL) is ideally efficient and can contribute to the exploitation of solar energy. BaSi2 is an attractive solar absorber material possessing a band gap of 1.3 eV and high absorption coefficients. However, finding proper ETL/HTL materials remains challenging. Here, limiting efficiency calculation, device simulation, and computational material screening are combined to design BaSi2 solar cells of near-limiting efficiency (> 28%). The limiting efficiency is calculated considering radiative and trap-assisted Auger recombinations, which shows that the Lambertian limit efficiency (32%) exceeds that of Si cells. Device simulations of double heterojunction BaSi2 cells were performed with different values of band gap, ionization potential, and electron affinity, which yields criteria for band-edge energy levels of the ETL and HTL. Candidate materials for the ETL and HTL are identified from the Materials Project database by three-step screening. The first step screens the materials for band gap, interface reactivity, lattice matching, etc. The second step is a literature survey to exclude air-sensitive or unstable materials under ambient conditions. In the third step, band-edge levels are calculated using density functional theory, and eight ETL and seven HTL candidate materials are identified. This device design method is applicable to any solar absorber material and promotes accelerated solar cell development.

Beyond Lambertian light trapping for large-area silicon solar cells: fabrication methods

Light trapping photonic crystal (PhC) patterns on the surface of Si solar cells provides a novel opportunity to approach the theoretical efficiency limit of 32.3%, for light-to-electrical power conversion with a single junction cell. This is beyond the efficiency limit implied by the Lambertian limit of ray trapping ~ 29%. The interference and slow light effects are harnessed for collecting light even at the long wavelengths near the Si band-gap. We compare two different methods for surface patterning, that can be extended to large area surface patterning: 1) laser direct write and 2) step-&-repeat 5^× reduction projection lithography. Large area throughput limitations of these methods are compared with the established electron beam lithography (EBL) route, which is conventionally utilised but much slower than the presented methods. Spectral characterisation of the PhC light trapping is compared for samples fabricated by different methods. Reflectance of Si etched via laser patterned mask was ~ 7% at visible wavelengths and was comparable with Si patterned via EBL made mask. The later pattern showed a stronger absorbance than the Lambertian limit. (M.-L. Hsieh et al., Sci. Rep. 10, 11857 (2020)).

Photonic crystals for highly efficient silicon single junction solar cells

The maximum achievable silicon single junction solar cell efficiency is limited by intrinsic recombination and by its limited capability of absorbing sun light. For Lambertian light trapping the maximum theoretical solar cell efficiency is around 29.5%. Recently a new approach for light trapping has been proposed for silicon photovoltaics. Highly regular structures with a size in the range of the wavelengths of the incident light act as so-called photonic crystals. Such structures allow wave-interference light trapping beyond the Lambertian limit. Applying these photonic crystals to silicon solar cells can help to reduce the absorber thickness and thus to minimizing the unavoidable intrinsic recombination. From a simulation study, we can conclude that 31.6% is the maximum possible single junction solar cell efficiency for a 15 μm-thin substrate. Furthermore, we present a process flow for the preparation of regular inverted pyramid structure, that acts as photonic crystal. Finally, regular inverted pyramid structures are prepared on polished and shiny-etched, i. e. on surfaces with a certain roughness, substrates. Surface passivation of these structured surfaces shows as good lifetimes as on conventional randomly pyramid textured surface. Excellent total saturation current densities on asymmetric samples of 4 ± 2 fA/cm2 for n-type and of 4.5 ± 2.2 fA/cm2 on p-type substrates are obtained.

Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals

The tantalizing possibility of 31% solar-to-electric power conversion efficiency in thin film crystalline silicon solar cell architectures relies essentially on solar absorption well beyond the Lambertian light trapping limit (Bhattacharya and John in Nat Sci Rep 9:12482, 2019). Up to now, no solar cell architecture has exhibited above-Lambertian solar absorption, integrated over the broad solar spectrum. In this work, we experimentally demonstrate two types of photonic crystal (PhC) solar cells architectures that exceed Lambertian light absorption, integrated over the entire 300–1,200 nm wavelength band. These measurements confirm theoretically predicted wave-interference-based optical resonances associated with long lifetime, slow-light modes and parallel-to-interface refraction. These phenomena are beyond the realm of ray optics. Using two types of 10-μm thick PhC’s, first an Inverted Pyramid PhC with lattice constant a = 2,500 nm and second a Teepee PhC with a = 1,200 nm, we observe solar absorption well beyond the Lambertian limit over λ = 950–1,200 nm. Our absorption measurements correspond to the maximum-achievable-photocurrent-density (MAPD), under AM1.5G illumination at 4-degree incident angle, 41.29 and 41.52 mA/cm2 for the Inverted Pyramid and Teepee PhC, respectively, in agreement with wave-optics, numerical simulations. Both of these values exceed the MAPD (= 39.63 mA/cm2) corresponding to the Lambertian limit for a 10-μm thick silicon for solar absorption over the 300–1,200 nm band.

Design of wave-optical structured substrates for ultra-thin perovskite solar cells

Photonic micro/nano-structures in the wave-optics regime have shown to be a promising strategy for effective broadband light capture in ultra-thin devices, opening a window of opportunity for cheap, efficient, lightweight and flexible photovoltaics (PV). Here we design, from an optical standpoint, a novel industrially-attractive concept where light trapping is obtained by conformably depositing the solar cell materials onto previously-patterned photonic substrates. This solution is applied and optimized for perovskite solar cells (PSCs) with distinct thicknesses of the perovskite absorber - the conventional (500 nm) and ultra-thin (300 nm) in view of enhanced flexibility - yielding photocurrent improvements up to 22.8% in superstrate cell configuration and 24.4% in substrate-type configuration; thereby coming relatively close to the fundamental Lambertian limits. Furthermore, these structures also show an omni-direction optical response for incidence angles up to 70° for all cases, therefore demonstrating the viability of this light trapping method for implementation in flexible PV devices operating under bending. The photonic-enhanced ultra-thin solar cells designed here ultimately support the reduction of material usage in PSC technology, which is especially beneficial to mitigate lead usage, without impacting the device's performance.

Comparison of Light Trapping Limits Derived Using Various Methods for Thin Film GaAs Solar Cells.

The paper discusses and compares the Lambertian limits for light trapping (LT) in GaAs active layer based thin film solar cells as described by different mathematical theories and expressions. The Lambertian limits for thin film GaAs solar cell provide the maximum efficiency that can be achieved through LT structures and also indicate the advantage that these structure can provide for the design of GaAs thin film solar cell structure. The purpose to discuss difference Lambertian limit expressions is to understand and predict, which limiting benchmark value is more suited for nano LT structures based GaAs active material solar cells, considering GaAs material properties. The paper also compares these calculated limiting values with different nano LT structures including photonic crystal structures based designs proposed by the author. The aim is to check how much close a particular proposed structure is to the Lambertian values, so that we can predict that which is more suitable design to get best efficiency out of the single junction GaAs material based structure. The paper discussed the three Lambertian theories including that of Yablonovitch, Green and Schuster.

Photonic crystal light trapping: Beyond 30% conversion efficiency for silicon photovoltaics

The power conversion efficiency of single-junction silicon solar cells has increased only by 1.5% despite extensive efforts over the past two decades. The current world-record efficiencies of silicon solar cells, within the 25%–26.7% range, fall well below the thermodynamic limit of 32.3%. We review the recent progress in photonic crystal light-trapping architectures poised to achieve 28%–31% conversion efficiency in flexible 3–20 μm-thick, single-junction crystalline-silicon solar cells. These photonic crystals utilize wave-interference based light-trapping, enabling solar absorption well beyond the Lambertian limit in the 300–1200 nm wavelength range. Using experimentally feasible doping profiles, carrier lifetimes, surface recombination velocities, and established Auger recombination losses, we review considerations leading to the prediction of 31% efficiency in a 15 μm-thick silicon photonic crystal cell with interdigitated back-contacts. This is beyond the conversion efficiency of any single-material photovoltaic device of any thickness.

Absorption enhancement in hole Interface layer free perovskite solar cells using periodic photonic nanostructures

The study of Hole Interface Layer (HIL) free Perovskite Material (PM) solar cells have shown good potential in the recent years to simplify the PM solar cells design. However, the elimination of HIL suffers from device performance degradation. Herein, the article presents the optical design and optimization study of the 2D periodic photonic nanostructured HIL free PM material active layer based solar cells. Methyl Ammonium Lead Iodide (MAPbI3) is used as a PM material. PM layer is itself designed as a periodic nanostructure, also known as Photonic Crystal (PhC) structures. The article deals with the demonstration of the theoretical optical study and optimization of all the required parameters to design a PhC structure based proposed design having only 100 nm PM active layer thickness. The article also presents the Lambertian limit values for light trapping for MAPbI3 solar cells. The paper deals with the comparison of the proposed design performance with the Lambertian values, bare cell and reference planar HIL free structure of same active layer thickness. The study predicts that the optical performance of the proposed structure based on periodic nanostructures greatly surpasses that of reference structure. There is a comparative enhancement of around 44% in the proposed design as compared to planar reference structure. The absorption enhancement is basically accounted to the better trapping of incident photons, reduction in reflections, improved diffraction capability and index matching due to periodic nanostructures patterning of active layer in the proposed design. The parameters have been optimized and calculated using rigorous coupled wave analysis (RCWA).

Photonic-structured TiO2 for high-efficiency, flexible and stable Perovskite solar cells

Optical solutions are promising for Perovskite solar cell (PSC) technology, not only to increase efficiency, but also to allow thinner absorber layers (higher flexibility) and improve stability. This work optimized the combined anti-reflection and scattering properties of two types of light trapping (LT) structures, based on TiO2 semi-spheroidal geometries with honeycomb periodicity, for application in PSCs with substrate configuration and different perovskite layer thicknesses. Their optically lossless material (TiO2) allows the structures to be patterned in the final processing steps, integrated in the cells’ top n contact, therefore not increasing the surface area of the PV layers and not degrading the electric performance via recombination. Therefore, this strategy circumvents the typical compromise of state-of-the-art LT approaches between optical improvements and electrical deterioration, which is particularly relevant for PSCs since their main recombination is caused by surface defects. When patterned on the cells’ front, the wave-optical micro-features composing the LT structures yield up to 21% and 27% photocurrent enhancement in PSCs with conventional (500 nm thick) and ultra-thin (250 nm) perovskite layers, respectively; which are improvements close to those predicted by theoretical Lambertian limits. In addition, such features are shown to provide an important encapsulation role, preventing the cells’ degradation from UV penetration.

Analysis of Photonic Crystal Diffraction Grating Based Light Trapping Structure for GaAs Solar Cell

The paper presents a design and quantitative analysis for an efficient light-trapping structure (LTS) based on Photonic Crystals (PhC) to enhance the performance of thin-film GaAs solar cells. LTS consists of single planar Anti-Reflection coating (ARC) layer at the top assisted by 2D PhC diffraction grating and Distributed Bragg Reflector (DBR) having alternate dielectric layers at the back of the active layer. The structure has been optically analyzed for various absorption layer thicknesses and compared with Lambertian limits, and it has been shown that with optimization of the design carefully, significant enhancement in the cell efficiency will take place for the presented LTS, especially for the devices with very thin absorption layers (typically less than 1000 nm). Further, it is demonstrated that this efficiency enhancement is attributed to the improvement in photon absorption in the wavelength range for which active layer thickness itself is not sufficient for absorption. According to the simulation analysis, the proposed cell efficiency can be enhanced 3.5 times for a 100 nm cell with LTS, and this enhancement shrinks only to 1.5 times for 1500 nm cell. The analysis has shown that for thin cells, the contribution by the optimized LTS is the main reason behind efficiency enhancement whereas the contribution from ARC remains almost constant. The evaluation of the performance of the proposed structure concerning the angle of incident light and fabrication tolerances has also been done, indicating improved performance. The paper also presents the quantitative and comparative analysis of the proposed design with different compatible designs such as a cell having double layer ARC and a cell having pyramidal ARC with PhC as BR design. Their analysis also predicts that the LTS especially BR are more important for thinner active layer cells and the cell with a pyramidal ARC with PhC outperforms the other designs.

Disordered nanophotonic surfaces for enhanced light collection in semiconductor solar cells

We present a theoretical study of rough photonic surfaces and disordered photonic crystal wire and hole (slab) geometries as a scattering entrance layer to enhance the absorption in thin-film photovoltaic solar cells. One commonly accepted gold standard for scattering enhanced absorption in solar films is given by the Lambertian limit, which results in an optical path length enhancement of 4n2, where n is the refractive index. However, this limit is often an idealized upper limit and hard to realize in practice. Exploiting finite-difference time-domain simulations of realistic rough surfaces, we first explore the limitations and potential practical implementation of this ideal enhancement. A practical rough film, characterized by the RMS height (σRMS) and correlation length (Lx,y) of the random peaks, is numerically optimized for different substrate thicknesses over an optical wavelength range of 400–1100 nm. This optimized surface reflects one practical solution for Lambertian slab thicknesses above 500 nm and wavelengths in the near-UV, but performs worse in the near-IR (∼80%). The physical total height of the optimal rough surfaces is found to be of the order of 2 μm, which contradicts the common assumption that absorption losses within the rough film are negligible. We also investigate photonic crystal wire and slab holes structures with positional and radial disorder, for a fixed height of 1 μm with reflective Ag substrates, considering both GaAs and c-Si semiconductors. We show that the best performing GaAs nanowires give the largest total short-circuit current density (Jsc) of 30  mA/cm2. Relative to the unpatterned slabs of the same height, the greatest photonic crystal enhancements in absorption were seen for c-Si nanoholes and GaAs nanowires (enhancement factors of 1.65 and 1.33, respectively). The inclusion of lattice disorder is shown to increase the absorption enhancement in all photonic crystal structures by 4%–15%, except GaAs nanoholes, which remained within 1% of the ordered structure. Using an analysis of the computed local density of photon states, which is strongly dependent on the complex dielectric constant of the semiconductor, we demonstrate that, due to the higher inherent material losses in GaAs, the useful effects of disorder-induced broadening are minimized in GaAs, compared to c-Si.

Lambertian and photonic light trapping analysis with thickness for GaAs solar cells based on 2D periodic pattern

The study proposes designs using 2D photonic crystal (PhC) structure-based thin film heterojunction gallium arsenide (GaAs) solar cell with a periodic pattern having PhC structure extends from top transparent conducting oxide (TCO) to inside the p-AlGaAs window layer placed just above the active layer of GaAs material in one design and in another PhC structure is etched only in TCO. The work presents the comparative analysis of the proposed structure with Lambertian light trapping limits and the planar cell, taken as reference. The study is also performed for double-layer anti-reflective coating (ARC) structure. The study presents the quantitative analysis of the effect of PhC structure in the performance of the design and how the effect varies with the thickness of absorption layer. It has been found that a considerable increase in efficiency has been achieved, especially for thinner active layers, demonstrating the advantage of a wavelength-scale, PhC-based structures for thin-film solar cells. The results have shown that PhC structure (etched till inside p-AlGaAs)-based solar cell exceeds the efficiency of the double ARC-based structure by more than 18% for 50 nm thin active layer cell. The parameters have been optimised and calculated by means of rigorous coupled wave analysis (RCWA).

Design and Analysis of Light Trapping in Thin Film GaAs Solar Cells Using 2-D Photonic Crystal Structures at Front Surface

This paper proposes a design using a 2-D photonic crystal (PhC) structure-based thin film heterojunction GaAs solar cell with a periodic pattern extending from top transparent conducting oxide to inside the p-AlGaAs window layer placed just above the active layer of GaAs material. This paper presents the theoretical optical study and optimization of all the required parameters. This paper presents the optical optimization study for thin active layer cell in the generalized manner for 50-nm active layer, and then the performance of the proposed structure is compared with Lambertian limits and the planar cell, taken as reference. It has been predicted that these wavelength scale periodic structures greatly enhances the performance of the cell. The improvement in the performance is basically accounted for the better diffraction capability, impedance matching, trapping of high wavelength photons, and reduction in reflections from the top due to the PhC structure. The parameters have been optimized and calculated by means of rigorous coupled wave analysis.

Nano-Photonic Structures for Light Trapping in Ultra-Thin Crystalline Silicon Solar Cells.

Thick wafer-silicon is the dominant solar cell technology. It is of great interest to develop ultra-thin solar cells that can reduce materials usage, but still achieve acceptable performance and high solar absorption. Accordingly, we developed a highly absorbing ultra-thin crystalline Si based solar cell architecture using periodically patterned front and rear dielectric nanocone arrays which provide enhanced light trapping. The rear nanocones are embedded in a silver back reflector. In contrast to previous approaches, we utilize dielectric photonic crystals with a completely flat silicon absorber layer, providing expected high electronic quality and low carrier recombination. This architecture creates a dense mesh of wave-guided modes at near-infrared wavelengths in the absorber layer, generating enhanced absorption. For thin silicon (<2 μm) and 750 nm pitch arrays, scattering matrix simulations predict enhancements exceeding 90%. Absorption approaches the Lambertian limit at small thicknesses (<10 μm) and is slightly lower (by ~5%) at wafer-scale thicknesses. Parasitic losses are ~25% for ultra-thin (2 μm) silicon and just 1%–2% for thicker (>100 μm) cells. There is potential for 20 μm thick cells to provide 30 mA/cm2 photo-current and >20% efficiency. This architecture has great promise for ultra-thin silicon solar panels with reduced material utilization and enhanced light-trapping.

Enhanced efficiency of ultrathin (∼500 nm)-film microcrystalline silicon photonic crystal solar cells

Enhancing the absorption of thin-film microcrystalline silicon solar cells at 600–1000 nm wavelengths is very important to the improvement of the energy conversion efficiency. This can be achieved by creating a large number of resonant modes utilizing two-dimensional photonic crystal band edges, which exceeds the Lambertian limit of absorption in random textures. We focus on suppressing the parasitic absorption of back-reflector metal and doped layers in photonic crystal microcrystalline silicon solar cells. We achieve a high active-area current density of 22.6 mA cm−2 for an ultrathin (∼500 nm)-film silicon layer and obtain an active-area efficiency of ∼9.1%, as independently confirmed by the CSMT of AIST.

Simulation and analysis of the absorption enhancement in p-i-n InGaN/GaN solar cell using photonic crystal light trapping structures

The structure of p-i-n InGaN/GaN based solar cell having a photonic crystal (PhC)-based light trapping structure (LTS) at the top assisted by the planar metallic (aluminum) back reflector (BR) is proposed. We propose two different designs for efficiency enhancement: in one we keep the PhC structure etching depth extending from the top antireflective coating (ARC) of indium tin oxide (ITO) up to the p-GaN layer (which is beneath the ITO and above the active layer), whereas in the other design, the PhC LTS etching depth has been extended up to the In x Ga 1 − x N absorbing layer, starting from the top ITO layer. The theoretical optical simulation studies and optimization of the required parameters of the structure, which help to investigate and demonstrate the effectiveness of the LTS in the efficiency enhancement of the structure, are presented. The work also demonstrates the Lambertian light trapping limits for the practical indium concentrations in a In x Ga 1 − x N active layer cell. The paper also presents the comparison between the proposed designs and compares their results with that of a planar reference cell. The studies are carried out for various indium concentrations. The results indicate considerable enhancement in the efficiency due to the PhC LTS, mainly because of better coupling, low reflectance, and diffraction capability of the proposed LTS, although it is still under the Lambertian limits. The performance evaluation of the proposed structure with respect to the angle of incident light has also been done, indicating improved performance. The parameters have been optimized and calculated by means of rigorous coupled wave analysis (RCWA) method.

Light-trapping in perovskite solar cells

We numerically demonstrate enhanced light harvesting efficiency in both CH3NH3PbI3 and CH(NH2)2PbI3-based perovskite solar cells using inverted vertical-cone photonic-crystal nanostructures. For CH3NH3PbI3 perovskite solar cells, the maximum achievable photocurrent density (MAPD) reaches 25.1 mA/cm2, corresponding to 92% of the total available photocurrent in the absorption range of 300 nm to 800 nm. Our cell shows 6% absorption enhancement compared to the Lambertian limit (23.7 mA/cm2) and has a projected power conversion efficiency of 12.9%. Excellent solar absorption is numerically demonstrated over a broad angular range from 0 to 60 degree for both S- and P- polarizations. For the corresponding CH(NH2)2PbI3 based perovskite solar cell, with absorption range of 300 nm to 850 nm, we find a MAPD of 29.1 mA/cm2, corresponding to 95.4% of the total available photocurrent. The projected power conversion efficiency of the CH(NH2)2PbI3 based photonic crystal solar cell is 23.4%, well above the current world record efficiency of 20.1%.

Design of optimized wave-optical spheroidal nanostructures for photonic-enhanced solar cells

The interaction of light with wavelength-sized photonic nanostructures is highly promising for light management applied to thin-film photovoltaics. Several light trapping effects come into play in the wave optics regime of such structures that crucially depend on the parameters of the photonic and absorbing elements. Thus, multi-parameter optimizations employing exact numerical models, as performed in this work, are essential to determine the maximum photocurrent enhancement that can be produced in solar cells.Generalized spheroidal geometries and high-index dielectric materials are considered here to model the design of the optical elements providing broadband absorption enhancement in planar silicon solar cells. The physical mechanisms responsible for such enhancement are schematized in a spectral diagram, providing a deeper understanding of the advantageous characteristics of the optimized geometries. The best structures, composed of TiO2 half-spheroids patterned on the cells' top surface, yield two times higher photocurrent (up to 32.5mA/cm2 in 1.5µm thick silicon layer) than the same devices without photonic schemes.These results set the state-of-the-art closer to the theoretical Lambertian limit. In addition, the considered light trapping designs are not affected by the traditional compromise between absorption enhancement versus current degradation by recombination, which is a key technological advantage.