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For the thin-film solar cells embedded with nanostructures at their rear dielectric layer, the shape and location of the nanostructures are crucial for higher conversion efficiency. A novel two-level hierarchical nanostructure (a sphere evenly covered with half truncated smaller spheres) can facilitate stronger intensity and wider scattering angles due to the coexistence of the merits of the nanospheres in two scales. We show in this article that the evolutionary algorithm allows for obtaining the optimal parameters of this two-scale nanostructure in terms of the maximization of the short circuit current density. In comparison with the thin-film solar cells with convex and flat metal back, whose parameters are optimized singly, the short circuit current density is improved by 7.48% and 10.23%, respectively. The exploration of such a two-level hierarchical nanostructure within an optimization framework signifies a new domain of study and allows to better identify the role of sophisticated shape in light trapping in the absorbing film, which is believed to be the main reason for the enhancement of short circuit current density.

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... It has been demonstrated that the use of metal nanostructures in solar cells could produce stronger field and greater absorption enhancement [6]. Only light absorbed by the absorption layer can contribute to the external electricity, thus it is essential to analyze the absorption enhancement in the absorption layer of the thin film solar cell [8]. In the present study, the absorption enhancement of silicon solar cell with spherical metal (Ag and Au) nanoparticles has been performed using Lumerical FDTD Solutions. ...

... The Figure 6 shows the profile of the relative absorption distribution of solar cell solar cell with Ag metal nanoparticles. The solar cell without metal nanostructure exhibits parallel absorption distribution in the Si film because part of the incident light is reflected from the back contact in a direction opposite to that of the incident light, which shows that the light propagates in the Si film through the shortest path [8]. For the solar cell with the optimized silver nanoparticles at the front end, the effective absorption is enhanced reason behind this is the distance between the nanoparticles and Si is relatively small, coupling of surface plasmon resonance near-field into the lower part of Si film is possible, as shown in Figure 6. ...

Thin film silicon solar cells have the potential to considerably decrease the cost of photovoltaic. To increase the conversion efficiency of thin film solar cells, nano-sized structures, such as nanoparticle deposition at the front end, were proposed. In the present study, spherical metal nanoparticles such as gold (Au) and silver (Ag) were deployed at the front of the silicon solar cell. The effect of metal nanoparticles on the absorption enhancement factor of the thin film solar cells was investigated using Lumerical Finite Difference Time Domain (FDTD) solutions. Also the influence of geometrical parameters of spherical nanoparticles on absorption enhancement factor was examined. The maximum absorption enhancement factor was achieved by optimizing the geometrical parameters of nanoparticles. The structure with Ag nanoparticles at the front end of the silicon solar cell exhibits higher absorption enhancement factor than the structure with Au nanoparticles.

... As shown in Figure 1, the structure of a thin-film solar cell studied in this paper consists of four ordered layers: an 80-nm SnO 2 :F transparent conductive oxide layer on the front, followed by a 350-nm hydrogenated amorphous silicon (a-Si:H) active layer, subsequently a layer of Al-doped ZnO (ZnO:Al) thin film into which the Ag nanoparticles are periodically deposited, and finally a 120-nm Ag back reflector. The idea of such a layered configuration comes from the attempts in two-scale nanospheres, which is desirable for thin-film solar cells as the merits of large sphere (strong resonant intensity of field) and small spheres (large scattering angles) coexist [5,18,23]. ...

... Now that the number of design variables is relatively small, we adopt the evolutional algorithm [20] for the optimization. Such a non-gradient method is rather simple but fairly efficient and is especially suitable for optical optimization in which the gradient of the cost function with respect to the design variables is often too sensitive to be controlled and stabilized numerically in terms of our previous studies [22,23,[27][28][29]. The evolutionary algorithm starts from a set of parent vectors randomly selected in the given parametric space. ...

The shape of metallic nanoparticles used to enhance the performance of thin-film solar cells is described by Gielis' superformula and optimized by an evolutionary algorithm. As a result, we have found a lens-like nanoparticle capable of improving the short circuit current density to 19.93 mA/cm2. Compared with a two-scale nanospherical configuration recently reported to synthesize the merits of large and small spheres into a single structure, the optimized nanoparticle enables the solar cell to achieve a further 7.75% improvement in the current density and is much more fabrication friendly due to its simple shape and tolerance to geometrical distortions.

... Previous literature investigated that electric power depends on the size and location of nanoparticles. 31 Figure 9 shows the electric power of three structures. It is clear that the nanoparticles affect the electric power so that the bare silicon has the minimum electric power in (x − z) plane and solar cell coated with Au 105 nm radius has the maximum electric power in (x − z) plane. ...

Plasmonic nanoparticles are promising ways for the efficiency enhancement of thinfilm solar cells. We have taken into account the bare silicon wafer and the embedded thin-film
silicon solar cells with Au nanodiscs array. We study these geometries of thin-film silicon solar
cells and find the effect of Au nanoparticles on light transmission and reflection spectrum, power
absorption, generation rate, power electric, and short-circuit current density; and for this, we
have used finite difference time domain, FDTD software. We also consider the near-field electric
intensity in the vicinity of nanoparticles with different sizes, which are known as a solar cells
efficiency enhancement mechanism. Our study can be useful for new perspectives for antireflection coating applications and light management in silicon solar cells. © 2021 Society of
Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.JNP.15.036010]

... [13] Silver [14] is a good choice for the PCBR because its plasmonic nature can be harnessed to launch surface-plasmon-polariton (SPP) waves inside the device and thereby enhance the optical electric field and optical absorption [15,16,17]. With the foregoing choices, our results indicate that maximization of the optical short-circuit current density, the standard figure of merit, [18,19,20] does not result in a desirable design. Instead, we found that the maximum power density is a better figure of merit. ...

The rigorous coupled-wave approach (RCWA) and the differential evolution algorithm (DEA) were coupled in a practicable approach to maximize absorption in optical structures with three-dimensional morphology. As a model problem, optimal values of four geometric parameters and the bandgaps of three i-layers were found for an amorphous-silicon, multiterminal, thin-film tandem solar cell comprising three p - i - n junctions with a metallic hexagonally corrugated backreflector. When the optical short-circuit current density was chosen as the figure of merit to be maximized, only the bandgap of the topmost i-layer was significant and the remaining six parameters played minor roles. While this configuration would absorb light very well, it would have poor electrical performance. This issue arises because the optimization problem allows for the thicknesses and bandgaps of the semiconductor layers to change. We therefore devised another figure of merit that takes into account bandgap changes by estimating the open-circuit voltage. The resulting configuration was found to be optimal with respect to all seven variable parameters. The RCWA + DEA optimization approach is applicable to other types of photovoltaic solar cells as well as optical absorbers, with the choice of the figure of merit being vital to a successful outcome. © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE).

... The absorption enhancement g(λ) also decreases in shorter wavelength range (300 nm to 600 nm) but redshift with broadening due to LSPR.The absorption enhancement g(D, λ) of thin film silicon with different nanoparticle diameters, (a) -TiN, (b) -Au. parison Figure 5(a), (b) show that the light absorption distribution profile in Silicon with TiN and Au metal nanoparticles and light propagates in silicon film through shortest path[46].Figure 4shows that the Enhancement Factor (G) varying with the diameter(0-200 nm) of TiN and Au. It is observed that Enhancement Factor (G) of TiN comparable to Au with an increment of nanoparticle diameters. ...

Light trapping is a crucial prominence to improve the efficiency in thin film solar cells. However, last few years, plasmonic based thin film solar cells shows potential structure to improve efficiency in photovoltaics. In order to achieve the high efficiency in plasmonic based thin film solar cells, traditionally noble metals like Silver (Ag) and Gold (Au) are extensively used due to their ability to localize the light in nanoscale structures. In this paper, we numerically demonstrated the absorption enhancement due to the incorporation of novel plasmonic TiN nanoparticles on thin film Silicon Solar cells. Absorption enhancement significantly affected by TiN plasmonic nanoparticles on thin film silicon was studied using Finite-Difference-Time-Domain Method (FDTD). The optimal absorption enhancement 1.2 was achieved for TiN nanoparticles with the diameter of 100 nm. The results show that the plasmonic effect significantly dominant to achieve maximum absorption enhancement at longer wavelengths (red and near infrared) and as comparable with Au nanoparticle on thin film Silicon. The absorption enhancement can be tuned to the desired position of solar spectrum by adjusting the size of TiN nanoparticles. Effect of nanoparticle diameters on the absorption enhancement was also thoroughly analyzed. The numerically simulated results show that TiN can play the similar role as gold nanoparticles on thin film silicon solar cells. Furthermore, TiN plasmonic material is cheap, abundant and more Complementary Metal Oxide Semiconductor (CMOS) compatible material than traditional plasmonic metals like Ag and Au, which can be easy integration with other optoelectronic devices.

... In fact, the formed nanostructures appear to be constituted by a principal larger particle, having on its surface, a collection of smaller nanoparticles. Such complex surface morphology was previously observed only for Ag NPs produced by wet chemical reactions and was named as lumpy morphology [54][55][56][57][58]. In the plasmonic solar cell field, these lumpy metal NPs attract much interest: in fact, due to the resonant nature of the plasmonic effect, useful absorption enhancements can only be realized at certain resonant scattering wavelengths determined by the nanoparticle size, shape, and their local dielectric environment. ...

In this work we report on the formation of lumpy Pd and Pt nanoparticles on fluorine-doped tin oxide/glass (FTO/glass) substrate by a laser-based approach. In general, complex-surface morphology metal nanoparticles can be used in several technological applications exploiting the peculiarities of their physical properties as modulated by nanoscale morphology. For example plasmonic metal nanoparticles presenting a lumpy morphology (i. e. larger particles coated on the surface by smaller particles) can be used in plasmonic solar cell devices providing broadband scattering enhancement over the smooth nanoparticles leading, so, to the increase of the device efficiency. However, the use of plasmonic lumpy nanoparticles remains largely unexplored due to the lack of simply, versatile, low-cost and high-throughput methods for the controllable production of such nanostructures.

... 17,18 More importantly, solar cells based on bumped nanoparticles harvest enhanced energy transfer efficiency and photocurrent density. [19][20][21] Usually, metal NCs can be prepared by physical methods and chemical methods. Physical methods, including ion beam [22][23][24] and laser beam [25][26][27] etching methods, can produce robust, polydispersed and ill-faceted nano-scale metal particles from a metal bulk or film. ...

Gold nanocrystals (NCs) with regular multi-bumps have been prepared through incoherent growth of the surface of seeded gold rhombic dodecahedra (RD) with the aid of Ag cations in a PVP/DMF system. After the Ag cations and HAuCl4 were added together into the growth system to react for 45, 60, 75 and 90 minutes, three kinds of intermediate products with pyramid-type bumps and final products with block-type bumps can be obtained, respectively. The facet variation from {110}-type, via {980}-type to {210}-type and finally to {100}-type in the bumped structure has been clearly defined to understand the morphology evolution and the corresponding process of incoherent growth. Different addition sequences of Ag cations and HAuCl4 have been carried out to explore the interaction between the additives and the surface. It is speculated that the absorption of AgCl on the surface of Au RD NCs inhibits the deposition of gold atoms, which may induce the incoherent growth of the surface of Au NCs. To further validate the inhibition effect of AgCl on the surface, highly concentrated NaCl solution was added into the growth solution to dissolve AgCl and only normal cubes without any bumps can be obtained.

... This phenomenon can lead to broadband electromagnetic field trapping and make the periodic plasmonic nanoparticle arrays competitive candidates for broadband electromagnetic absorbers combined with designed dielectric thin films [10][11][12][13]. Recently, plasmonic nanoparticles have been proved to be capable of significantly enhancing the light absorption in single junction thin film solar cells via plasmonic light scattering or near-field enhancement [14,15] when they are integrated on the top or at the rear surfaces of the solar cells, including organic solar cells [16][17][18], GaAs based solar cells [19,20], dye sensitized solar cells [21][22][23], Si based solar cells [24][25][26][27][28][29][30][31] and perovskite solar cells [32,33]. For tandem thin film solar cell geometry, the synergistic influence to the two subcells from the nanoparticles is more complicated but critical to improve the efficiency and cost-effectiveness of the tandem solar cells, however, it has remained unexplored. ...

Enhancing the light absorption in microcrystalline silicon bottom cell of a silicon-based tandem solar cell for photocurrent matching holds the key to achieving the overall solar cell performance breakthroughs. Here, we present a concept for significantly improving the absorption of both subcells simultaneously by simply applying tailored metallic nanoparticles both on the top and at the rear surfaces of the solar cells. Significant light absorption enhancement as large as 56% has been achieved in the bottom subcells. More importantly the thickness of the microcrystalline layer can be reduced by 57% without compromising the optical performance of the tandem solar cell, providing a cost-effective strategy for high performance tandem solar cells.

... This nanoparticle structure combines large Ag nanoparticle with small nucleated Ag nanoparticles to effectively scatter light in a broadband wavelength with large oblique angles. Significant efficiency enhancement of more than 20% has been achieved and further enhancement is possible with an optimized particle design [5]. However, the nucleated Ag nanoparticles only work efficiently when being embedded at the back side of the solar cells because when being integrated on the front surface of the solar cells, it will introduce high light loss due to the high nanoparticle absorption and light blockage. ...

Hetero-structured lumpy nanoparticles, combining the scattering effect of dielectric nanoparticle and near field light concentration of metallic nanoparticles, are placed on top of a-Si. 84% absorbance enhancement is achieved with the optimized design.

... Such a non-gradient method is fairly simple but rather efficient, especially suitable for optical optimization problems in which the gradient of the cost function with respect to the design variables is sometimes too sensitive to be stabilized. [24][25][26][27] The evolutionary algorithm starts from a set of parent vectors randomly selected in the given parametric space. For each parent vector, a fitness (to be maximized) is obtained by solving Maxwells equations. ...

By optimizing the shape and scale of perforations as well as the depth of different layers, we obtained a metal- dielectric-metal double fishnet metamaterial with an unbroken 38-nm bandwidth of negative refractive index in visible spectrum, spaning from 459 to 497 nm. Moreover, the real parts of permittivity and permeability of this metamaterial are simultaneously negative from 460 to 478 nm in wavelength, reaching a frequency band as high as to the blue region - a territory that has never been explored before in visible spectrum.

... 2 Recently, the nucleated nanoparticle geometry (or the lumpy geometry) was demonstrated to be an effective way to mitigate these challenges in thin film solar cells. [9][10][11] Through combining a large core Ag particle with a number of small Ag surface nanoparticles, the strong scattering effect and the near field effect can be enabled leading to a significant enhancement of more than 20% in the solar cell conversion efficiency. However, the intrinsic absorption and the light blockage from the silver nanoparticles cannot be avoided, limiting the integration of the nucleated nanoparticles only to the back contact layer of the thin film solar cells. ...

We present a concept for enhancing the absorbance of amorphous-silicon solar cells by using heterostructured
nanoparticles consisting of dielectric core particles combined with small metallic surface
nanoparticles half embedded in the core to harness both the scattering effect and the near field light
concentration. Through optimising key parameters, including the relative distance of the
nanoparticles to the solar cell, the radius ratio of the core to the surface nanoparticles, and the
refractive index of the core particles, the short circuit current density in a 20 nm nanoparticleintegrated
active layer is equivalent to that in a 300 nm flat active layer.

The interaction between light and subwavelength structures provides tailorable optical properties that can be useful in many engineering applications. These properties strongly depend on the material shape, which provides obtaining unique scattering characteristics when rigorously designed. However, the conventional design methods require precise modeling and characterization of the shapes of the scattering objects, thus requiring a lot of intuition and knowledge about light radiation at small scales, as well as many rounds of experimental trial and error. We propose a framework to discover new nanoparticle designs for improved scattering based on topology optimization. The framework allows us to maximize the scattering cross section of the particle domain. Increased scattering cross-section at nanoscale leads to improved light trapping, which is critical in many applications such as thin film solar cells and biological imaging. Topology optimization offers a knowledge independent design procedure, therefore revealing relationships between specific regions in the design domain and the light behavior for maximum scattering cross section.

Photovoltaic (PV) technologies have attracted great interest due to their capability of generating electricity directly from sunlight. Machine learning (ML) is a technique for computer to learn how to perform a specific task using known data. It can be used in many areas and has become a hot research topic recently due to the rapid accumulation of data and advancement of computer hardware. The application of ML techniques in the design and fabrication of solar cells started slowly but has recently gained tremendous momentum. An exhaustive compilation of the literatures indicates that all the major aspects in the research and development of solar cells can be effectively assisted by ML techniques. If combined with other tools and fed with additional theoretical and experimental data, more accurate and robust results can be achieved from ML techniques. The aspects can be grouped into four categories: prediction of material properties, optimization of device structures, optimization of fabrication processes, and reconstruction of measurement data. A statistical analysis of the literatures shows that artificial neural network (ANN) and genetic algorithm (GA) are the two most applied ML techniques and the topics in the optimization of device structures and optimization of fabrication processes are more popular. This article can be used as a reference by all PV researchers who are interested in ML techniques. The application of ML techniques in the design and fabrication of solar cells started slowly but has recently gained tremendous momentum. ML techniques have been demonstrated to be very effective in assisting the design and fabrication of solar cells when data are properly collected. The application of ML techniques not only reduces the cost and time, but also sometimes can lead to better properties and higher performances. This article presents a comprehensive review on the design and fabrication of solar cells assisted by ML techniques.

We propose a technique capable of designing fishnet metamaterials that have a negative refractive index (NRI) over a broad range in the visible and infrared. The technique relies on optimizing the shape and scale of the fishnet apertures as well as the depth of different layers of the composite. A metamaterial is obtained that exhibits an unbroken 552 nm bandwidth of NRI, covering the entire red and infrared regions. Moreover, two fishnet structures perforated with star-like holes are found to render refractive index negative in the yellow and green spectra.

Plasmonic nanostructures have been recently investigated as a possible way to improve absorption of light in solar cells. The strong interaction of small metal nanostructures with light allows control over the propagation of light at the nanoscale and thus the design of ultrathin solar cells in which light is trapped in the active layer and efficiently absorbed. In this paper we review some of our recent work in the field of plasmonics for improved solar cells. We have investigated two possible ways of integrating metal nanoparticles in a solar cell. First, a layer of Ag nanoparticles that improves the standard antireflection coating used for crystalline and amorphous silicon solar cells has been designed and fabricated. Second, regular and random arrays of metal nanostructures have been designed to couple light in waveguide modes of thin semiconductor layers. Using a large-scale, relative inexpensive nano-imprint technique, we have designed a back-contact light trapping surface for a-Si:H solar cells which show enhanced efficiency over standard randomly textured cells.

Nanoplasmonics recently has emerged as a new frontier of photovoltaic research. Noble metal nanostructures that can concentrate and guide light have demonstrated great capability for dramatically improving the energy conversion efficiency of both laboratory and industrial solar cells, providing an innovative pathway potentially transforming the solar industry. However, to make the nanoplasmonic technology fully appreciated by the solar industry, key challenges need to be addressed; including the detrimental absorption of metals, broadband light trapping mechanisms, cost of plasmonic nanomaterials, simple and inexpensive fabrication and integration methods of the plasmonic nanostructures, which are scalable for full size manufacture. This article reviews the recent progress of plasmonic solar cells including the fundamental mechanisms, material fabrication, theoretical modelling and emerging directions with a distinct emphasis on solutions tackling the above-mentioned challenges for industrial relevant applications.

Experimental characterization and finite-element numerical simulations of the electromagnetic interaction between Au nanoparticles positioned atop a Si pn junction photodiode and incident electromagnetic plane waves have been performed as a function of wavelength. The presence of the Au nanoparticles is found to lead to increased electromagnetic field amplitude within the semiconductor, and consequently increased photocurrent response, over a broad range of wavelengths extending upward from the nanoparticle surface plasmon polariton resonance wavelength. At shorter wavelengths, a reduction in electromagnetic field amplitude and a corresponding decrease in photocurrent response in the semiconductor are observed. Numerical simulations reveal that these different behaviors are a consequence of a shift in the phase of the nanoparticle polarizability near the surface plasmon polariton wavelength, leading to interference effects within the semiconductor that vary strongly with wavelength. These observations have substantial implications for the optimization of device structures in which surface plasmon polariton resonances in metallic nanoparticles are exploited to engineer the performance of semiconductor photodetectors and related devices.

Thin-film solar cells have the potential to significantly decrease the cost of photovoltaics. Light trapping is particularly critical in such thin-film crystalline silicon solar cells in order to increase light absorption and hence cell efficiency. In this article we investigate the suitability of localized surface plasmons on silver nanoparticles for enhancing the absorbance of silicon solar cells. We find that surface plasmons can increase the spectral response of thin-film cells over almost the entire solar spectrum. At wavelengths close to the band gap of Si we observe a significant enhancement of the absorption for both thin-film and wafer-based structures. We report a sevenfold enhancement for wafer-based cells at λ = 1200 nm and up to 16-fold enhancement at λ = 1050 nm for 1.25 μm thin silicon-on-insulator (SOI) cells, and compare the results with a theoretical dipole-waveguide model. We also report a close to 12-fold enhancement in the electroluminescence from ultrathin SOI light-emitting diodes and investigate the effect of varying the particle size on that enhancement.

This paper presents a bidirectional evolutionary structural optimization (BESO) method for designing periodic microstructures of two-phase composites with extremal electromagnetic permeability and permittivity. The effective permeability and effective permittivity of the composite are obtained by applying the homogenization technique to the representative periodic base cell (PBC). Single or multiple objectives are defined to maximize or minimize the electromagnetic properties separately or simultaneously. The sensitivity analysis of the objective function is conducted using the adjoint method. Based on the established sensitivity number, BESO gradually evolves the topology of the PBC to an optimum. Numerical examples demonstrate that the electromagnetic properties of the resulting 2D and 3D microstructures are very close to the theoretical Hashin-Shtrikman (HS) bounds. The proposed BESO algorithm is computationally efficient as the solution usually converges in less than 50 iterations. The proposed BESO method can be implemented easily as a post-processor to standard commercial finite element analysis software packages, e.g. ANSYS which has been used in this study. The resulting topologies are clear black-and-white solutions (with no grey areas). Some interesting topological patterns such as Vigdergauz-type structure and Schwarz primitive structure have been found which will be useful for the design of electromagnetic materials.

We develop fundamental design principles for increasing the efficiency of solar cells using light trapping by scattering from metal nanoparticles. We show that cylindrical and hemispherical particles lead to much higher path length enhancements than spherical particles, due to enhanced near-field coupling, and that the path length enhancement for an electric point dipole is even higher than the Lambertian value. Silver particles give much higher path length enhancements than gold particles. The scattering cross section of the particles is very sensitive to the thickness of a spacer layer at the substrate, which provides additional tunability in the design of particle arrays.

This work numerically demonstrates a new anti-reflection coupler (ARC) with high coupling efficiency in a Si substrate solar cell. The ARC in which the grating is integrated on a glass encapsulation and a three-layer impedance match layer is proposed. A coupling efficiency of 90% is obtained at wavelengths between 350 and 1200 nm in the TE and TM modes when the incident angle is less than 30°. In comparison with a 1µm absorber layer, the integrated absorption of an a-Si thin-film solar cell without a new ARC is doubled, at long wavelengths (750 nm ≤ λ ≤ 1200 nm), as calculated by FDTD method.

This paper aims to develop a level-set-based topology optimization approach for the design of negative permeability electromagnetic metamaterials, where the topological configuration of the base cell is represented by the zero-level contour of a higher-dimensional level-set function. Such an implicit expression enables us to create a distinct interface between the free space and conducting phase (metal). By seeking for an optimality of a Lagrangian functional in terms of the objective function and the governing wave equation, we derived an adjoint system. The normal velocity (sensitivity) of the level-set model is determined by making the Eulerian derivative of the Lagrangian functional non-positive. Both the governing and adjoint systems are solved by a powerful finite-difference time-domain algorithm. The solution to the adjoint system is separated into two parts, namely the self-adjoint part, which is linearly proportional to the solution of the governing equation; and the non-self-adjoint part, which is obtained by swapping the locations of the incident wave and the receiving planes in the simulation model. From the demonstrative examples, we found that the well-known U-shaped metamaterials might not be the best in terms of the minimal value of the imaginary part of the effective permeability. Following the present topology optimization procedure, some novel structures with desired negative permeability at the specified frequency are obtained.

A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.

Effective light management is imperative in maintaining high efficiencies as photovoltaic devices become thinner. We demonstrate a simple and effective method of enhancing light trapping in solar cells with thin absorber layers by tuning localized surface plasmons in arrays of Ag nanoparticles. By redshifting the surface plasmon resonances by up to 200 nm, through the modification of the local dielectric environment of the particles, we can increase the optical absorption in an underlying Si wafer fivefold at a wavelength of 1100 nm and enhance the external quantum efficiency of thin Si solar cells by a factor of 2.3 at this wavelength where transmission losses are prevalent. Additionally, by locating the nanoparticles on the rear of the solar cells, we can avoid absorption losses below the resonance wavelength due to interference effects, while still allowing long wavelength light to be coupled into the cell. Results from numerical simulations support the experimental findings and show that the fraction of light backscattered into the cell by nanoparticles located on the rear is comparable to the forward scattering effects of particles on the front. Using nanoparticle self-assembly methods and dielectrics commonly used in photovoltaic fabrication this technology is relevant for application to large-scale photovoltaic devices.

We design three‐phase composites having maximum thermal expansion, zero thermal expansion, or negative thermal expansion using a numerical topology optimization method. It is shown that composites with effective negative thermal expansion can be obtained by mixing two phases of positive thermal expansions with a void phase. We also show that there is no mechanistic relationship between negative thermal expansion and negative Poisson’s ratio. © 1996 American Institute of Physics.

This paper presents a new homogenization formula to compute the effective electromagnetic properties for periodic metamaterials. Numerical examples showed that the effective permittivity and permeability of the composites with cubic inclusions, formerly known to have the lowest permittivity, are closer to the Hashin-Strikman bounds than those obtained from other methods. To tailor the specific effective properties, an inverse homogenization procedure is proposed within the framework of vector wave equations. Some novel metamaterial microstructures with a range of specific effective permittivity and/or permeability are obtained. By maximizing the permittivity and permeability at the same time, a structure with minimal surface area (the mean curvature of the surface equals zero everywhere), namely, the well-known Schwarz primitive structure, is obtained. Similarly to the nano-spheres (dielectric spheres covered by plasmonic shells) with negative refraction, we generalize the Schwarz primitive structure and its analogy (e.g., those with a constant mean curvature surface) to one class of chiral composites by embedding one of these structures with smaller volume fraction (nonmagnetic inclusive cores) into another with large volume fraction (metal shell). Such composites have potential to provide better behaviors because they can best utilize different components. The anisotropic composites and multiple solutions to the inverse homogenization are also illustrated.

Combining two indirect-gap materials-with different electronic and optical gaps-to create a direct gap material represents an ongoing theoretical challenge with potentially rewarding practical implications, such as optoelectronics integration on a single wafer. We provide an unexpected solution to this classic problem, by spatially melding two indirect-gap materials (Si and Ge) into one strongly dipole-allowed direct-gap material. We leverage a combination of genetic algorithms with a pseudopotential Hamiltonian to search through the astronomic number of variants of Si(n)/Ge(m)/…/Si(p)/Ge(q) superstructures grown on (001) Si(1-x)Ge(x). The search reveals a robust configurational motif-SiGe(2)Si(2)Ge(2)SiGe(n) on (001) Si(x)Ge(1-x) substrate (x≤0.4) presenting a direct and dipole-allowed gap resulting from an enhanced Γ-X coupling at the band edges.

We report on the design, fabrication, and measurement of ultrathin film a-Si:H solar cells with nanostructured plasmonic back contacts, which demonstrate enhanced short circuit current densities compared to cells having flat or randomly textured back contacts. The primary photocurrent enhancement occurs in the spectral range from 550 nm to 800 nm. We use angle-resolved photocurrent spectroscopy to confirm that the enhanced absorption is due to coupling to guided modes supported by the cell. Full-field electromagnetic simulation of the absorption in the active a-Si:H layer agrees well with the experimental results. Furthermore, the nanopatterns were fabricated via an inexpensive, scalable, and precise nanopatterning method. These results should guide design of optimized, non-random nanostructured back reflectors for thin film solar cells.

The emerging field of plasmonics has yielded methods for guiding and
localizing light at the nanoscale, well below the scale of the
wavelength of light in free space. Now plasmonics researchers are
turning their attention to photovoltaics, where design approaches based
on plasmonics can be used to improve absorption in photovoltaic devices,
permitting a considerable reduction in the physical thickness of solar
photovoltaic absorber layers, and yielding new options for solar-cell
design. In this review, we survey recent advances at the intersection of
plasmonics and photovoltaics and offer an outlook on the future of solar
cells based on these principles.

The reconstruction problem in diffuse optical tomography can be formulated as an optimization problem, in which an objective function has to be minimized. Current model-based iterative image reconstruction schemes commonly use information about the gradient of the objective function to locate the minimum. These gradient-based search algorithms often find local minima close to an initial guess, or do not converge if the gradient is very small. If the initial guess is too far from the solution, gradient-based schemes prove inefficient for finding the global minimum. In this work we introduce evolution-strategy (ES) algorithms for diffuse optical tomography. These algorithms seek to find the global minimum and are less sensitive to initial guesses and regions with small gradients. We illustrate the fundamental concepts by comparing the performance of gradient-based schemes and ES algorithms in finding optical properties (absorption coefficient microa , scattering coefficient micros , and anisotropy factor g) of a homogenous medium.

In this article, we present a genetic algorithm (GA) as one branch of artificial intelligence (AI) for the optimization-design of the artificial magnetic metamaterial whose structure is automatically generated by computer through the filling element methodology. A representative design example, metamaterials with permeability of negative unity, is investigated and the optimized structures found by the GA are presented. It is also demonstrated that our approach is effective for the synthesis of functional magnetic and electric metamaterials with optimal structures. This GA-based optimization-design technique shows great versatility and applicability in the design of functional metamaterials.

The advantages and limitations of photovoltaic solar modules for energy generation are reviewed with their operation principles
and physical efficiency limits. Although the main materials currently used or investigated and the associated fabrication
technologies are individually described, emphasis is on silicon-based solar cells. Wafer-based crystalline silicon solar modules
dominate in terms of production, but amorphous silicon solar cells have the potential to undercut costs owing, for example,
to the roll-to-roll production possibilities for modules. Recent developments suggest that thin-film crystalline silicon (especially
microcrystalline silicon) is becoming a prime candidate for future photovoltaics.

A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.

A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.

A two-stage genetic algorithm (GA) with a floating mutation probability is developed to design a two-dimensional (2D) photonic crystal of a square lattice with the maximal absolute band gap. The unit cell is divided equally into many square pixels, and each filling pattern of pixels with two dielectric materials corresponds to a chromosome consisting of binary digits 0 and 1. As a numerical example, the two-stage GA gives a 2D GaAs structure with a relative width of the absolute band gap of about 19%. After further optimization, a new 2D GaAs photonic crystal is found with an absolute band gap much larger than those reported before.

Efficient light trapping structures for amorphous hydrogenated silicon (a-Si:H) solar cells have been realized using periodically structured aluminum doped zinc oxide (ZnO:Al) with periods between 390 and 980 nm as a transparent front contact. Atomic force microscopy, optical reflection, and diffraction efficiency measurements were applied to characterize solar cells deposited on such gratings. A simple formula for the threshold wavelength of total internal reflection is derived. Periodic light coupler gratings reduce the reflectance to a value below 10% in the wavelength range of 400–800 nm which is comparable to cells with an optimized statistical texture. Diffraction efficiency measurements and theoretical considerations indicate that a combination of transmission and reflection gratings contribute to the observed reduction of the reflectance. © 2001 American Institute of Physics.

We investigate the energy of arrangements of N points on the surface of a sphere in R 3 , interacting through a power law potential V = r α , −2 < α < 2, where r is Euclidean distance. For α = 0, we take V = log(1/r). An area-regular partitioning scheme of the sphere is devised for the purpose of obtaining bounds for the extremal (equilibrium) energy for such points. For α = 0, finer estimates are obtained for the dominant terms in the minimal energy by considering stereographical projections on the plane and analyzing certain logarithmic potentials. A general conjecture on the asymptotic form (as N → ∞) of the extremal energy, along with its supporting numerical evidence, is presented. Also we introduce explicit sets of points, called "generalized spiral points", that yield good estimates for the extremal energy. At least for N ≤ 12, 000 these points provide a reasonable solution to a problem of M. Shub and S. Smale arising in complexity theory.

This paper reviews recent developments in the field of amorphous-silicon-based thin-film solar cells and discusses potentials
for further improvements. Creative efforts in materials research, device physics, and process engineering have led to highly
efficient solar cells based on amorphous hydrogenated silicon. Sophisticated multijunction solar cell designs make use of
its unique material properties and strongly suppress light induced degradation. Texture-etching of sputtered ZnO:Al films
is presented as a novel technique to design optimized light trapping schemes for silicon thin-film solar cells in both p-i-n
and n-i-p device structure. Necessary efforts will be discussed to close the efficiency gap between the highest stabilized
efficiencies demonstrated on lab scale and efficiencies achieved in production. In case of a-Si:H/a-Si:H stacked cells prepared
on glass substrates, significant reduction of process-related losses and the development of superior TCO substrates on large
areas promise distinctly higher module efficiencies. A discussion of future perspectives comprises the potential of new deposition
techniques and concepts combining the advantages of amorphous and crystalline silicon thin-film solar cells.

The optics of microcrystalline silicon thin-film solar cells with integrated light trapping structures was investigated. Periodic grating couplers were integrated in microcrystalline silicon thin-film solar cells and the influence of the grating dimensions on the short circuit current and the quantum efficiency was investigated by the numerical simulation of Maxwell’s equations utilizing the finite difference time domain algorithm. The grating structure leads to scattering and higher order diffraction resulting in an increased absorption of the incident light in the silicon thin-film solar cell. The influence of the grating period and the grating height on the short circuit current and the quantum efficiency was investigated. Enhanced quantum efficiencies are observed for the red and infrared parts of the optical spectrum. Optimal dimensions of the grating coupler were obtained.

Recently plasmonic effects have gained tremendous interest in solar cell research because they are deemed to be able to dramatically boost the efficiency of thin-film solar cells. However, despite of the intensive efforts, the desired broadband enhancement, which is critical for real device performance improvement, has yet been achieved with simple fabrication and integration methods appreciated by the solar industry. We propose in this paper a novel idea of using nucleated silver nanoparticles to effectively scatter light in a broadband wavelength range to realize pronounced absorption enhancement in the silicon absorbing layer. Since it does not require critical patterning, experimentally these tailored nanoparticles were achieved by the simple, low-cost and upscalable wet chemical synthesis method and integrated before the back contact layer of the amorphous silicon thin-film solar cells. The solar cells incorporated with 200 nm nucleated silver nanoparticles at 10% coverage density clearly demonstrate a broadband absorption enhancement and significant superior performance including a 14.3% enhancement in the short-circuit photocurrent density and a 23% enhancement in the energy conversion efficiency, compared with the randomly textured reference cells without nanoparticles. Among the measured plasmonic solar cells the highest efficiency achieved was 8.1%. The significant enhancement is mainly attributed to the broadband light scattering arising from the integration of the tailored nucleated silver nanoparticles.

The characteristics of the waves guided along a plane [I] P. S. Epstein, “On the possibility of electromagnetic surface waves, ” Proc. Nat’l dcad. Sciences, vol. 40, pp. 1158-1165, Deinterface which separates a semi-infinite region of free cember 1954. space from that of a magnetoionic medium are investi- [2] T. Tamir and A. A. Oliner, “The spectrum of electromagnetic waves guided by a plasma layer, ” Proc. IEEE, vol. 51, pp. 317gated for the case in which the static magnetic field is 332, February 1963. oriented perpendicular to the plane interface. It is [3] &I. A. Gintsburg, “Surface waves on the boundary of a plasma in a magnetic field, ” Rasprost. Radwvoln i Ionosf., Trudy found that surface waves exist only when w,<wp and NIZMIRAN L’SSR, no. 17(27), pp. 208-215, 1960. that also only for angular frequencies which lie bet\\-een [4] S. R. Seshadri and A. Hessel, “Radiation from a source near a plane interface between an isotropic and a gyrotropic dielectric,” we and 1/42 times the upper hybrid resonant frequency. Canad. J. Phys., vol. 42, pp. 2153-2172, November 1964. The surface waves propagate with a phase velocity [5] G. H. Owpang and S. R. Seshadri, “Guided waves propagating along the magnetostatic field at a plane boundary of a semiwhich is always less than the velocity of electromagnetic infinite magnetoionic medium, ” IEEE Trans. on Miomave waves in free space. The attenuation rates normal to the Tbory and Techniques, vol. MTT-14, pp. 136144, March 1966. [6] S. R. Seshadri and T. T. \Vu, “Radiation condition for a maginterface of the surface wave fields in both the media are netoionic medium. ” to be Dublished. examined. Kumerical results of the surface wave characteristics are given for one typical case.

The enhancement of solar light absorption in a solar cell is a challenging issue. In this article we show that in a thin-film silicon solar cell covered with silver nanoparticles on the surface, the absorption of the incident light can be particularly enhanced at certain angular range and wavelength. Such absorption enhancements are associated with the resonant localized surface plasmon (LSP) modes of the nanoparticle and nanoparticle-induced local Fabry-Perot (FP) modes. Our simulations suggest that the spectral shift of the LSP modes due to changing the incident angle leads to an incident-angle-sensitive absorption enhancement of the solar cell. Selecting the incident angle in a well-defined range of 0° to 35° is essential for optimizing the performance of a thin-film solar cell.

In this study, an evolutionary algorithm (EA), which consists of genetic and immune algorithms, is introduced to design the optical geometry of a nonimaging Fresnel lens; this lens generates the uniform flux concentration required for a photovoltaic cell. Herein, a design procedure that incorporates a ray-tracing technique in the EA is described, and the validity of the design is demonstrated. The results show that the EA automatically generated a unique geometry of the Fresnel lens; the use of this geometry resulted in better uniform flux concentration with high optical efficiency.

The influence of nano textured front contacts on the optical wave propagation within microcrystalline thin-film silicon solar cell was investigated. Periodic triangular gratings were integrated in solar cells and the influence of the profile dimensions on the quantum efficiency and the short circuit current was studied. A Finite Difference Time Domain approach was used to rigorously solve the Maxwell's equations in two dimensions. By studying the influence of the period and height of the triangular profile, the design of the structures were optimized to achieve higher short circuit currents and quantum efficiencies. Enhancement of the short circuit current in the blue part of the spectrum is achieved for small triangular periods (P<200 nm), whereas the short circuit current in the red and infrared part of the spectrum is increased for triangular periods (P = 900nm) comparable to the optical wavelength. The influence of the surface texture on the solar cell performance will be discussed.

The intrinsic limits on the energy conversion efficiency of silicon solar cells when used under concentrated sunlight are calculated. It is shown that Auger recombination processes are even more important under concentrated sunlight than nonconcentrated sunlight. However, light trapping can be far more effective under concentrated light due to the better defined direction of incident light. As a result of these effects, the limiting efficiency lies in tile 36-37-percent range regardless of concentration ratio compared to the limiting value of 29.8 percent for a nonconcentrating cell with isotropic response.

Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors

- M Avezac
- J W Luo
- T Chanier
- A Zunger

M. d'Avezac, J. W. Luo, T. Chanier, and A. Zunger, "Genetic-algorithm discovery of a direct-gap and optically
allowed superstructure from indirect-gap Si and Ge semiconductors," Phys. Rev. Lett. 108(2), 027401 (2012).

- Atwater