Complex refractive indices of Spiro-TTB and C60 for optical analysis of perovskite silicon tandem solar cells.

Evaporated charge extraction layers from organic molecular materials are vital in perovskite-based solar cells. For opto-electronic device optimization their complex refractive indices must be known for the visible and near infrared wavelength regime; however, accurate determination from thin organic films below 50 nm can be challenging. By combining spectrophotometry, variable angle spectroscopic ellipsometry, and X-ray reflectivity with an algorithm that simultaneously fits all available spectra, the complex refractive index of evaporated Spiro-TTB and C60 layers is determined with high accuracy. Based on that, an optical losses analysis for perovskite silicon solar cells shows that 15 nm of Spiro-TTB in the front of a n-i-p device reduces current by only 0.1 mA/cm2, compared to a substantial loss of 0.5 mA/cm2 due to 15 nm of C60 in a p-i-n device. Optical device simulation predicts high optical generation current densities of 19.7 and 20.1 mA/cm2 for the fully-textured, module-integrated p-i-n and n-i-p devices, respectively.

Experimental validation of a modeling framework for upconversion enhancement in 1D-photonic crystals.

Photonic structures can be designed to tailor luminescence properties of materials, which becomes particularly interesting for non-linear phenomena, such as photon upconversion. However, there is no adequate theoretical framework to optimize photonic structure designs for upconversion enhancement. Here, we present a comprehensive theoretical model describing photonic effects on upconversion and confirm the model's predictions by experimental realization of 1D-photonic upconverter devices with large statistics and parameter scans. The measured upconversion photoluminescence enhancement reaches 82 ± 24% of the simulated enhancement, in the mean of 2480 separate measurements, scanning the irradiance and the excitation wavelength on 40 different sample designs. Additionally, the trends expected from the modeled interaction of photonic energy density enhancement, local density of optical states and internal upconversion dynamics, are clearly validated in all experimentally performed parameter scans. Our simulation tool now opens the possibility of precisely designing photonic structure designs for various upconverting materials and applications.

Vapor-Phase Formation of a Hole-Transporting Thiophene Polymer Layer for Evaporated Perovskite Solar Cells.

Homogeneous layer formation on textured silicon substrates is essential for the fabrication of highly efficient monolithic perovskite silicon tandem solar cells. From all well-known techniques for the fabrication of perovskite solar cells (PSCs), the evaporation method offers the highest degree of freedom for layer-by-layer deposition independent of the substrate's roughness or texturing. Hole-transporting polymers with high hole mobility and structural stability have been used as effective hole-transporting materials (HTMs) of PSCs. However, the strong intermolecular interactions of the polymers do not allow for a layer formation via the evaporation method, which is a big challenge for the perovskite community. Herein, we first applied a hole-transporting terthiophene polymer (PTTh) as an HTM for evaporated PSCs via an in situ vapor-phase polymerization using iodine (I2) as a sublimable oxidative agent. PTTh showed high hole mobility of 1.2 × 10-3 cm2/(V s) and appropriate energy levels as HTM in PSCs (EHOMO = -5.3 eV and ELUMO = -3.3 eV). The PSCs with the in situ vapor-phase polymerized PTTh hole-transporting layer and a co-evaporated perovskite layer exhibited a photovoltaic conversion efficiency of 5.9%, as a proof of concept, and high cell stability over time. Additionally, the polymer layer could fully cover the pyramidal structure of textured silicon substrates and was identified as an effective hole-transporting material for perovskite silicon tandem solar cells by optical simulation.

Semi-Transparent Perovskite Solar Cells with ITO Directly Sputtered on Spiro-OMeTAD for Tandem Applications.

Perovskite silicon tandem solar cells have the potential to overcome the efficiency limit of single-junction solar cells. For both monolithic and mechanically stacked tandem devices, a semi-transparent perovskite top solar cell, including a transparent contact, is required. Usually, this contact consists of a metal oxide buffer layer and a sputtered transparent conductive oxide. In this work, semi-transparent perovskite solar cells in the regular n-i-p structure are presented with tin-doped indium oxide (ITO) directly sputtered on the hole conducting material Spiro-OMeTAD. ITO process parameters such as sputter power, temperature, and pressure in the chamber are systematically varied. While a low temperature of 50 °C is crucial for good device performance, a low sputter power has only a slight effect, and an increased chamber pressure has no influence on device performance. For the 5 × 5 mm2 perovskite cell with a planar front side, a 105 nm thick ITO layer with a sheet resistance of 44 Ω sq-1 allowing for the omission of grid fingers and a MgF2 antireflection coating are used to improve transmission into the solar cells. The best device achieved an efficiency of 14.8%, which would result in 24.2% in a four-terminal tandem configuration.

Efficiency Enhancement and Hysteresis Mitigation by Manipulation of Grain Growth Conditions in Hybrid Evaporated-Spin-coated Perovskite Solar Cells.

Perovskite solar cells have become a game changer in the field of photovoltaics by reaching power conversion efficiencies beyond 23%. To achieve even higher efficiencies, it is necessary to increase the understanding of crystallization, grain formation, and layer ripening. In this study, by a systematic variation of methylammonium iodide (MAI) concentrations, we changed the stoichiometry and thereupon the crystal growth conditions in MAPbI3 perovskite solar cells, prepared by a two-step hybrid evaporation-spin-coating deposition method. Utilizing X-ray diffraction, scanning electron microscopy, atomic force microscopy, photoluminescence, and current-voltage ( J- V) characterization, we found that a relatively lower concentration of MAI, or in other words higher content of remnant and unconverted PbI2, correlates with smaller and stronger interconnected grains, as well as with an improved optoelectronic performance of the solar cells and mitigation of hysteresis. The possible explanations are grain and interface passivation by the excess PbI2 and a positive contribution of the grain boundaries to current extraction.

Optical modeling of structured silicon-based tandem solar cells and module stacks.

Silicon-based tandem solar cells and modules are complex systems that require optical modeling for the optimization towards highest efficiencies. The fact that such devices typically incorporate surface structures of different optical regimes poses high requirements to the involved simulation tools. The OPTOS formalism is ideally suited to deal with such complexity. Within this work OPTOS is extended in order to calculate the layer resolved absorptance in silicon-based tandem solar cells and module stacks. After describing the relevant mathematical details, a good agreement between OPTOS absorptance simulation results and EQE measurements of the current 33.3% record efficiency III-V on silicon two-terminal tandem solar cell is found. Furthermore, a detailed loss analysis is performed for an exemplary perovskite silicon solar cell with and without module encapsulation. The comparison reveals a lower photocurrent density for the module stack due to increased reflectance and absorption in the EVA.

Detailed Investigation of Evaporated Perovskite Absorbers with High Crystal Quality on Different Substrates.

Dual-source vapor-phase deposition enables low-temperature fabrication of high-performance planar structure perovskite (CH3NH3PbI3) solar cells (PSCs), applicable in tandem devices or for industrial production with high homogeneity. Herein, we report low-temperature fabrication of high-efficiency PSCs by dual-source vapor-phase deposition and significance of TiO2 surface modification with [6,6]-phenyl C61 butyric acid methyl ester (PCBM) on cell performance. Co-evaporation of PbI2 and CH3NH3I, as confirmed by X-ray diffraction and high-resolution transmission electron microscopy analyses, results in CH3NH3PbI3 layers with a well-crystallized tetragonal phase formed on both TiO2 and TiO2/PCBM electron-transport layers (ETLs). The devices with PCBM interlayer between TiO2 and CH3NH3PbI3 showed remarkably higher performance than those with TiO2 only, which was attributed to enhance charge extraction and reduced recombination at the TiO2/PCBM/CH3NH3PbI3 interface. The devices composed of evaporated CH3NH3PbI3 on top of the TiO2/PCBM and [2,2',7,7'-tetrakis( N, N-di- p-methoxyphenyl-amine)-9,9'-spirobifluorene] (Spiro-OMeTAD) as hole-transport material demonstrated power conversion efficiencies of 17.1% (reverse scan) and 13.4% (forward scan) with stabilized efficiency of over 16%, which is, to the best of our knowledge, the highest efficiency reported for evaporated perovskite solar cells using low-temperature fabrication method involving compact TiO2 layer as ETL. Furthermore, we show that this process can be used to deposit a CH3NH3PbI3 layer on top of a textured silicon substrate, which is the first step for preparing perovskite-silicon tandem devices with enhanced antireflection and light-trapping properties.

Enhanced upconversion in one-dimensional photonic crystals: a simulation-based assessment within realistic material and fabrication constraints.

This paper presents a simulation-based assessment of the potential for improving the upconversion efficiency of ß-NaYF4:Er3+ by embedding the upconverter in a one-dimensional photonic crystal. The considered family of structures consists of alternating quarter-wave layers of the upconverter material and a spacer material with a higher refractive index. The two photonic effects of the structures, a modified local energy density and a modified local density of optical states, are considered within a rate-equation-modeling framework, which describes the internal dynamics of the upconversion process. Optimal designs are identified, while taking into account production tolerances via Monte Carlo simulations. To determine the maximum upconversion efficiency across all realistically attainable structures, the refractive index of the spacer material is varied within the range of existing materials. Assuming a production tolerance of σ = 1 nm, the optimized structures enable more than 300-fold upconversion photoluminescence enhancements under one sun and upconversion quantum yields exceeding 15% under 30 suns concentration.

Novel Low-Temperature Process for Perovskite Solar Cells with a Mesoporous TiO2 Scaffold.

The most efficient organic-inorganic perovskite solar cells (PSCs) contain the conventional n-i-p mesoscopic device architecture using a semiconducting TiO2 scaffold combined with a compact TiO2 blocking layer for selective electron transport. These devices achieve high power conversion efficiencies (15-22%) but mainly require high-temperature sintering (>450 °C), which is not possible for temperature-sensitive substrates. Thus far, comparably little effort has been spent on alternative low-temperature (<150 °C) routes to realize high-efficiency TiO2-based PSCs; instead, other device architectures have been promoted for low-temperature processing. In this paper the compatibility of the conventional mesoscopic TiO2 device architecture with low-temperature processing is presented for the first time with the combination of electron beam evaporation for the compact TiO2 and UV treatment for the mesoporous TiO2 layer. Vacuum evaporation is introduced as an excellent deposition technique of uniform compact TiO2 layers, adapting smoothly to the rough fluorine-doped tin oxide substrate surface. Effective removal of organic binders by UV light is shown for the mesoporous scaffold. Entirely low-temperature-processed PSCs with TiO2 scaffold reach encouraging stabilized efficiencies of up to 18.2%. This process fulfills all requirements for monolithic tandem devices with high-efficiency silicon heterojunction solar cells as the bottom cell.

Upconversion in a Bragg structure: photonic effects of a modified local density of states and irradiance on luminescence and upconversion quantum yield.

In this paper, we present a comprehensive simulation-based analysis of the two photonic effects of a Bragg stack - a modified local density of photon states (LDOS) and an enhanced local irradiance - on the upconversion (UC) luminescence and quantum yield of the upconverter ß-NaYF₄ doped with 25% Er³⁺. The investigated Bragg stack consists of alternating layers of TiO₂ and Poly(methylmethacrylate), the latter containing upconverter nanoparticles. Using experimentally determined input parameters, the photonic effects are first simulated separately and subsequently coupled in a rate equation model, describing the dynamics of the UC processes within ß-NaYF₄:25% Er³⁺. With this integrated simulation model, the Bragg stack design is optimized to maximize either the UC quantum yield (UCQY) or UC luminescence. We find that in an optimized Bragg stack, due to the modified LDOS, the maximum UCQY is enhanced from 14% to 16%, compared to an unstructured layer of upconverter material. Additionally, this maximum UCQY can already be reached at an incident irradiance as low as 100 W/m². With a Bragg stack design that maximizes UC luminescence, enhancement factors of up to 480 of the UC luminescence can be reached.

Optical simulation of photovoltaic modules with multiple textured interfaces using the matrix-based formalism OPTOS.

The OPTOS formalism is a matrix-based approach to determine the optical properties of textured optical sheets. It is extended within this work to enable the modelling of systems with an arbitrary number of textured, plane-parallel interfaces. A matrix-based system description is derived that accounts for the optical reflection and transmission interaction between all textured interfaces. Using OPTOS, we calculate reflectance and absorptance of complete photovoltaic module stacks, which consist of encapsulated silicon solar cells featuring textures that operate in different optical regimes. As exemplary systems, solar cells with and without module encapsulation are shown to exhibit a considerable absorptance gain if the random pyramid front side texture is combined with a diffractive rear side grating. A variation of the sunlight's angle of incidence reveals that the grating gain is almost not affected for incoming polar angles up to 60°. Considering as well the good agreement with alternative simulation techniques, OPTOS is demonstrated to be a versatile and efficient method for the optical analysis of photovoltaic modules.

Wave optical simulation of the light trapping properties of black silicon surface textures.

Due to their low reflectivity and effective light trapping properties black silicon nanostructured surfaces are promising front side structures for thin crystalline silicon solar cells. For further optimization of the light trapping effect, particularly in combination with rear side structures, it is necessary to simulate the optical properties of black silicon. Especially, the angular distribution of light in the silicon bulk after passage through the front side structure is relevant. In this paper, a rigorous coupled wave analysis of black silicon is presented, where the black silicon needle shaped structure is approximated by a randomized cone structure. The simulated absorptance agrees well with measurement data. Furthermore, the simulated angular light distribution within the silicon bulk shows that about 70% of the light can be subjected to internal reflection, highlighting the good light trapping properties.

Enhanced upconversion quantum yield near spherical gold nanoparticles - a comprehensive simulation based analysis.

Photon upconversion is promising for many applications. However, the potential of lanthanide doped upconverter materials is typically limited by low absorption coefficients and low upconversion quantum yields (UCQY) under practical irradiance of the excitation. Modifying the photonic environment can strongly enhance the spontaneous emission and therefore also the upconversion luminescence. Additionally, the non-linear nature of the upconversion processes can be exploited by an increased local optical field introduced by photonic or plasmonic structures. In combination, both processes may lead to a strong enhancement of the UCQY at simultaneously lower incident irradiances. Here, we use a comprehensive 3D computation-based approach to investigate how absorption, upconversion luminescence, and UCQY of an upconverter are altered in the vicinity of spherical gold nanoparticles (GNPs). We use Mie theory and electrodynamic theory to compute the properties of GNPs. The parameters obtained in these calculations were used as input parameters in a rate equation model of the upconverter ß-NaYF₄: 20% Er³⁺. We consider different diameters of the GNP and determine the behavior of the system as a function of the incident irradiance. Whether the UCQY is increased or actually decreased depends heavily on the position of the upconverter in respect to the GNP. Whereas the upconversion luminescence enhancement reaches a maximum around a distance of 35 nm to the surface of the GNP, we observe strong quenching of the UCQY for distances <40 nm and a UCQY maximum around 125 to 150 nm, in the case of a 300 nm diameter GNP. Hence, the upconverter material needs to be placed at different positions, depending on whether absorption, upconversion luminescence, or UCQY should be maximized. At the optimum position, we determine a maximum UCQY enhancement of 117% for a 300 nm diameter GNP at a low incident irradiance of 0.01 W/cm². As the irradiance increases, the maximum UCQY enhancement decreases to 20% at 1 W/cm². However, this UCQY enhancement translates into a significant improvement of the UCQY from 12.0% to 14.4% absolute.

3D optical simulation formalism OPTOS for textured silicon solar cells.

In this paper we introduce the three-dimensional formulation of the OPTOS formalism, a matrix-based method that allows for the efficient simulation of non-coherent light propagation and absorption in thick textured sheets. As application examples, we calculate the absorptance of solar cells featuring textures on front and rear side with different feature sizes operating in different optical regimes. A discretization of polar and azimuth angle enables a three-dimensional description of systems with arbitrary surface textures. We present redistribution matrices for 3D surface textures, including pyramidal textures, binary crossed gratings and a Lambertian scatterer. The results of the OPTOS simulations for silicon sheets with different combinations of these surfaces are in accordance with both optical measurements and results based on established simulation methods like ray tracing. Using OPTOS, we show that the integration of a diffractive grating at the rear side of a silicon solar cell featuring a pyramidal front side results in absorption close to the Yablonovitch Limit enhancing the photocurrent density by 0.6 mA/cm² for a 200 µm thick cell.

Matrix formalism for light propagation and absorption in thick textured optical sheets.

In this paper, we introduce a simulation formalism for determining the Optical Properties of Textured Optical Sheets (OPTOS). Our matrix-based method allows for the computationally-efficient calculation of non-coherent light propagation and absorption in thick textured sheets, especially solar cells, featuring different textures on front and rear side that may operate in different optical regimes. Within the simulated system, the angular power distribution is represented by a vector. This light distribution is modified by interaction with the surfaces of the textured sheets, which are described by redistribution matrices. These matrices can be calculated for each individual surface texture with the most appropriate technique. Depending on the feature size of the texture, for example, either ray- or wave-optical methods can be used. The comparison of the simulated absorption in a sheet of silicon for a variety of surface textures, both with the results from other simulation techniques and experimentally measured data, shows very good agreement. To demonstrate the versatility of this newly-developed approach, the absorption in silicon sheets with a large-scale structure (V-grooves) at the front side and a small-scale structure (diffraction grating) at the rear side is calculated. Moreover, with minimal computational effort, a thickness parameter variation is performed.

Hexagonal sphere gratings for enhanced light trapping in crystalline silicon solar cells.

Enhanced absorption of near infrared light in silicon solar cells is important for achieving high conversion efficiencies while reducing the solar cell's thickness. Hexagonal gratings on the rear side of solar cells can achieve such absorption enhancement. Our wave optical simulations show photocurrent density gains of up to 3 mA/cm2 for solar cells with a thickness of 40 µm and a planar front side. Hexagonal sphere gratings have been fabricated and optical measurements confirm the predicted absorption enhancement. The measured absorption enhancement corresponds to a photocurrent density gain of 1.04 mA/cm2 for planar wafers with a thickness of 250 µm and 1.49 mA/cm2 for 100 µm.

Enhanced up-conversion for photovoltaics via concentrating integrated optics.

Concentrating optics are integrated into up-conversion photovoltaic (UC-PV) devices to independently concentrate sub-band-gap photons on the up-conversion layer, without affecting the full solar concentration on the overlying solar cell. The UC-PV devices consist of silicon solar cells optimized for up-conversion, coupled with tapered and parabolic dielectric concentrators, and hexagonal sodium yttrium fluoride (ß-NaYF4) up-converter doped with 25% trivalent erbium (Er³âº). A normalized external quantum efficiency of 1.75x10⁻² cm²/W and 3.38x10⁻² cm²/W was obtained for the UC-PV device utilizing tapered and parabolic concentrators respectively. Although low to moderate concentration was shown to maximize UC, higher concentration lead to saturation and reduced external quantum efficiency. The presented work highlights some of the implications associated with the development of UC-PV devices and designates a substantial step for integration in concentrating PV.

Increased upconversion quantum yield in photonic structures due to local field enhancement and modification of the local density of states--a simulation-based analysis.

In upconversion processes, two or more low-energy photons are converted into one higher-energy photon. Besides other applications, upconversion has the potential to decrease sub-band-gap losses in silicon solar cells. Unfortunately, upconverting materials known today show quantum yields, which are too low for this application. In order to improve the upconversion quantum yield, two parameters can be tuned using photonic structures: first, the irradiance can be increased within the structure. This is beneficial, as upconversion is a non-linear process. Second, the rates of the radiative transitions between ionic states within the upconverter material can be altered due to a varied local density of photonic states. In this paper, we present a theoretical model of the impact of a photonic structure on upconversion and test this model in a simulation based analysis of the upconverter material ß -NaYF(4):20% Er(3+) within a dielectric waveguide structure. The simulation combines a finite-difference time-domain simulation model that describes the variations of the irradiance and the change of the local density of photonic states within a photonic structure, with a rate equation model of the upconversion processes. We find that averaged over the investigated structure the upconversion luminescence is increased by a factor of 3.3, and the upconversion quantum yield can be improved in average by a factor of 1.8 compared to the case without the structure for an initial irradiance of 200 Wm(-2).