A New Family of Layered Metal-Organic Semiconductors: Cu/V-Organophosphonates.

Herein, we report the design and synthesis of a layered redox-active, antiferromagnetic metal organic semiconductor crystals with the chemical formula [Cu(H2 O)2 V(µ-O)(PPA)2 ] (where PPA is phenylphosphonate). The crystal structure of [Cu(H2 O)2 V(µ-O)(PPA)2 ] shows that the metal phosphonate layers are separated by phenyl groups of the phenyl phosphonate linker. Tauc plotting of diffuse reflectance spectra indicates that [Cu(H2 O)2 V(µ-O)(PPA)2 ] has an indirect band gap of 2.19 eV. Photoluminescence (PL) spectra indicate a complex landscape of energy states with PL peaks at 1.8 and 2.2 eV. [Cu(H2 O)2 V(µ-O)(PPA)2 ] has estimated hybrid ionic and electronic conductivity values between 0.13 and 0.6 S m-1 . Temperature-dependent magnetization measurements show that [Cu(H2 O)2 V(µ-O)(PPA)2 ] exhibits short range antiferromagnetic order between Cu(II) and V(IV) ions. [Cu(H2 O)2 V(µ-O)(PPA)2 ] is also photoluminescent with photoluminescence quantum yield of 0.02%. [Cu(H2 O)2 V(µ-O)(PPA)2 ] shows high electrochemical, and thermal stability.

Structuring of perovskite-silicon tandem solar cells for reduced reflectance and thermalization losses.

Perovskite-silicon tandem solar cells have made rapid progress in the last decade. Still, they suffer from multiple loss channels, one of them being optical losses including reflection and thermalization. In this study, the effect of structures at the air-perovskite and perovskite-silicon interface of the tandem solar cell stack on these two loss channels are evaluated. Regarding reflectance, every structure evaluated led to a reduction relative to the optimized planar stack. The best combination of structures evaluated reduced the reflection loss from 3.1 mA/cm2 (planar reference) to 1.0 mA/cm2 equivalent current. Additionally, nanostructured interfaces can lead to a reduction in thermalization losses by enhancing the absorptance in the perovskite sub-cell close to the bandgap. This means that more current can be generated at a higher voltage under the assumption that current-matching is maintained and the perovskite bandgap is increased accordingly, pathing the way towards higher efficiencies. Here, the largest benefit was obtained using a structure at the upper interface. The best result yielded an increase of 4.9%rel in efficiency. A comparison to a tandem solar cell using a fully textured approach with random pyramids on silicon shows potential benefits for the suggested nanostructured approach regarding thermalization losses, while reflectance is reduced at a similar level. In addition, the applicability of the concept in the module context is shown.

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.

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.

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.

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.

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.

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.

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.

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.

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).

Plasmon enhanced upconversion luminescence near gold nanoparticles--simulation and analysis of the interactions: errata.

The procedure used in our previous publication [Opt. Express 20, 271, (2012)] to calculate how coupling to a spherical gold nanoparticle changes the upconversion luminescence of Er(3+) ions contained several errors. The errors are corrected here.

Photovoltaics at multi-terawatt scale: Waiting is not an option.

25% annual PV growth is possible over the next decade.

Electromagnetic simulations of a photonic luminescent solar concentrator.

Luminescent solar concentrators (LSC) are used in photovoltaic applications to concentrate direct and diffuse sunlight without tracking. We employed 2D FDTD simulations to investigate the concept of a photonic LSC (PLSC), where the luminescent material is embedded in a photonic crystal to mitigate the primary losses in LSCs: the escape cone and reabsorption. We obtain suppressed emission inside the photonic band gap, which can be utilized to reduce reabsorption. Furthermore, the efficiency of light guiding is strongly enhanced in a broad spectral range, reaching up to 99.7%. Our optimization of design parameters suggests emitting layers of sub-wavelength thickness.

Directionally selective light trapping in a germanium solar cell.

Restricting the angular range in which a photovoltaic system emits light, is a promising but rather unexplored approach to enhance conversion efficiency. In this paper we analyze and discuss the effect of a directionally selective filter on the absorption of light and the generation of charge carriers in a germanium solar cell. A directionally selective filter transmits photons of perpendicular incidence and reflects photons under oblique incidence in a given spectral range. To investigate its effect on light trapping, we perform reflection and quantum efficiency measurements. The reflection measurements show that a wavelength dependent absorption enhancement is induced by the application of the directionally selective filter. We calculate a maximum absorption enhancement of 45% at λ ≈ 1900 nm. We show that the absorption enhancement is caused by light trapping of non-absorbed and scattered light and is not due to a suppression of radiative processes. A trapping of photons generated by radiative recombination could not be detected. Measurements of the quantum efficiency confirm the results of the reflection measurements. The generation of charge carriers is increased by up to 33% at λ ≈1900 nm. A comparison of path length enhancement factors calculated from reflection and quantum efficiency measurements indicates a low parasitic absorption in the solar cell device.

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.