Martin Hammerschmidt

5 × 5 cm² silicon photonic crystal slabs on glass and plastic foil exhibiting broadband absorption and high-intensity near-fields.

Crystalline silicon photonic crystal slabs are widely used in various photonics applications. So far, the commercial success of such structures is still limited owing to the lack of cost-effective fabrication processes enabling large nanopatterned areas (≫ 1 cm2). We present a simple method for producing crystalline silicon nanohole arrays of up to 5 × 5 cm2 size with lattice pitches between 600 and 1000 nm on glass and flexible plastic substrates. Exclusively up-scalable, fast fabrication processes are applied such as nanoimprint-lithography and silicon evaporation. The broadband light trapping efficiency of the arrays is among the best values reported for large-area experimental crystalline silicon nanostructures. Further, measured photonic crystal resonance modes are in good accordance with light scattering simulations predicting strong near-field intensity enhancements greater than 500. Hence, the large-area silicon nanohole arrays might become a promising platform for ultrathin solar cells on lightweight substrates, high-sensitive optical biosensors, and nonlinear optics.

Implications of TCO Topography on Intermediate Reflector Design for a-Si/μc-Si Tandem Solar Cells—Experiments and Rigorous Optical Simulations

The influence of the transparent conducting oxide (TCO) topography was studied on the performance of a silicon oxide intermediate reflector layer (IRL) in a-Si/μc-Si tandem cells, both experimentally and by 3-D optical simulations. Therefore, cells with varying IRL thickness were deposited on three different types of TCOs. Clear differences were observed regarding the performance of the IRL as well as its ideal thickness, both experimentally and in the simulations. Optical modeling suggests that a small autocorrelation length is essential for a good performance. Design rules for both the TCO topography and the IRL thickness can be derived from this interplay.

Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells.

We numerically study coupling of light into silicon (Si) on glass using different square and hexagonal sinusoidal nanotextures. After describing sinusoidal nanotextures mathematically, we investigate how their design affects coupling of light into Si using a rigorous solver of Maxwells equations. We discuss nanotextures with periods between 350 nm and 1050 nm and aspect ratios up to 0.5. The maximally observed gain in the maximal achievable photocurrent density coupled into the Si absorber is 7.0 mA/cm2 and 3.6 mA/cm2 for a layer stack without and with additional antireflective silicon nitride layers, respectively. A promising application is the use as smooth anti-reflective coatings in liquid-phase crystallized Si thin-film solar cells.

Time-Harmonic Optical Chirality in Inhomogeneous Space

Optical chirality has been recently suggested to complement the physically relevant conserved quantities of the well-known Maxwells equations. This time-even pseudoscalar is expected to provide further insight in polarization phenomena of electrodynamics such as spectroscopy of chiral molecules. Previously, the corresponding continuity equation was stated for homogeneous lossless media only. We extend the underlying theory to arbitrary setups and analyse piecewise-constant material distributions in particular. Our implementation in a Finite Element Method framework is applied to illustrative examples in order to introduce this novel tool for the analysis of time-harmonic simulations of nano-optical devices.

Optical modelling of incoherent substrate light-trapping in silicon thin film multi-junction solar cells with finite elements and domain decomposition

In many experimentally realized applications, e.g. photonic crystals, solar cells and light-emitting diodes, nanophotonic systems are coupled to a thick substrate layer, which in certain cases has to be included as a part of the optical system. The finite element method (FEM) yields rigorous, high accuracy solutions of full 3D vectorial Maxwells equations1 and allows for great flexibility and accuracy in the geometrical modelling. Time-harmonic FEM solvers have been combined with Fourier methods in domain decomposition algorithms to compute coherent solutions of these coupled system.2, 3 The basic idea of a domain decomposition approach lies in a decomposition of the domain into smaller subdomains, separate calculations of the solutions and coupling of these solutions on adjacent subdomains. In experiments light sources are often not perfectly monochromatic and hence a comparision to simulation results might only be justified if the simulation results, which include interference patterns in the substrate, are spectrally averaged. In this contribution we present a scattering matrix domain decomposition algorithm for Maxwells equations based on FEM. We study its convergence and advantages in the context of optical simulations of silicon thin film multi-junction solar cells. This allows for substrate lighttrapping to be included in optical simulations and leads to a more realistic estimation of light path enhancement factors in thin-film devices near the band edge.

FEM-based optical modeling of silicon thin-film tandem solar cells with randomly textured interfaces in 3D

Light trapping techniques are one of the key research areas in thin film silicon photovoltaics. Since the 1980s randomly rough textured front transparent oxides (TCOs) have been the methods of choice as light trapping strategies for thin-film devices. Light-trapping efficiency can be optimized by means of optical simulations of nano-structured solar cells. We present a FEM based simulator for 3D rigorous optical modeling of amorphous silicon / microcrystalline silicon tandem thin-film solar cells with randomly textured layer interfaces. We focus strongly on an error analysis study for the presented simulator to demonstrate the numerical convergence of the method and investigate grid and finite element degree refinement strategies in order to obtain reliable simulation results.

Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs

Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.

On accurate simulations of thin-film solar cells with a thick glass superstrate

The optical response of periodically nanotextured layer stacks with dimensions comparable to the wavelength of the incident light can be computed with rigorous Maxwell solvers, such as the finite element method (FEM). Experimentally, such layer stacks are often prepared on glass superstrates with a thickness, which is orders of magnitude larger than the wavelength. For many applications, light in these thick superstrates can be treated incoherently. The front side of thick superstrate is located far away from the computational domain of the Maxwell solvers. Nonetheless, it has to be considered in order to achieve accurate results. In this contribution, we discuss how solutions of rigorous Maxwell solvers can be corrected for flat front sides of the superstrates with an incoherent a posteriori approach. We test these corrections for hexagonal sinusoidal nanotextured silica-silicon interfaces, which are applied in certain silicon thin-film solar cells. These corrections are determined via a scattering matrix, which contains the full scattering information of the periodically nanotextured structure. A comparison with experimental data reveals that higher-order corrections can predict the measured reflectivity of the samples much better than an often-applied zeroth-order correction.

Increased fluorescence of PbS quantum dots in photonic crystals by excitation enhancement

We report on enhanced fluorescence of lead sulfide quantum dots interacting with leaky modes of slab-type silicon photonic crystals. The photonic crystal slabs were fabricated supporting leaky modes in the near infrared wavelength range. Lead sulfite quantum dots which are resonant the same spectral range were prepared in a thin layer above the slab. We selectively excited the leaky modes by tuning wavelength and angle of incidence of the laser source and measured distinct resonances of enhanced fluorescence. By an appropriate experiment design, we ruled out directional light extraction effects and determined the impact of enhanced excitation. Three-dimensional numerical simulations consistently explain the experimental findings by strong near-field enhancements in the vicinity of the photonic crystal surface. Our study provides a basis for systematic tailoring of photonic crystals used in biological applications such as biosensing and single molecule detection, as well as quantum dot solar cells and spectral conversion applications.

Reduced basis method for Maxwell's equations with resonance phenomena

Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwells equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwells equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field.