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- ItemFrom atomistic tight-binding theory to macroscale drift–diffusion: Multiscale modeling and numerical simulation of uni-polar charge transport in (In,Ga)N devices with random fluctuations(Melville, NY : American Inst. of Physics, 2021) O’Donovan, Michael; Chaudhuri, Debapriya; Streckenbach, Timo; Farrell, Patricio; Schulz, Stefan; Koprucki, ThomasRandom alloy fluctuations significantly affect the electronic, optical, and transport properties of (In,Ga)N-based optoelectronic devices. Transport calculations accounting for alloy fluctuations currently use a combination of modified continuum-based models, which neglect to a large extent atomistic effects. In this work, we present a model that bridges the gap between atomistic theory and macroscopic transport models. To do so, we combine atomistic tight-binding theory and continuum-based drift–diffusion solvers, where quantum corrections are included via the localization landscape method. We outline the ingredients of this framework in detail and present first results for uni-polar electron transport in single and multi- (In,Ga)N quantum well systems. Overall, our results reveal that both random alloy fluctuations and quantum corrections significantly affect the current–voltage characteristics of uni-polar electron transport in such devices. However, our investigations indicate that the importance of quantum corrections and random alloy fluctuations can be different for single and multi-quantum well systems.
- ItemComparison of finite difference and finite volume simulations for a sc-drying mass transport model(Basel : MDPI AG, 2020) Selmer, Ilka; Farrell, Patricio; Smirnova, Irina; Gurikov, PavelDifferent numerical solutions of a previously developed mass transport model for supercritical drying of aerogel particles in a packed bed [Part 1: Selmer et al. 2018, Part 2: Selmer et al. 2019] are compared. Two finite difference discretizations and a finite volume method were used. The finite volume method showed a higher overall accuracy, in the form of lower overall Euclidean norm (l2) and maximum norm (l∞) errors, as well as lower mole balance errors compared to the finite difference methods. Additionally, the finite volume method was more efficient when the condition numbers of the linear systems to be solved were considered. In case of fine grids, the computation time of the finite difference methods was slightly faster but for 16 or fewer nodes the finite volume method was superior. Overall, the finite volume method is preferable for the numerical solution of the described drying model for aerogel particles in a packed bed. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
- ItemTetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Dassi, Franco; Kamenski, Lennard; Farrell, Patricio; Si, HangGiven a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.
- ItemModeling and simulation of the lateral photovoltage scanning method(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Farrell, Patricio; Kayser, Stefan; Rotundo, NellaThe fast, cheap and nondestructive lateral photovoltage scanning (LPS) method detects inhomogeneities in semiconductors crystals. The goal of this paper is to model and simulate this technique for a given doping profile. Our model is based on the semiconductor device equations combined with a nonlinear boundary condition, modelling a volt meter. To validate our 2D and 3D finite volume simulations, we use theory developed by Tauc [21] to derive three analytical predictions which our simulation results corroborate, even for anisotropic 2D and 3D meshes. Our code runs about two orders of magnitudes faster than earlier implementations based on commercial software [15]. It also performs well for small doping concentrations which previously could not be simulated at all due to numerical instabilities. Our simulations provide experimentalists with reference laser powers for which meaningful voltages can still be measured. For higher laser power the screening effect does not allow this anymore.
- ItemDetecting striations via the lateral photovoltage scanning method without screening effect(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Kayser, Stefan; Farrell, Patricio; Rotundo, NellaThe lateral photovoltage scanning method (LPS) detects doping inhomogeneities in semiconductors such as Si, Ge and Si(x)Ge(1-x) in a cheap, fast and nondestructive manner. LPS relies on the bulk photovoltaic effect and thus can detect any physical quantity affecting the band profiles of the sample. LPS finite volume simulation using commercial software suffer from long simulation times and convergence instabilities. We present here an open-source finite volume simulation for a 2D Si sample using the ddfermi simulator. For low injection conditions we show that the LPS voltage is proportional to the doping gradient as previous theory suggested under certain conditions. For higher injection conditions we directly show how the LPS voltage and the doping gradient differ and link the physical effect of lower local resolution to the screening effect. Previously, the loss of local resolution was assumed to be only connected to the enlargement of the excess charge carrier distribution.
- ItemHighly accurate quadrature-based Scharfetter-Gummel schemes for charge transport in degenerate semiconductors(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Patriarca, Matteo; Farrell, Patricio; Fuhrmann, Jürgen; Koprucki, ThomasWe introduce a family of two point flux expressions for charge carrier transport described by drift-diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoi finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newtons method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter-Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed.
- ItemAn Anisoptropic Surface Remeshing Strategy Combining Higher Dimensional Embedding with Radial Basis Functions(Amsterdam [u.a.] : Elsevier, 2016) Dassi, Franco; Farrell, Patricio; Si, HangMany applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy.
- ItemModelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Abdel, Dilara; Vágner, Petr; Fuhrmann, Jürgen; Farrell, PatricioFrom Maxwell--Stefan diffusion and general electrostatics, we derive a drift-diffusion model for charge transport in perovskite solar cells (PSCs) where any ion in the perovskite layer may flexibly be chosen to be mobile or immobile. Unlike other models in the literature, our model is based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on Fermi--Dirac, Gauss--Fermi or Blakemore statistics for example) as well as limit the ion depletion (via the Fermi--Dirac integral of order-1). The latter will be motivated by a grand-canonical formalism of ideal lattice gas. Furthermore, our model allows to use different statistics for different species. We discuss the thermodynamic equilibrium, electroneutrality as well as generation/recombination. Finally, we present numerical finite volume simulations to underline the importance of limiting ion depletion.
- ItemChallenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Farrell, Patricio; Peschka, DirkWe analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.
- ItemComputational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Farrell, Patricio; Koprucki, Thomas; Fuhrmann, JürgenFor a Voronoi finite volume discretization of the van Roosbroeck system with general charge carrier statistics we compare three thermodynamically consistent numerical fluxes known in the literature. We discuss an extension of the Scharfetter-Gummel scheme to non-Boltzmann (e.g. Fermi-Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.