Weierstrass Institute WIAS

Berlin, Germany

Weierstrass Institute WIAS

Berlin, Germany
SEARCH FILTERS
Time filter
Source Type

Kohlhase M.,Informatik | Koprucki T.,Weierstrass Institute WIAS | Muller D.,Informatik | Tabelow K.,Weierstrass Institute WIAS
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2017

Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open. In this paper we propose a solution - to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexiformal framework, which has enough structure to support the various uses of models in scientific and technology workflows. Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but non-trivial model: van Roosbroeck’s driftdiffusion model for one-dimensional devices. This formalization - and future extensions - allows us to support the modeler by e.g., flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating mathematical models as “research data” and opens the way towards more MKM services for models. © Springer International Publishing AG 2017.


Farrell P.,Weierstrass Institute WIAS | Koprucki T.,Weierstrass Institute WIAS | Fuhrmann J.,Weierstrass Institute WIAS
Journal of Computational Physics | Year: 2017

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes 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. © 2017 Elsevier Inc.


Peschka D.,Weierstrass Institute WIAS | Thomas M.,Weierstrass Institute WIAS | Glitzky A.,Weierstrass Institute WIAS | Nurnberg R.,Weierstrass Institute WIAS | And 5 more authors.
Optical and Quantum Electronics | Year: 2016

We consider a device concept for edge-emitting lasers based on strained germanium microstrips. The device features an inhomogeneous tensile strain distribution generated by a SiN stressor deposited on top of the Ge microstrip. This geometry requires a lateral contact scheme and hence a full two-dimensional description. The two-dimensional simulations of the carrier transport and of the optical field, carried out in a cross section of the device orthogonal to the optical cavity, use microscopic calculations of the strained Ge material gain as an input. In this paper we study laser performance and robustness against Shockley–Read–Hall lifetime variations and device sensitivity to different strain distributions. © 2016, Springer Science+Business Media New York.


Peschka D.,Weierstrass Institute WIAS | Thomas M.,Weierstrass Institute WIAS | Glitzky A.,Weierstrass Institute WIAS | Nurnberg R.,Weierstrass Institute WIAS | And 6 more authors.
Proceedings of the International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD | Year: 2015

We consider a device concept for edge-emitting lasers based on strained germanium (Ge) microstrips. The special SiN stressor design induces an inhomogeneous (tensile) strain distribution and requires lateral current injection. Microscopic calculations of the material gain for strained Ge enter our two-dimensional simulation of the carrier transport and of the optical field within a cross section of the device orthogonal to the optical cavity. We study the optoelectronic properties of the device concept for two different carrier injection schemes. © 2015 IEEE.


Fischer A.,TU Dresden | Koprucki T.,Weierstrass Institute WIAS | Glitzky A.,Weierstrass Institute WIAS | Liero M.,Weierstrass Institute WIAS | And 8 more authors.
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2015

Large area OLEDs show pronounced Joule self-heating at high brightness. This heating induces brightness inhomogeneities, drastically increasing beyond a certain current level. We discuss this behavior considering 'S'-shaped negative differential resistance upon self-heating, even allowing for 'switched-back' regions where the luminance finally decreases (Fischer et al., Adv. Funct. Mater. 2014, 24, 3367). By using a multi-physics simulation the device characteristics can be modeled, resulting in a comprehensive understanding of the problem. Here, we present results for an OLED lighting panel considered for commercial application. It turns out that the strong electrothermal feedback in OLEDs prevents high luminance combined with a high degree of homogeneity unless new optimization strategies are considered. © 2015 SPIE.


Koprucki T.,Weierstrass Institute WIAS | Gartner K.,Weierstrass Institute WIAS
Optical and Quantum Electronics | Year: 2013

Inspired by organic semiconductor models based on hopping transport introducing Gauss-Fermi integrals a nonlinear generalization of the classical Scharfetter-Gummel scheme is derived for the distribution function F γ(η) = 1/(\exp (-η)+γ). This function provides an approximation of the Fermi-Dirac integrals of different order and restricted argument ranges. The scheme requires the solution of a nonlinear equation per edge and continuity equation to calculate the edge currents. In the current formula the density-dependent diffusion enhancement factor, resulting from the generalized Einstein relation, shows up as a weighting factor. Additionally the current modifies the argument of the Bernoulli functions. © 2013 Springer Science+Business Media New York.


Glitzky A.,Weierstrass Institute WIAS | Gartner K.,Weierstrass Institute WIAS | Fuhrmann J.,Weierstrass Institute WIAS | Koprucki T.,Weierstrass Institute WIAS | And 4 more authors.
13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013 | Year: 2013

We discuss self-heating of organic semiconductor devices based on Arrhenius-like conductivity laws. The self-consistent calculation of charge and heat transport explains thermal switching, bistability, and hysteresis resulting from S-shaped current-voltage curves with regions of negative differential resistance (NDR). For large area thin film organic devices we study the appearance of a spatially localized NDR region and the spatial evolution of this NDR region in dependence on the total current. We propose that in organic light emitting diodes (OLEDs) these effects are responsible for spatially inhomogeneous current flow and inhomogeneous luminance at high power. © 2013 IEEE.


Koprucki T.,Weierstrass Institute WIAS | Gartner K.,Weierstrass Institute WIAS
13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013 | Year: 2013

For Blakemore-type distribution functions F(η) = 1/(exp(-η) +γ) describing the carrier density in semiconductors a generalization of the classical Scharfetter-Gummel scheme can be derived resulting in a nonlinear equation per edge to calculate the edge current. This approach provides a good approximation of the carrier density in degenerate semiconductors for values of the chemical potential η < 1.3kBT. We discuss an extension of this approach based on a piecewise approximation of the distribution function by functions of that type in order improve the approximation for larger values of the chemical potential. © 2013 IEEE.


Koprucki T.,Weierstrass Institute WIAS | Rotundo N.,Weierstrass Institute WIAS | Farrell P.,Weierstrass Institute WIAS | Doan D.H.,Weierstrass Institute WIAS | Fuhrmann J.,Weierstrass Institute WIAS
Optical and Quantum Electronics | Year: 2015

Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with arbitrary statistical distribution functions. This requires numerical schemes that preserve qualitative properties of the solutions, such as positivity of densities, dissipativity and consistency with thermodynamic equilibrium. An extension of the Scharfetter–Gummel scheme guaranteeing consistency with thermodynamic equilibrium is studied. It is derived by replacing the thermal voltage with an averaged diffusion enhancement for which we provide a new explicit formula. This approach avoids solving the costly local nonlinear equations defining the current for generalized Scharfetter–Gummel schemes. © 2014, Springer Science+Business Media New York.


Koprucki T.,Weierstrass Institute WIAS | Tabelow K.,Weierstrass Institute WIAS
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2016

Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines and application areas. It is common to categorize the involved numerical data and to some extend the corresponding scientific software as research data. Both have their origin in mathematical models. In this contribution we propose a holistic approach to research data in MMS by including the mathematical models and discuss the initial requirements for a conceptual data model for this field. © Springer International Publishing Switzerland 2016.

Loading Weierstrass Institute WIAS collaborators
Loading Weierstrass Institute WIAS collaborators