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- ItemOperation mechanism of high performance organic permeable base transistors with an insulated and perforated base electrode(Melville, NY : American Inst. of Physics, 2016) Kaschura, Felix; Fischer, Axel; Klinger, Markus P.; Doan, Duy Hai; Koprucki, Thomas; Glitzky, Annegret; Kasemann, Daniel; Widmer, Johannes; Leo, KarlThe organic permeable base transistor is a vertical transistor architecture that enables high performance while maintaining a simple low-resolution fabrication. It has been argued that the charge transport through the nano-sized openings of the central base electrode limits the performance. Here, we demonstrate by using 3D drift-diffusion simulations that this is not the case in the relevant operation range. At low current densities, the applied base potential controls the number of charges that can pass through an opening and the opening is the current limiting factor. However, at higher current densities, charges accumulate within the openings and in front of the base insulation, allowing for an efficient lateral transport of charges towards the next opening. The on-state in the current-voltage characteristics reaches the maximum possible current given by space charge limited current transport through the intrinsic semiconductor layers. Thus, even a small effective area of the openings can drive huge current densities, and further device optimization has to focus on reducing the intrinsic layer thickness to a minimum.
- ItemEfficient Current Injection Into Single Quantum Dots Through Oxide-Confined p-n-Diodes(New York, NY : IEEE, 2016) Kantner, Markus; Bandelow, Uwe; Koprucki, Thomas; Schulze, Jan-Hindrik; Strittmatter, Andre; Wunsche, Hans-JurgenCurrent injection into single quantum dots embedded in vertical p-n-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. The experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional p-i-n-design. By an alternative design employing p-doping up to the oxide aperture, the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.
- ItemOn thermodynamic consistency of a Scharfetter-Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Koprucki, Thomas; Rotundo, Nella; Farrell, Patricio; Doan, Duy Hai; Fuhrmann, JürgenDriven 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.
- ItemFeel the heat: Nonlinear electrothermal feedback in organic LEDs(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fischer, Axel; Koprucki, Thomas; Gärtner, Klaus; Tietze, Max L.; Brückner, Jacqueline; Lüssem, Björn; Leo, Karl; Glitzky, Annegret; Scholz, ReinhardFor lighting applications, Organic light-emitting diodes (OLED) need much higher brightness than for displays, leading to self-heating. Due to the temperature-activated transport in organic semiconductors, this can result in brightness inhomogeneities and catastrophic failure. Here, we show that due to the strong electrothermal feedback of OLEDs, the common spatial current and voltage distribution is completely changed, requiring advanced device modeling and operation concepts. Our study clearly demonstrates the effect of negative differential resistance (NDR) in OLEDs induced by self-heating. As a consequence, for increasing voltage, regions with declining voltages are propagating through the device, and even more interestingly, a part of these regions show even decreasing currents, leading to strong local variation in luminance. The expected breakthrough of OLED lighting technology will require an improved price performance ratio, and the realization of modules with very high brightness but untainted appearance is considered to be an essential step into this direction. Thus, a deeper understanding of the control of electrothermal feedback will help to make OLEDs in lighting more competitive.
- ItemInfluence of the carrier reservoir dimensionality on electron-electron scattering in quantum dot materials(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Wilms, Alexander; Mathé, Peter; Schulze, Franz; Koprucki, Thomas; Knorr, Andreas; Bandelow, UweWe calculated Coulomb scattering rates from quantum dots (QDs) coupled to a 2D carrier reservoir and QDs coupled to a 3D reservoir. For this purpose, we used a microscopic theory in the limit of Born-Markov approximation, in which the numerical evaluation of high dimensional integrals is done via a quasi-Monte Carlo method. Via a comparison of the so determined scattering rates, we investigated the question whether scattering from 2D is generally more efficient than scattering from 3D. In agreement with experimental findings, we did not observe a significant reduction of the scattering efficiency of a QD directly coupled to a 3D reservoir. In turn, we found that 3D scattering benefits from it’s additional degree of freedom in the momentum space
- ItemConvergence of a finite volume scheme to the eigenvalues of a Schrödinger operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Koprucki, Thomas; Eymard, Robert; Fuhrmann, JürgenWe consider the approximation of a Schrödinger eigenvalue problem arising from the modeling of semiconductor nanostructures by a finite volume method in a bounded domain $OmegasubsetR^d$. In order to prove its convergence, a framework for finite dimensional approximations to inner products in the Sobolev space $H^1_0(Omega)$ is introduced which allows to apply well known results from spectral approximation theory. This approach is used to obtain convergence results for a classical finite volume scheme for isotropic problems based on two point fluxes, and for a finite volume scheme for anisotropic problems based on the consistent reconstruction of nodal fluxes. In both cases, for two- and three-dimensional domains we are able to prove first order convergence of the eigenvalues if the corresponding eigenfunctions belong to $H^2(Omega)$. The construction of admissible meshes for finite volume schemes using the Delaunay-Voronoï method is discussed. As numerical examples, a number of one-, two- and three-dimensional problems relevant to the modeling of semiconductor nanostructures is presented. In order to obtain analytical eigenvalues for these problems, a matching approach is used. To these eigenvalues, and to recently published highly accurate eigenvalues for the Laplacian in the L-shape domain, the results of the implemented numerical method are compared. In general, for piecewise $H^2$ regular eigenfunctions, second order convergence is observed experimentally.
- ItemMathematical models: A research data category?(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Koprucki, Thomas; Tabelow, KarstenMathematical 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.
- Item3D electrothermal simulations of organic LEDs showing negative differential resistance(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Liero, Matthias; Fuhrmann, Jürgen; Glitzky, Annegret; Koprucki, Thomas; Fischer, Axel; Reineke, SebastianOrganic semiconductor devices show a pronounced interplay between temperature-activated conductivity and self-heating which in particular causes inhomogeneities in the brightness of large-area OLEDs at high power. We consider a 3D thermistor model based on partial differential equations for the electrothermal behavior of organic devices and introduce an extension to multiple layers with nonlinear conductivity laws, which also take the diode-like behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finite-volume approximation of this model. The appearance of S-shaped current-voltage characteristics with regions of negative differential resistance in a measured device can be quantitatively reproduced. Furthermore, this simulation study reveals a propagation of spatial zones of negative differential resistance in the electron and hole transport layers toward the contact.
- ItemReproducible research through persistently linked and visualized data(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Drees, Bastian; Kraft, Angelina; Koprucki, ThomasThe demand of reproducible results in the numerical simulation of opto-electronic devices or more general in mathematical modeling and simulation requires the (long-term) accessibility of data and software that were used to generate those results. Moreover, to present those results in a comprehensible manner data visualizations such as videos are useful. Persistent identifier can be used to ensure the permanent connection of these different digital objects thereby preserving all information in the right context. Here we give an overview over the state-of-the art of data preservation, data and software citation and illustrate the benefits and opportunities of enhancing publications with visual simulation data by showing a use case from opto-electronics.
- Itemp-Laplace thermistor modeling of electrothermal feedback in organic semiconductors(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Liero, Matthias; Koprucki, Thomas; Fischer, Axel; Scholz, Reinhard; Glitzky, AnnegretIn large-area Organic Light-Emitting Diodes (OLEDs) spatially inhomogeneous luminance at high power due to inhomogeneous current flow and electrothermal feedback can be observed. To describe these self-heating effects in organic semiconductors we present a stationary thermistor model based on the heat equation for the temperature coupled to a p-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p-Laplacian describes the non-Ohmic electrical behavior of the organic material. Moreover, an Arrhenius-like temperature dependency of the electrical conductivity is considered. We introduce a finite-volume scheme for the system and discuss its relation to recent network models for OLEDs. In two spatial dimensions we derive a priori estimates for the temperature and the electrostatic potential and prove the existence of a weak solution by Schauder's fixed point theorem.
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