Modern semiconductor devices and optoelectronic devices such as semiconductor lasers or solar cells are based on semiconductor structures, which e.g. can be given by doping profiles, hetero or nanostructures. For the qualitative and quantitative understanding of the properties of these devices, mathematical modeling and simulation of the most relevant and, respectively, of the limiting carrier transport processes is necessary.
Current research also focuses on the improvement of energy efficiency of new devices and the development of novel technologies for applications in renewable energies, communication, and lighting. This topic, which is also called Green Photonics, is one of the essential technological challenges for the coming years. The Weierstrass Institute actively contributes to the fundamental and applicationdriven research and development of novel solutions.
Driftdiffusion models are well established for the description of carrier transport in semiconductor devices. The van Roosbroeck system is the basic model. It describes the motion of negatively and positively charged carriers (electrons and holes) in a selfconsistent electrical field by drift and diffusion.
On the one hand, the research in this application area is focused on the development and investigation of mathematical modeling approaches for taking into account additional important physical effects. On the other hand, the emphasis is on the development of fast and robust numerical methods for the solution of the coupled model equations. The particular research goals often arise from challenging problems of collaborators.
The Weierstrass Institute has a long tradition in mathematical modeling and numerical simulation of semiconductor materials. Many analytical results for the systems of partial differential equations that describe the behavior of complex semiconductor structures have been published in the past and also several software packages have been developed: WIASTeSCA, WIASQW, ddfermi.
However, new technologies are changing fast and they require new methodologies. At WIAS different aspects are nowadays under consideration:
 New tools for the mathematical analysis such as gradient structures
 Further analytical results for coupled models like for example transport equations coupled with quantum mechanical system
 New mathematical models for innovative materials: organic semiconductors (see Matheon project SE2)
 Study of different numerical schemes which can deal with specific physical situations for example cryogenic temperature
 Development of a new simulation software: ddfermi
 Doping and topology optimization (see Matheon project OT1)

P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, Th. Koprucki, Chapter 50: DriftDiffusion Models, in: Vol. 2 of Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 733771, (Chapter Published).

H.Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci, eds., PDE 2015: Theory and Applications of Partial Differential Equations, 10 of Discrete and Continuous Dynamical Systems  Series S, American Institute of Mathematical Science, Springfield, 2017, iv+933 pages, (Collection Published).

A. Zisowsky, A. Arnold, M. Ehrhardt, Th. Koprucki, Chapter 7: Transient Simulation of k$cdot$pSchrödinger Systems Using Discrete Transparent Boundary Conditions, in: MultiBand Effective Mass Approximations  Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 247272, (Chapter Published).

D. Klindworth, M. Ehrhardt, Th. Koprucki, Chapter 8: Discrete Transparent Boundary Conditions for Multiband Effective Mass Approximations, in: MultiBand Effective Mass Approximations  Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 273318, (Chapter Published).

M. Ehrhardt, Th. Koprucki, eds., MultiBand Effective Mass Approximations  Advanced Mathematical Models and Numerical Techniques, 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, xvi+318 pages, (Monograph Published).

U. Bandelow, H. Gajewski, R. Hünlich, Chapter 3: FabryPerot Lasers: Thermodynamicsbased Modeling, in: Optoelectronic Devices  Advanced Simulation and Analysis, J. Piprek, ed., Springer, New York, 2005, pp. 6385, (Chapter Published).

L. Adam, M. Hintermüller, D. Peschka, Th.M. Surowiec, Optimization of a multiphysics problem in semiconductor laser design, SIAM Journal on Applied Mathematics, 79 (2019), pp. 257283, DOI 10.1137/18M1179183 .
Abstract
A multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a GeonSi microbridge are given. The highly favorable electronic properties of this design are demonstrated by steadystate simulations of the corresponding van Roosbroeck (driftdiffusion) system. 
J. Lähnemann, M.O. Hill, J. Herranz, O. Marquardt, G. Gao, A. Al Hassan, A. Davtyan, S.O. Hruszkewycz, M.V. Holt, Ch. Huang, I. CalvoAlmazán, U. Jahn, U. Pietsch, L.J. Lauhon, L. Geelhaar, Correlated nanoscale analysis of the emission from wurtzite versus zincblende (In,Ga)As/GaAs nanowire coreshell quantum wells, ACS Nano, 19 (2019), pp. 44484457, DOI 10.1021/acs.nanolett.9b01241 .
Abstract
While the properties of wurtzite GaAs have been extensively studied during the past decade, little is known about the influence of the crystal polytype on ternary (In,Ga)As quantum well structures. We address this question with a unique combination of correlated, spatially resolved measurement techniques on coreshell nanowires that contain extended segments of both the zincblende and wurtzite polytypes. Cathodoluminescence hyperspectral imaging reveals a blueshift of the quantum well emission energy by 75 ± 15 meV in the wurtzite polytype segment. Nanoprobe Xray diffraction and atom probe tomography enable k•p calculations for the specific sample geometry to reveal two comparable contributions to this shift. First, there is a 30% drop in In mole fraction going from the zincblende to the wurtzite segment. Second, the quantum well is under compressive strain, which has a much stronger impact on the hole ground state in the wurtzite than in the zincblende segment. Our results highlight the role of the crystal structure in tuning the emission of (In,Ga)As quantum wells and pave the way to exploit the possibilities of threedimensional band gap engineering in coreshell nanowire heterostructures. At the same time, we have demonstrated an advanced characterization toolkit for the investigation of semiconductor nanostructures. 
A. Glitzky, M. Liero, Instationary driftdiffusion problems with GaussFermi statistics and fielddependent mobility for organic semiconductor devices, Communications in Mathematical Sciences, 17 (2019), pp. 3359, DOI 10.4310/cms.2019.v17.n1.a2 .
Abstract
This paper deals with the analysis of an instationary driftdiffusion model for organic semiconductor devices including GaussFermi statistics and applicationspecific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent energetic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength. To prove the existence of global weak solutions, we consider a problem with (for small densities) regularized state equations on any arbitrarily chosen finite time interval. We ensure its solvability by time discretization and passage to the timecontinuous limit. Positive lower a priori estimates for the densities of its solutions that are independent of the regularization level ensure the existence of solutions to the original problem. Furthermore, we derive for these solutions global positive lower and upper bounds strictly below the density of transport states for the densities. The estimates rely on Moser iteration techniques. 
P. Farrell, D. Peschka, Challenges for driftdiffusion simulations of semiconductors: A comparative study of different discretization philosophies, Computers & Mathematics with Applications. An International Journal, published online on 18.06.2019, DOI 10.1016/j.camwa.2019.06.007 .
Abstract
We analyze and benchmark the error and the convergence order of finite difference, finiteelement as well as Voronoi finitevolume discretization schemes for the driftdiffusion 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 Lshaped 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. 
D. Peschka, N. Rotundo, M. Thomas, Doping optimization for optoelectronic devices, Optical and Quantum Electronics, 50 (2018), pp. 125/1125/9, DOI 10.1007/s1108201813934 .
Abstract
We present a mathematical and numerical framework for the optimal design of doping profiles for optoelectronic devices using methods from mathematical optimization. With the goal to maximize light emission and reduce the threshold of an edgeemitting laser, we consider a driftdiffusion model for charge transport and include modal gain and total current into a cost functional, which we optimize in cross sections of the emitter. We present 1D and 2D results for exemplary setups that point out possible routes for device improvement. 
A.W. Achtstein, O. Marquardt, R. Scott, M. Ibrahim, Th. Riedl, A.V. Prudnikau, A. Antanovich, N. Owchimikow, J.K.N. Lindner, M. Artemyev, U. Woggon, Impact of shell growth on recombination dynamics and excitonphonon interaction in CdSeCdS coreshell nanoplatelets, ACS Nano, 12 (2018), pp. 94769483, DOI 10.1021/acsnano.8b04803 .

A. Fischer, M. Pfalz, K. Vandewal, M. Liero, A. Glitzky, S. Lenk, S. Reineke, Full electrothermal OLED model including nonlinear selfheating effects, Physical Review Applied, 10 (2018), pp. 014023/1014023/12, DOI 10.1103/PhysRevApplied.10.014023 .
Abstract
Organic lightemitting diodes (OLEDs) are widely studied semiconductor devices for which a simple description by a diode equation typically fails. In particular, a full description of the currentvoltage relation, including temperature effects, has to take the low electrical conductivity of organic semiconductors into account. Here, we present a temperaturedependent resistive network, incorporating recombination as well as electron and hole conduction to describe the currentvoltage characteristics of an OLED over the entire operation range. The approach also reproduces the measured nonlinear electrothermal feedback upon Joule selfheating in a selfconsistent way. Our model further enables us to learn more about internal voltage losses caused by the charge transport from the contacts to the emission layer which is characterized by a strong temperatureactivated electrical conductivity, finally determining the strength of the electrothermal feedback. In general, our results provide a comprehensive picture to understand the electrothermal operation of an OLED which will be essential to ensure and predict especially longterm stability and reliability in superbright OLED applications. 
J. Haskovec, S. Hittmeir, P. Markowich, A. Mielke, Decay to equilibrium for energyreactiondiffusion systems, SIAM Journal on Mathematical Analysis, 50 (2018), pp. 10371075, DOI 10.1137/16M1062065 .
Abstract
We derive thermodynamically consistent models of reactiondiffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusionreaction bipolar energy transport system, and a driftdiffusionreaction energy transport system with confining potential. We prove corresponding entropyentropy production inequalities with explicitely calculable constants and establish the convergence to thermodynamical equilibrium, at first in entropy and further in L^{1} using CziszarKullbackPinsker type inequalities. 
F.M. Sawatzki, D.H. Doan, H. Kleemann, M. Liero, A. Glitzky, Th. Koprucki, K. Leo, Balance of horizontal and vertical charge transport in organic fieldeffect transistors, Physical Review Applied, 10 (2018), pp. 034069/1034069/10, DOI 10.1103/PhysRevApplied.10.034069 .
Abstract
Highperformance organic fieldeffect transistors (OFETs) are an essential building block for future flexible electronics. Although there has been steady progress in the development of highmobility organic semiconductors, the performance of lateral stateoftheart OFETs still falls short, especially with regard to the transition frequency. One candidate to overcome the shortcomings of the lateral OFET is its vertical embodiment, the vertical organic fieldeffect transistor (VOFET). However, the detailed mechanism of VOFET operation is poorly understood and a matter of discussion. Proposed descriptions of the formation and geometry of the vertical channel vary significantly. In particular, values for lateral depth of the vertical channel reported so far show a large variation. This is an important question for the transistor integration, though, since a channel depth in the micrometer range would severely limit the possible integration density. Here, we investigate charge transport in such VOFETs via driftdiffusion simulations and experimental measurements. We use a (vertical) organic lightemitting transistor ((V)OLET) as a means to map the spatial distribution of charge transport within the vertical channel. Comparing simulation and experiment, we can conclusively describe the operation mechanism which is mainly governed by an accumulation of charges at the dielectric interface and the channel formation directly at the edge of the source electrode. In particular, we quantitatively describe how the channel depth depends on parameters such as gatesource voltage, drainsource voltage, and lateral and vertical mobility. Based on the proposed operation mechanism, we derive an analytical estimation for the lateral dimensions of the channel, helping to predict an upper limit for the integration density of VOFETs. 
P. Corfdir, H. Li, O. Marquardt, G. Gao, M.R. Molas, J.K. Zettler, D. VAN Treeck, T. Flissikowski, M. Potemski, C. Draxl, A. Trampert, S. FernándezGarrido, H.T. Grahn, O. Brandt, Crystalphase quantum wires: Onedimensional heterostructures with atomically flat interfaces, Nano Letters, 18 (2018), pp. 247254, DOI 10.1021/acs.nanolett.7b03997 .

P. Corfdir, O. Marquardt, R.B. Lewis , Ch. Sinito, M. Ramsteiner, A. Trampert, U. Jahn, L. Geelhaar, O. Brandt, W.M. Fomin, Excitonic AharonovBohm oscillations in coreshell nanowires, Advanced Materials, 31 (2019), pp. 1805645/11805645/6 (published online on 20.11.2018), DOI 10.1002/adma.201805645 .

P. Farrell, M. Patriarca, J. Fuhrmann, Th. Koprucki, Comparison of thermodynamically consistent charge carrier flux discretizations for FermiDirac and GaussFermi statistics, Optical and Quantum Electronics, 50 (2018), pp. 101/1101/10, DOI 10.1007/s1108201813498 .
Abstract
We compare three thermodynamically consistent ScharfetterGummel schemes for different distribution functions for the carrier densities, including the FermiDirac integral of order 1/2 and the GaussFermi integral. The most accurate (but unfortunately also most costly) generalized ScharfetterGummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newton's method. We discuss the quality of this approximation and plot the resulting currents for FermiDirac and GaussFermi statistics. Finally, by comparing two modified (diffusionenhanced and inverse activity based) ScharfetterGummel schemes with the more accurate generalized scheme, we show that the diffusionenhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497513, 2017). 
P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on unstructured 1D grids for a singularly perturbed advectiondiffusion equation and some multidimensional extensions, Journal of Scientific Computing, 72 (2017), pp. 373395, DOI 10.1007/s1091501703617 .
Abstract
The accurate and efficient discretization of singularly perturbed advectiondiffusion equations on arbitrary 2D and 3D domains remains an open problem. An interesting approach to tackle this problem is the complete flux scheme (CFS) proposed by G. D. Thiart and further investigated by J. ten Thije Boonkkamp. For the CFS, uniform second order convergence has been proven on structured grids. We extend a version of the CFS to unstructured grids for a steady singularly perturbed advectiondiffusion equation. By construction, the novel finite volume scheme is nodally exact in 1D for piecewise constant source terms. This property allows to use elegant continuous arguments in order to prove uniform second order convergence on unstructured onedimensional grids. Numerical results verify the predicted bounds and suggest that by aligning the finite volume grid along the velocity field uniform second order convergence can be obtained in higher space dimensions as well. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantumclassical modeling of quantum dot devices, Phys. Rev. B., 96 (2017), pp. 205301/1205301/17, DOI 10.1103/PhysRevB.96.205301 .
Abstract
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantumclassical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven singlephoton source based on a single quantum dot in the stationary and transient operation regime. 
O. Marquardt, Th. Krause, V. Kaganer, J. MartinSánchez, M. Hanke, O. Brandt, Influence of strain relaxation in axial $In_xGa_1xN/GaN$ nanowire heterostructures on their electronic properties, Nanotechnology, 28 (2017), pp. 215204/1215204/6, DOI 10.1088/13616528/aa6b73 .
Abstract
We present a systematic theoretical study of the influence of elastic strain relaxation on the builtin electrostatic potentials and the electronic properties of axial In_{x}Ga_{1x}N/GaN nanowire (NW) heterostructures. Our simulations reveal that for a sufficiently large ratio between the thickness of the In_{x}Ga_{1x}N disk and the diameter of the NW, the elastic relaxation leads to a significant reduction of the builtin electrostatic potential in comparison to a planar system of similar layer thickness and In content. In this case, the ground state transition energies approach constant values with increasing thickness of the disk and only depend on the In content, a behavior usually associated to that of a quantum well free of builtin electrostatic potentials. We show that the structures under consideration are by no means fieldfree, and the builtin potentials continue to play an important role even for ultrathin NWs. In particular, strain and the resulting polarization potentials induce complex confinement features of electrons and holes, which depend on the In content, shape, and dimensions of the heterostructure. 
O. Marquardt, M. Ramsteiner, P. Corfdir, L. Geelhaar, O. Brandt, Modeling the electronic properties of GaAs polytype nanostructures: Impact of strain on the conduction band character, Phys. Rev. B., 95 (2017), pp. 245309/1245309/8, DOI 10.1103/PhysRevB.95.245309 .
Abstract
We study the electronic properties of GaAs nanowires composed of both the zincblende and wurtzite modifications using a tenband kp model. In the wurtzite phase, two energetically close conduction bands are of importance for the confinement and the energy levels of the electron ground state. These bands form two intersecting potential landscapes for electrons in zincblende/wurtzite nanostructures. The energy difference between the two bands depends sensitively on strain, such that even small strains can reverse the energy ordering of the two bands. This reversal may already be induced by the nonnegligible lattice mismatch between the two crystal phases in polytype GaAs nanostructures, a fact that was ignored in previous studies of these structures. We present a systematic study of the influence of intrinsic and extrinsic strain on the electron ground state for both purely zincblende and wurtzite nanowires as well as for polytype superlattices. The coexistence of the two conduction bands and their opposite strain dependence results in complex electronic and optical properties of GaAs polytype nanostructures. In particular, both the energy and the polarization of the lowest intersubband transition depends on the relative fraction of the two crystal phases in the nanowire. 
M. Mittnenzweig, A. Mielke, An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models, Journal of Statistical Physics, 167 (2017), pp. 205233, DOI 10.1007/s1095501717564 .
Abstract
We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finitedimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems. 
M. Sawatzki, A.A. Hauke, D.H. Doan, P. Formanek, D. Kasemann, Th. Koprucki, K. Leo, On razors edge: Influence of the source insulator edge on the charge transport of vertical organic field effect transistors, MRS Advances, 2 (2017), pp. 12491257, DOI 10.1557/adv.2017.29 .
Abstract
To benefit from the many advantages of organic semiconductors like flexibility, transparency, and small thickness, electronic devices should be entirely made from organic materials. This means, additionally to organic LEDs, organic solar cells, and organic sensors, we need organic transistors to amplify, process, and control signals and electrical power. The standard lateral organic field effect transistor (OFET) does not offer the necessary performance for many of these applications. One promising candidate for solving this problem is the vertical organic field effect transistor (VOFET). In addition to the altered structure of the electrodes, the VOFET has one additional part compared to the OFET  the sourceinsulator. However, the influence of the used material, the size, and geometry of this insulator on the behavior of the transistor has not yet been examined. We investigate keyparameters of the VOFET with different source insulator materials and geometries. We also present transmission electron microscopy (TEM) images of the edge area. Additionally, we investigate the charge transport in such devices using driftdiffusion simulations and the concept of a vertical organic light emitting transistor (VOLET). The VOLET is a VOFET with an embedded OLED. It allows the tracking of the local current density by measuring the light intensity distribution.
We show that the insulator material and thickness only have a small influence on the performance, while there is a strong impact by the insulator geometry  mainly the overlap of the insulator into the channel. By tuning this overlap, on/offratios of 9x10^{5} without contact doping are possible, 
A. Glitzky, M. Liero, Analysis of p(x)Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 34 (2017), pp. 536562.
Abstract
We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring nonOhmic currentvoltage laws and selfheating effects. The coupled system consists of the currentflow equation for the electrostatic potential and the heat equation with Joule heating term as source. The selfheating in the device is modeled by an Arrheniuslike temperature dependency of the electrical conductivity. Moreover, the nonOhmic electrical behavior is modeled by a power law such that the electrical conductivity depends nonlinearly on the electric field. Notably, we allow for functional substructures with different power laws, which gives rise to a $p(x)$Laplacetype problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the twodimensional case. The crucial point is to establish the higher integrability of the gradient of the electrostatic potential to tackle the Joule heating term. The proof of the improved regularity is based on Caccioppolitype estimates, Poincaré inequalities, and a Gehringtype Lemma for the $p(x)$Laplacian. Finally, Schauder's fixedpoint theorem is used to show the existence of solutions. 
A. Caiazzo, F. Caforio, G. Montecinos, L.O. Müller, P.J. Blanco, E.F. Toro, Assessment of reduced order Kalman filter for parameter identification in onedimensional blood flow models using experimental data, International Journal of Numerical Methods in Biomedical Engineering, 33 (2017), pp. e2843/1e2843/26, DOI 10.1002/cnm.2843 .
Abstract
This work presents a detailed investigation of a parameter estimation approach based on the reduced order unscented Kalman filter (ROUKF) in the context of onedimensional blood flow models. In particular, the main aims of this study are (i) to investigate the effect of using real measurements vs. synthetic data (i.e., numerical results of the same in silico model, perturbed with white noise) for the estimation and (ii) to identify potential difficulties and limitations of the approach in clinically realistic applications in order to assess the applicability of the filter to such setups. For these purposes, our numerical study is based on the in vitro model of the arterial network described by [Alastruey et al. 2011, J. Biomech. bf 44], for which experimental flow and pressure measurements are available at few selected locations. In order to mimic clinically relevant situations, we focus on the estimation of terminal resistances and arterial wall parameters related to vessel mechanics (Young's modulus and thickness) using few experimental observations (at most a single pressure or flow measurement per vessel). In all cases, we first perform a theoretical identifiability analysis based on the generalized sensitivity function, comparing then the results obtained with the ROUKF, using either synthetic or experimental data, to results obtained using reference parameters and to available measurements. 
P. Farrell, Th. Koprucki, J. Fuhrmann, Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics, Journal of Computational Physics, 346 (2017), pp. 497513, DOI 10.1016/j.jcp.2017.06.023 .
Abstract
For a Voronoï 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 ScharfetterGummel scheme to nonBoltzmann (e.g. FermiDirac) statistics. It is based on the analytical solution of a twopoint 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 nonBoltzmann 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 pin 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. 
M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, 3D electrothermal simulations of organic LEDs showing negative differential resistance, Optical and Quantum Electronics, 49 (2017), pp. 330/1330/8, DOI 10.1007/s1108201711674 .
Abstract
Organic semiconductor devices show a pronounced interplay between temperatureactivated conductivity and selfheating which in particular causes inhomogeneities in the brightness of largearea 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 diodelike behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finitevolume approximation of this model. The appearance of Sshaped currentvoltage 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. 
M. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Optical and Quantum Electronics, 48 (2016), pp. 543/1543/7, DOI 10.1007/s1108201608172 .
Abstract
At cryogenic temperatures the electron?hole plasma in semiconductors becomes strongly degenerate, leading to very sharp internal layers, extreme depletion in intrinsic domains and strong nonlinear diffusion. As a result, the numerical simulation of the drift?diffusion system suffers from serious convergence issues using standard methods. We consider a onedimensional pin diode to illustrate these problems and present a simple temperatureembedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forwardbiased devices as they appear e.g. in optoelectronic applications. Moreover, the method can be applied to wide band gap semiconductors where similar numerical issues occur already at room temperature. 
M. Kantner, U. Bandelow, Th. Koprucki, J.H. Schulze, A. Strittmatter, H.J. Wünsche, Efficient current injection into single quantum dots through oxideconfined pndiodes, IEEE Transactions on Electron Devices, 63 (2016), pp. 20362042.
Abstract
Current injection into single quantum dots embedded in vertical pndiodes featuring oxide apertures is analyzed in the lowinjection regime suitable for singlephoton emitters. Experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional pindesign. By an alternative design employing pdoping 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. 
D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, M. Virgilio, S. Guha, Th. Schröder, G. Cappellini, Th. Koprucki, Robustness analysis of a device concept for edgeemitting lasers based on strained germanium, Optical and Quantum Electronics, 48 (2016), pp. 156/1156/7, DOI 10.1007/s1108201603944 .
Abstract
We consider a device concept for edgeemitting 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 twodimensional description. The twodimensional 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 ShockleyReadHall lifetime variations and device sensitivity to different strain distributions. 
D. Peschka, N. Rotundo, M. Thomas, Towards doping optimization of semiconductor lasers, Journal of Computational and Theoretical Transport, 45 (2016), pp. 410423.
Abstract
We discuss analytical and numerical methods for the optimization of optoelectronic devices by performing optimal control of the PDE governing the carrier transport with respect to the doping profile. First, we provide a cost functional that is a sum of a regularization and a contribution, which is motivated by the modal net gain that appears in optoelectronic models of bulk or quantumwell lasers. Then, we state a numerical discretization, for which we study optimized solutions for different regularizations and for vanishing weights. 
A. Bercegol, B. Chacko, R. Klenk, I. Lauermann, M.Ch. LuxSteiner, M. Liero, Point contacts at the copperindiumgalliumselenide interface  A theoretical outlook, Journal of Applied Physics, 119 (2016), pp. 155304/1155304/7, DOI 10.1063/1.4947267 .
Abstract
For a long time, it has been assumed that recombination in the spacecharge region of CIGS is dominant, at least in high efficiency solar cells with low band gap. The recent developments like KF post deposition treatment and pointcontact junction may call this into question. In this work a theoretical outlook is made using threedimensional simulations to investigate the effect of pointcontact openings through a passivation layer on CIGS solar cell performance. A large set of solar cells is modeled under different scenarios for the charged defect levels and density, radius of the openings, interface quality and conduction band offset. The positive surface charge created by the passivation layer induces band bending and this influences the contact (CdS) properties, making it beneficial for the open circuit voltage and efficiency, and the effect is even more pronounced when coverage area is more than 95 %, and also makes a positive impact on the device performance, even in the presence of a spike at CIGS/CdS heterojunction. 
F. Kaschura, A. Fischer, M.P. Klinger, D.H. Doan, Th. Koprucki, A. Glitzky, D. Kasemann, J. Widmer, K. Leo, Operation mechanism of high performance organic permeable base transistors with an insulated and perforated base electrode, Journal of Applied Physics, 120 (2016), pp. 094501/1094501/8, DOI 10.1063/1.4962009 .

TH. Koprucki, N. Rotundo, P. Farrell, D.H. Doan, J. Fuhrmann, On thermodynamic consistency of a ScharfetterGummel scheme based on a modified thermal voltage for driftdiffusion equations with diffusion enhancement, Optical and Quantum Electronics, 47 (2015), pp. 13271332.
Abstract
Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on driftdiffusion 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 ScharfetterGummel 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 ScharfetterGummel schemes. 
M. Liero, Th. Koprucki, A. Fischer, R. Scholz, A. Glitzky, pLaplace thermistor modeling of electrothermal feedback in organic semiconductors, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 66 (2015), pp. 29572977.
Abstract
In largearea Organic LightEmitting Diodes (OLEDs) spatially inhomogeneous luminance at high power due to inhomogeneous current flow and electrothermal feedback can be observed. To describe these selfheating effects in organic semiconductors we present a stationary thermistor model based on the heat equation for the temperature coupled to a pLaplacetype equation for the electrostatic potential with mixed boundary conditions. The pLaplacian describes the nonOhmic electrical behavior of the organic material. Moreover, an Arrheniuslike temperature dependency of the electrical conductivity is considered. We introduce a finitevolume 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. 
D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, G. Capellini, Th. Koprucki, Th. Schröder, Modeling of edgeemitting lasers based on tensile strained germanium microstrips, IEEE Photonics Journal, 7 (2015), pp. 1502115/11502115/15, DOI 10.1109/JPHOT.2015.2427093 .
Abstract
In this paper we present a thorough modeling of an edgeemitting laser based on strained germanium microstrips. The full band structure of the tensile strained germanium (Ge) layer enters the calculation of optical properties. Material gain for strained Ge is used in the twodimensional simulation of the carrier transport and of the optical field within a cross section of the microstrips orthogonal to the optical cavity. We study optoelectronic properties of the device for two different designs. The simulation results are very promising as they show feasible ways towards Ge emitter devices with lower threshold currents and higher efficiency as published insofar. 
G. Ali, A. Bartel, N. Rotundo, Index2 elliptic partial differentialalgebraic models for circuits and devices, Journal of Mathematical Analysis and Applications, 423 (2015), pp. 13481369.

C. Kreisbeck, L. Mascarenhas, Asymptotic spectral analysis in semiconductor nanowire heterostructures, Applicable Analysis. An International Journal, (published online on June 2, 2014), DOI 10.1080/00036811.2014.919052 .

P. Exner, H. Neidhardt, M. Tatar, V. Zagrebnov, Nonequilibrium current via geometric scatterers, Journal of Physics. A. Mathematical and General, 47 (2014), pp. 395301/1395301/16.

A. Fischer, Th. Koprucki, K. Gärtner, M.L. Tietze, J. Brückner, B. Lüssem, K. Leo, A. Glitzky, R. Scholz, Feel the heat: Nonlinear electrothermal feedback in Organic LEDs, Advanced Functional Materials, 24 (2014), pp. 33673374.
Abstract
For lighting applications, Organic lightemitting diodes (OLED) need much higher brightness than for displays, leading to selfheating. Due to the temperatureactivated 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 selfheating. 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. 
TH. Koprucki, K. Gärtner, Discretization scheme for driftdiffusion equations with strong diffusion enhancement, Optical and Quantum Electronics, 45 (2013), pp. 791796.
Abstract
Inspired by organic semiconductor models based on hopping transport introducing GaussFermi integrals a nonlinear generalization of the classical ScharfetterGummel scheme is derived for the distribution function F(η)=1/(exp(η)+γ). This function provides an approximation of the FermiDirac 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 densitydependent 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. 
M. Liero, A. Mielke, Gradient structures and geodesic convexity for reactiondiffusion systems, Philosophical Transactions of the Royal Society A : Mathematical, Physical & Engineering Sciences, 371 (2013), pp. 20120346/120120346/28.
Abstract
We consider systems of reactiondiffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a socalled Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambdaconvexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a driftdiffusion system, provide a survey on the applicability of the theory. We consider systems of reactiondiffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a socalled Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambdaconvexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a driftdiffusion system, provide a survey on the applicability of the theory. 
A. Fischer, P. Pahner, B. Lüssem, K. Leo, R. Scholz, Th. Koprucki, K. Gärtner, A. Glitzky, Selfheating, bistability, and thermal switching in organic semiconductors, Physical Review Letters, 110 (2013), pp. 126601/1126601/5.
Abstract
We demonstrate electric bistability induced by the positive feedback of selfheating onto the thermally activated conductivity in a twoterminal device based on the organic semiconductor C60. The central undoped layer with a thickness of 200 nm is embedded between thinner ndoped layers adjacent to the contacts minimizing injection barriers. The observed currentvoltage characteristics follow the general theory for thermistors described by an Arrheniuslike conductivity law. Our findings including hysteresis phenomena are of general relevance for the entire material class since most organic semiconductors can be described by a thermally activated conductivity. 
A. Glitzky, A. Mielke, A gradient structure for systems coupling reactiondiffusion effects in bulk and interfaces, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 64 (2013), pp. 2952.
Abstract
We derive gradientflow formulations for systems describing driftdiffusion processes of a finite number of species which undergo massaction type reversible reactions. Our investigations cover heterostructures, where material parameter may depend in a nonsmooth way on the space variable. The main results concern a gradient flow formulation for electroreactiondiffusion systems with active interfaces permitting driftdiffusion processes and reactions of species living on the interface and transfer mechanisms allowing bulk species to jump into an interface or to pass through interfaces. The gradient flows are formulated in terms of two functionals: the free energy and the dissipation potential. Both functionals consist of a bulk and an interface integral. The interface integrals determine the interface dynamics as well as the selfconsistent coupling to the model in the bulk. The advantage of the gradient structure is that it automatically generates thermodynamically consistent models. 
P.N. Racec, S. Schade, H.Chr. Kaiser, Eigensolutions of the WignerEisenbud problem for a cylindrical nanowire within finite volume method, Journal of Computational Physics, 252 (2013), pp. 5264.
Abstract
We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostructure features such as doublebarriers or quantum dots. The three dimensional Schrödinger operator is reduced to a family of two dimensional Schrödinger operators distinguished by a centrifugal potential. Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. The 1/r singularity is eliminated by approximating r at the vertexes of the Voronoi boxes. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy. This anisotropic discretization yields best accuracy also in the presence of a mildly varying scattering potential, shown exemplarily for a nanowire resonant tunneling diode. For potentials with 1/r singularity one retrieves the theoretically established first order convergence, while the second order convergence is recovered only on uniform grids with an anisotropy correction. 
A. Fischer, P. Pahner, B. Lüssem, K. Leo, R. Scholz, Th. Koprucki, J. Fuhrmann, K. Gärtner, A. Glitzky, Selfheating effects in organic semiconductor crossbar structures with small active area, Organic Electronics, 13 (2012), pp. 24612468.
Abstract
We studied the influence of heating effects in an organic device containing a layer sequence of ndoped / intrinsic / ndoped C_{60} between crossbar metal electrodes. A strong positive feedback between current and temperature occurs at high current densities beyond 100 A/cm^{2}, as predicted by the extended Gaussian disorder model (EGDM) applicable to organic semiconductors. These devices give a perfect setting for studying the heat transport at high power densities because C_{60} can withstand temperatures above 200° C. Infrared images of the device and detailed numerical simulations of the heat transport demonstrate that the electrical circuit produces a superposition of a homogeneous power dissipation in the active volume and strong heat sources localized at the contact edges. Hence, close to the contact edges, the current density is significantly enhanced with respect to the central region of the device, demonstrating that threedimensional effects have a strong impact on a device with seemingly onedimensional transport. 
A. Glitzky, An electronic model for solar cells including active interfaces and energy resolved defect densities, SIAM Journal on Mathematical Analysis, 44 (2012), pp. 38743900.
Abstract
We introduce an electronic model for solar cells taking into account heterostructures with active interfaces and energy resolved volume and interface trap densities. The model consists of continuity equations for electrons and holes with thermionic emission transfer conditions at the interface and of ODEs for the trap densities with energy level and spatial position as parameters, where the right hand sides contain generationrecombination as well as ionization reactions. This system is coupled with a Poisson equation for the electrostatic potential. We show the thermodynamic correctness of the model and prove a priori estimates for the solutions to the evolution system. Moreover, existence and uniqueness of weak solutions of the problem are proven. For this purpose we solve a regularized problem and verify bounds of the corresponding solution not depending on the regularization level. 
TH. Koprucki, A. Wilms, A. Knorr, U. Bandelow, Modeling of quantum dot lasers with microscopic treatment of Coulomb effects, Optical and Quantum Electronics, 42 (2011), pp. 777783.
Abstract
We present a spatially resolved semiclassical model for the simulation of semiconductor quantumdot lasers including a multispecies description for the carriers along the optical active region. The model links microscopic determined quantities like scattering rates and dephasing times, that essentially depend via Coulomb interaction on the carrier densities, with macroscopic transport equations and equations for the optical field. 
A. Glitzky, Analysis of electronic models for solar cells including energy resolved defect densities, Mathematical Methods in the Applied Sciences, 34 (2011), pp. 19801998.
Abstract
We introduce an electronic model for solar cells including energy resolved defect densities. The resulting driftdiffusion model corresponds to a generalized van Roosbroeck system with additional source terms coupled with ODEs containing space and energy as parameters for all defect densities. The system has to be considered in heterostructures and with mixed boundary conditions from device simulation. We give a weak formulation of the problem. If the boundary data and the sources are compatible with thermodynamic equilibrium the free energy along solutions decays monotonously. In other cases it may be increasing, but we estimate its growth. We establish boundedness and uniqueness results and prove the existence of a weak solution. This is done by considering a regularized problem, showing its solvability and the boundedness of its solutions independent of the regularization level. 
J.A. Griepentrog, L. Recke, Local existence, uniqueness, and smooth dependence for nonsmooth quasilinear parabolic problems, Journal of Evolution Equations, 10 (2010), pp. 341375.
Abstract
A general theory on local existence, uniqueness, regularity, and smooth dependence in Hölder spaces for a general class of quasilinear parabolic initial boundary value problems with nonsmooth data has been developed. As a result the gap between low smoothness of the data, which is typical for many applications, and high smoothness of the solutions, which is necessary for the applicability of differential calculus to the abstract formulations of the initial boundary value problems, has been closed. The main tools are new maximal regularity results of the first author in SobolevMorrey spaces, linearization techniques and the Implicit Function Theorem. Typical applications are transport processes of charged particles in semiconductor heterostructures, phase separation processes of nonlocally interacting particles, chemotactic aggregation in heterogeneous environments as well as optimal control by means of quasilinear elliptic and parabolic PDEs with nonsmooth data. 
M.R. Dachner, E. Malic, M. Richter, A. Carmele, J. Kabuss, A. Wilms, J.E. Kim, G. Hartmann, J. Wolters, U. Bandelow, A. Knorr, Theory of carrier and photon dynamics in quantum dot light emitters, physica status solidi (b), 247 (2010), pp. 809828.
Abstract
We present a microscopic theory describing the charge carrier and light emission dynamics in quantum dot (QD) light emitters. The theory covers nonclassical light emission (fluorescence and Raman emission) in the low carrier injection limit as well as laser emission and pulse amplification in the high carrier injection limit. The theoretical approach is based on QD Bloch equations including microscopically calculated Coulomb and electronphonon scattering rates between bound QD, continuous wetting layer (WL) and bulk states. In the low carrier density limit, multiphonon relaxation is the dominant process, while at high charge carrier densities, Coulomb scattering dominates the dynamics. Using an equation of motion approach, we address (i) timeresolved fluorescence and Raman emission, (ii) electrical injection and charge carrier transfer from bulk into WL and QD states, (iii) single photon emission and (iv) gain dynamics of QD amplifiers and lasing dynamics in QD verticalcavity surfaceemitting lasers (VCSELs) at high injection currents. 
A. Glitzky, J.A. Griepentrog, Discrete SobolevPoincaré inequalities for Voronoi finite volume approximations, SIAM Journal on Numerical Analysis, 48 (2010), pp. 372391.
Abstract
We prove a discrete SobolevPoincare inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev's integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove a discrete Poincare inequality for space dimensions greater or equal to two. 
A. Glitzky, K. Gärtner, Existence of bounded steady state solutions to spinpolarized driftdiffusion systems, SIAM Journal on Mathematical Analysis, 41 (2010), pp. 24892513.
Abstract
We study a stationary spinpolarized driftdiffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. In 3D we prove the existence and boundedness of steady states. If the Dirichlet conditions are compatible or nearly compatible with thermodynamic equilibrium the solution is unique. The same properties are obtained for a space discretized version of the problem: Using a ScharfetterGummel scheme on 3D boundary conforming Delaunay grids we show existence, boundedness and, for small applied voltages, the uniqueness of the discrete solution. 
K. Hoke, H.Chr. Kaiser, J. Rehberg, Analyticity for some operator functions from statistical quantum mechanics, Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics, 10 (2009), pp. 749771.
Abstract
For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with nonsmooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to threedimensional Lipschitz domain factorizes over the space of essentially bounded functions. 
P.N. Racec, R. Racec, H. Neidhardt, Evanescent channels and scattering in cylindrical nanowire heterostructures, Phys. Rev. B., 79 (2009), pp. 155305/1155305/14.
Abstract
We investigate the scattering phenomena produced by a general finite range nonseparable potential in a multichannel twoprobe cylindrical nanowire heterostructure. The multichannel current scattering matrix is efficiently computed using the Rmatrix formalism extended for cylindrical coordinates. Considering the contribution of the evanescent channels to the scattering matrix, we are able to put in evidence the specific dips in the tunneling coefficient in the case of an attractive potential. The cylindrical symmetry cancels the ”selection rules” known for Cartesian coordinates. If the attractive potential is superposed over a nonuniform potential along the nanowire, then resonant transmission peaks appear. We can characterize them quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances (dips and peaks). Our formalism is applied to a variety of model systems like a quantum dot, a core/shell quantum ring or a double barrier, embedded into the nanocylinder. 
R. HallerDintelmann, Ch. Meyer, J. Rehberg, A. Schiela, Hölder continuity and optimal control for nonsmooth elliptic problems, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 60 (2009), pp. 397428.
Abstract
The well known De Giorgi result on Hölder continuity for solutions of the Dirichlet problem is reestablished for mixed boundary value problems, provided that the underlying domain is a Lipschitz domain and the border between the Dirichlet and the Neumann boundary part satisfies a very general geometric condition. Implications of this result for optimal control theory are presented. 
R. HallerDintelmann, J. Rehberg, Maximal parabolic regularity for divergence operators including mixed boundary conditions, Journal of Differential Equations, 247 (2009), pp. 13541396.
Abstract
We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly nonsmooth and $A$ is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with nonsmooth data are presented. 
K. Gärtner, Existence of bounded discrete steady state solutions of the van Roosbroeck system on boundary conforming Delaunay grids, SIAM Journal on Scientific Computing, 31 (2009), pp. 13471362.
Abstract
The classic van Roosbroeck system describes the carrier transport in semiconductors in a drift diffusion approximation. Its analytic steady state solutions fulfill bounds for some mobility and recombination/generation models. The main goal of this paper is to establish the identical bounds for discrete in space, steady state solutions on 3d boundary conforming Delaunay grids and the classical ScharfetterGummelscheme. Together with a uniqueness proof for small applied voltages and the known dissipativity (continuous as well as space and time discrete) these discretization techniques carry over the essential analytic properties to the discrete case. The proofs are of interest for deriving averaging schemes for space or state dependent material parameters, which are preserving these qualitative properties, too. To illustrate the properties of the scheme 1, 4, 16 elementary cells of a modified CoolMOS like structure are depleted by increasing the applied voltage until steady state avalanche breakdown occurs. 
A. Glitzky, K. Gärtner, Energy estimates for continuous and discretized electroreactiondiffusion systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 70 (2009), pp. 788805.
Abstract
We consider electroreactiondiffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistic relations.
We investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. Here the essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly.
The same properties are shown for an implicit time discretized version of the problem. Moreover, we provide a space discretized scheme for the electroreactiondiffusion system which is dissipative (the free energy decays monotonously). On a fixed grid we use for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species. 
A. Glitzky, Energy estimates for electroreactiondiffusion systems with partly fast kinetics, Discrete and Continuous Dynamical Systems, 25 (2009), pp. 159174.
Abstract
We start from a basic model for the transport of charged species in heterostructures containing the mechanisms diffusion, drift and reactions in the domain and at its boundary. Considering limit cases of partly fast kinetics we derive reduced models. This reduction can be interpreted as some kind of projection scheme for the weak formulation of the basic electroreactiondiffusion system. We verify assertions concerning invariants and steady states and prove the monotone and exponential decay of the free energy along solutions to the reduced problem and to its fully implicit discretetime version by means of the results of the basic problem. Moreover we make a comparison of prolongated quantities with the solutions to the basic model. 
H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Classical solutions of driftdiffusion equations for semiconductor devices: The 2D case, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 71 (2009), pp. 15841605.
Abstract
We regard driftdiffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes. This evolution equation falls into a class of quasilinear parabolic systems which allow unique, local in time solution in certain Lebesgue spaces. In particular, it turns out that the divergence of the electron and hole current is an integrable function. Hence, Gauss' theorem applies, and gives the foundation for space discretization of the equations by means of finite volume schemes. Moreover, the strong differentiability of the electron and hole density in time is constitutive for the implicit time discretization scheme. Finite volume discretization of space, and implicit time discretization are accepted custom in engineering and scientific computing. This investigation puts special emphasis on nonsmooth spatial domains, mixed boundary conditions, and heterogeneous material compositions, as required in electronic device simulation. 
H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Monotonicity properties of the quantum mechanical particle density: An elementary proof, Monatshefte fur Mathematik, 158 (2009), pp. 179185.
Abstract
An elementary proof of the antimonotonicity of the quantum mechanical particle density with respect to the potential in the Hamiltonian is given for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included. 
H. Cornean, K. Hoke, H. Neidhardt, P.N. Racec, J. Rehberg, A KohnSham system at zero temperature, Journal of Physics. A. Mathematical and General, 41 (2008), pp. 385304/1385304/21.
Abstract
An onedimensional KohnSham system for spin particles is considered which effectively describes semiconductor nanostructures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective KohnSham potential and obtain $W^1,2$bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchangecorrelation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero. 
R. HallerDintelmann, H.Chr. Kaiser, J. Rehberg, Elliptic model problems including mixed boundary conditions and material heterogeneities, Journal de Mathématiques Pures et Appliquées, 89 (2008), pp. 2548.

M. Hieber, J. Rehberg, Quasilinear parabolic systems with mixed boundary conditions on nonsmooth domains, SIAM Journal on Mathematical Analysis, 40 (2008), pp. 292305.
Abstract
In this paper we investigate quasilinear systems of reactiondiffusion equations with mixed DirichletNeumann bondary conditions on non smooth domains. Using techniques from maximal regularity and heatkernel estimates we prove existence of a unique solution to systems of this type. 
A. Glitzky, R. Hünlich, Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains, Mathematische Nachrichten, 281 (2008), pp. 16761693.
Abstract
We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain $Omega_0$ of the domain of definition $Omega$ of the energy balance equation and of the Poisson equation. Here $Omega_0$ corresponds to the region of semiconducting material, $OmegasetminusOmega_0$ represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the twodimensional stationary energy model. For this purpose we derive a $W^1,p$regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem. 
A. Glitzky, Analysis of a spinpolarized driftdiffusion model, Advances in Mathematical Sciences and Applications, 18 (2008), pp. 401427.
Abstract
We introduce a spinpolarized driftdiffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. We give a weak formulation of this problem and prove an existence and uniqueness result for the instationary problem. If the boundary data is compatible with thermodynamic equilibrium the free energy along the solution decays monotonously and exponentially to its equilibrium value. In other cases it may be increasing but we estimate its growth. Moreover we give upper and lower estimates for the solution. 
A. Glitzky, Exponential decay of the free energy for discretized electroreactiondiffusion systems, Nonlinearity, 21 (2008), pp. 19892009.
Abstract
Our focus are electroreactiondiffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistical relations. We introduce a discretization scheme (in space and fully implicit in time) using a fixed grid but for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species. This scheme has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For the discretized electroreactiondiffusion system we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. The essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly. 
J.A. Griepentrog, Maximal regularity for nonsmooth parabolic problems in SobolevMorrey spaces, Advances in Differential Equations, 12 (2007), pp. 10311078.
Abstract
This text is devoted to maximal regularity results for second order parabolic systems on LIPSCHITZ domains of space dimension greater or equal than three with diagonal principal part, nonsmooth coefficients, and nonhomogeneous mixed boundary conditions. We show that the corresponding class of initial boundary value problems generates isomorphisms between two scales of SOBOLEVMORREY spaces for solutions and right hand sides introduced in the first part of our presentation. The solutions depend smoothly on the data of the problem. Moreover, they are HOELDER continuous in time and space up to the boundary for a certain range of MORREY exponents. Due to the complete continuity of embedding and trace maps these results remain true for a broad class of unbounded lower order coefficients. 
J.A. Griepentrog, SobolevMorrey spaces associated with evolution equations, Advances in Differential Equations, 12 (2007), pp. 781840.
Abstract
In this text we introduce new classes of SOBOLEVMORREY spaces being adequate for the regularity theory of second order parabolic boundary value problems on LIPSCHITZ domains of space dimension greater or equal than three with nonsmooth coefficients and mixed boundary conditions. We prove embedding and trace theorems as well as invariance properties of these spaces with respect to localization, LIPSCHITZ transformation, and reflection. In the second part of our presentation we show that the class of second order parabolic systems with diagonal principal part generates isomorphisms between the above mentioned SOBOLEVMORREY spaces of solutions and right hand sides. 
M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, W. Rehbein, Improving the modulation bandwidth in semiconductor lasers by passive feedback, IEEE J. Select. Topics Quantum Electron., 13 (2007), pp. 136142.

J. Even, F. Doré, C. Cornet, L. Pedesseau, A. Schliwa, D. Bimberg, Semianalytical evaluation of linear and nonlinear piezoelectric potentials for quantum nanostructures with axial symmetry, Applied Physics Letters, 91 (2007), pp. 122112/1122112/3.

A. Marent, M. Geller, A. Schliwa, D. Feise, K. Pötschke, D. Bimberg, N. Akcay, N. Öncan, 10$^6$ years extrapolated hole storage time in GaSb/AlAs quantum dots, Applied Physics Letters, 91 (2007), pp. 242109/1242109/3.

V. Mlinar, A. Schliwa, D. Bimberg, F.M. Peeters, Theoretical study of electronic and optical properties of inverted GaAs/AlGaAs quantum dots with smoothed interfaces in an external magnetic field, Phys. Rev. B., 75 (2007), pp. 205308/1205308/9.

M. Winkelnkemper, R. Seguin, S. Rodt, A. Schliwa, L. Reimann, A. Strittmatter, A. Hoffmann, D. Bimberg, Polarized emission lines from A and Btype excitonic complexes in single InGaN/GaN quantum dots, Journal of Applied Physics, 101 (2007), pp. 113708/1113708/4.

U. Wulf, P.N. Racec, E.R. Racec, Admittance of planar twoterminal quantum systems, Phys. Rev. B., 75 (2007), pp. 075320/1075320/9.

J. Elschner, H.Chr. Kaiser, J. Rehberg, G. Schmidt, $W^1,q$ regularity results for elliptic transmission problems on heterogeneous polyhedra, Mathematical Models & Methods in Applied Sciences, 17 (2007), pp. 593615.

J. Elschner, J. Rehberg, G. Schmidt, Optimal regularity for elliptic transmission problems including $C^1$ interfaces, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 9 (2007), pp. 233252.
Abstract
We prove an optimal regularity result for elliptic operators $nabla cdot mu nabla:W^1,q_0 rightarrow W^1,q$ for a $q>3$ in the case when the coefficient function $mu$ has a jump across a $C^1$ interface and is continuous elsewhere. A counterexample shows that the $C^1$ condition cannot be relaxed in general. Finally, we draw some conclusions for corresponding parabolic operators. 
A. Glitzky, R. Hünlich, Resolvent estimates in $W^1,p$ related to strongly coupled linear parabolic systems with coupled nonsmooth capacities, Mathematical Methods in the Applied Sciences, 30 (2007), pp. 22152232.
Abstract
We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in $W^1,p$ spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain $L^p$ estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. 
H. Neidhardt, J. Rehberg, Scattering matrix, phase shift, spectral shift and trace formula for onedimensional Schrödingertype operators, Integral Equations and Operator Theory, 58 (2007), pp. 407431.
Abstract
The paper is devoted to Schroedinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the LaxPhillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed, in particular, trace formula and BirmanKrein formula are verified directly. The results are used for dissipative SchroedingerPoisson systems. 
P.N. Racec, U. Wulf, Smallsignal circuit elements of MIStype nanostructures, Solid State Phenomena, 121123 (2007), pp. 549552.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Classical solutions of quasilinear parabolic systems on two dimensional domains, NoDEA. Nonlinear Differential Equations and Applications, 13 (2006), pp. 287310.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Convexity of trace functionals and Schrödinger operators, Journal of Functional Analysis, 234 (2006), pp. 4569.

M. Baro, N. Ben Abdallah, P. Degond, A. El Ayyadi, A 1D coupled Schrödinger driftdiffusion model including collisions, Journal of Computational Physics, 203 (2005), pp. 129153.

M. Baro, H. Neidhardt, J. Rehberg, Current coupling of driftdiffusion models and dissipative SchrödingerPoisson systems: Dissipative hybrid models, SIAM Journal on Mathematical Analysis, 37 (2005), pp. 941981.

M. Baro, M. Demuth, E. Giere, Stable continuous spectra for differential operators of arbitrary order, Analysis and Applications, 3 (2005), pp. 223250.

TH. Koprucki, M. Baro, U. Bandelow, Th. Tien, F. Weik, J.W. Tomm, M. Grau, M.Ch. Amann, Electronic structure and optoelectronic properties of strained InAsSb/GaSb multiple quantum wells, Applied Physics Letters, 87 (2005), pp. 181911/1181911/3.

H. Neidhardt, J. Rehberg, Uniqueness for dissipative SchrödingerPoisson systems, Journal of Mathematical Physics, 46 (2005), pp. 113513/1113513/28.

A. Glitzky, R. Hünlich, Global existence result for pair diffusion models, SIAM Journal on Mathematical Analysis, 36 (2005), pp. 12001225.

A. Glitzky, R. Hünlich, Stationary energy models for semiconductor devices with incompletely ionized impurities, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 85 (2005), pp. 778792.

J. Rehberg, Quasilinear parabolic equations in $L^p$, Progress in Nonlinear Differential Equations and their Applications, 64 (2005), pp. 413419.

M. Baro, H.Chr. Kaiser, H. Neidhardt, J. Rehberg, A quantum transmitting SchrödingerPoisson system, Reviews in Mathematical Physics. A Journal for Both Review and Original Research Papers in the Field of Mathematical Physics, 16 (2004), pp. 281330.

M. Baro, H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Dissipative SchrödingerPoisson systems, Journal of Mathematical Physics, 45 (2004), pp. 2143.

V. Maz'ya, J. Elschner, J. Rehberg, G. Schmidt, Solutions for quasilinear nonsmooth evolution systems in $L^p$, Archive for Rational Mechanics and Analysis, 171 (2004), pp. 219262.

A. Glitzky, W. Merz, Single dopant diffusion in semiconductor technology, Mathematical Methods in the Applied Sciences, 27 (2004), pp. 133154.

A. Glitzky, R. Hünlich, Stationary solutions of twodimensional heterogeneous energy models with multiple species, Banach Center Publications, 66 (2004), pp. 135151.

A. Glitzky, Electroreactiondiffusion systems with nonlocal constraints, Mathematische Nachrichten, 277 (2004), pp. 1446.

M. Baro, H. Neidhardt, Dissipative Schrödingertype operator as a model for generation and recombination, Journal of Mathematical Physics, 44 (2003), pp. 23732401.

H. Gajewski, I.V. Skrypnik, On the uniqueness of solutions for nonlinear ellipticparabolic equations, Journal of Evolution Equations, 3 (2003), pp. 247281.

H. Gajewski, I.V. Skrypnik, To the uniqueness problem for nonlinear elliptic equations, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 52 (2003), pp. 291304.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Macroscopic current induced boundary conditions for Schrödingertype operators, Integral Equations and Operator Theory, 45 (2003), pp. 3963.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, On 1dimensional dissipative Schrödingertype operators, their dilations and eigenfunction expansions, Mathematische Nachrichten, 252 (2003), pp. 5169.

G. Albinus, H. Gajewski, R. Hünlich, Thermodynamic design of energy models of semiconductor devices, Nonlinearity, 15 (2002), pp. 367383.

J.A. Griepentrog, K. Gröger, H.Chr. Kaiser, J. Rehberg, Interpolation for function spaces related to mixed boundary value problems, Mathematische Nachrichten, 241 (2002), pp. 110120.

J.A. Griepentrog, Linear elliptic boundary value problems with nonsmooth data: Campanato spaces of functionals, Mathematische Nachrichten, 243 (2002), pp. 1942.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Density and current of a dissipative Schrödinger operator, Journal of Mathematical Physics, 43 (2002), pp. 53255350.

A. Glitzky, R. Hünlich, Global properties of pair diffusion models, Advances in Mathematical Sciences and Applications, 11 (2001), pp. 293321.

J.A. Griepentrog, H.Chr. Kaiser, J. Rehberg, Heat kernel and resolvent properties for second order elliptic differential operators with general boundary conditions on $Lsp p$, Advances in Mathematical Sciences and Applications, 11 (2001), pp. 87112.

W. Merz, A. Glitzky, R. Hünlich, K. Pulverer, Strong solutions for pair diffusion models in homogeneous semiconductors, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 2 (2001), pp. 541567.

I.V. Skrypnik, H. Gajewski, On the uniqueness of solution to nonlinear elliptic problem (in Ukrainian), Dopovidi Natsionalnoi Akademii Nauk Ukraini. Matematika. Prirodoznavstvo. Tekhnichni Nauki, (2001), pp. 2832.

J.A. Griepentrog, L. Recke, Linear elliptic boundary value problems with nonsmooth data: Normal solvability on SobolevCampanato spaces, Mathematische Nachrichten, 225 (2001), pp. 3974.

U. Bandelow, H.Chr. Kaiser, Th. Koprucki, J. Rehberg, Spectral properties of $k cdot p$ Schrödinger operators in one space dimension, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 379409.

A. Glitzky, R. Hünlich, Electroreactiondiffusion systems including cluster reactions of higher order, Mathematische Nachrichten, 216 (2000), pp. 95118.

H.Chr. Kaiser, J. Rehberg, About a stationary SchrödingerPoisson system with KohnSham potential in a bounded two or threedimensional domain, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 41 (2000), pp. 3372.

J.A. Griepentrog, An application of the Implicit Function Theorem to an energy model of the semiconductor theory, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 79 (1999), pp. 4351.
Abstract
In this paper we deal with a mathematical model for the description of heat conduction and carrier transport in semiconductor heterostructures. We solve a coupled system of nonlinear elliptic differential equations consisting of the heat equation with Joule heating as a source, the Poisson equation for the electric field an driftdiffusion equations with temperature dependent coefficients describing the charge and current conservation, subject to general thermal and electrical boundary conditions. We prove the existence and uniqueness of Holder continuous weak solutions near thermodynamic equilibria points using the Implicit Function Theorem. To show the differentiability of maps corresponding to the weak formulation of the problem we use regularity results from the theory of nonsmooth linear elliptic boundary value problems in SobolevCampanato spaces. 
M. Kantner, Hybrid modeling of quantum light emitting diodes: Selfconsistent coupling of driftdiffusion, SchrödingerPoisson, and quantum master equations, in: Proceedings of ``SPIE Photonics West'', San Francisco, USA, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 10912 of Physics and Simulation of Optoelectronic Devices XXVII, SPIE Digital Library, Bellingham, 2019, pp. published online on 26.02.2019, DOI 10.1117/12.2515209 .
Abstract
The devicescale simulation of electrically driven solid state quantum light emitters, such as singlephoton sources and nanolasers based on semiconductor quantum dots, requires a comprehensive modeling approach, that combines classical device physics with cavity quantum electrodynamics. In a previous work, we have selfconsistently coupled the semiclassical driftdiffusion system with a Markovian quantum master equation in Lindblad form to describe (i) the spatially resolved current injection into a quantum dot embedded within a semiconductor device and (ii) the fully quantum mechanical lightmatter interaction in the coupled quantum dotphoton system out of one box. In this paper, we extend our hybrid quantumclassical modeling approach by including a Schroedinger?Poisson problem to account for energy shifts of the quantum dot carriers in response to modifications of its macroscopic environment (e.g., quantum confined Stark effect due to the diode's internal electric field and plasma screening). The approach is demonstrated by simulations of a singlephoton emitting diode. 
TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019), J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2019, pp. 1314 (appeared online 22.08.2019), DOI 10.1109/NUSOD.2019.8807025 .

A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, Modelbased geometry reconstruction of quantum dots from TEM, in: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), 18 of Proceedings in Applied Mathematics and Mechanics (PAMM), WileyVCH, Weinheim, 2018, pp. e201800398/1e201800398/2, DOI 10.1002/pamm.201800398 .

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, in: Proc. SPIE 10526, Physics and Simulation of Optoelectronic Devices XXVI, B. Witzigmann, M. Osiński, Y. Arakawa, eds., SPIE Digital Library, 2018, pp. 1052603/11052603/6, DOI 10.1117/12.2289185 .
Abstract
The design of electrically driven quantum light sources based on semiconductor quantum dots, such as singlephoton emitters and nanolasers, asks for modeling approaches combining classical device physics with cavity quantum electrodynamics. In particular, one has to connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems. We present a first step in this direction by coupling the van Roosbroeck system with a Markovian quantum master equation in Lindblad form. The resulting hybrid quantumclassical system obeys the fundamental laws of nonequilibrium thermodynamics and provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit (e.g. the second order intensity correlation function) together with the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Modeling and simulation of electrically driven quantum light sources: From classical device physics to open quantum systems, in: 14th International Conference on Nonlinear Optics and Excitation Kinetics in Semiconductors, September 2327, 2018, Berlin, Germany (Conference Program), 2018, pp. 135.

M. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, M. Auf DER Maur, Highly accurate discretizations for nonBoltzmann charge transport in semiconductors, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 5354.

TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards modelbased geometry reconstruction of quantum dots from TEM, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 115116.

O. Marquardt, P. Mathé, Th. Koprucki, M. Caro, M. Willatzen, Datadriven electronic structure calculations in semiconductor nanostructures  beyond the eightband k.p formalism, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 5556.

M. Liero, A. Fischer, J. Fuhrmann, Th. Koprucki, A. Glitzky, A PDE model for electrothermal feedback in organic semiconductor devices, in: Progress in Industrial Mathematics at ECMI 2016, P. Quintela, P. Barral, D. Gómez, F.J. Pena, J. Rodrígues, P. Salgado, M.E. VázquezMéndez, eds., 26 of Mathematics in Industry, Springer International Publishing AG, Cham, 2017, pp. 99106.

M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, Modeling and simulation of electrothermal feedback in largearea organic LEDs, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 105106, DOI 10.1109/NUSOD.2017.8010013 .

M. Bulíček, A. Glitzky, M. Liero, Thermistor systems of p(x)Laplacetype with discontinuous exponents via entropy solutions, in: PDE 2015: Theory and Applications of Partial Differential Equations, H.Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci, eds., 10 of Discrete and Continuous Dynamical Systems, Series S, no. 4, American Institute of Mathematical Sciences, Springfield, 2017, pp. 697713.
Abstract
We show the existence of solutions to a system of elliptic PDEs, that was recently introduced to describe the electrothermal behavior of organic semiconductor devices. Here, two difficulties appear: (i) the elliptic term in the currentflow equation is of p(x)Laplaciantype with discontinuous exponent p, which limits the use of standard methods, and (ii) in the heat equation, we have to deal with an a priori L^{1} term on the right hand side describing the Joule heating in the device. We prove the existence of a weak solution under very weak assumptions on the data. Our existence proof is based on Schauder's fixed point theorem and the concept of entropy solutions for the heat equation. Here, the crucial point is the continuous dependence of the entropy solutions on the data of the problem. 
P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on nonuniform 1D grids, in: Finite Volumes for Complex Applications VIII  Methods and Theoretical Aspects, FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 199 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing AG, Cham, 2017, pp. 303310.

P. Farrell, Th. Koprucki, J. Fuhrmann, Comparision of ScharfetterGummel flux discretizations under Blakemore statistics, in: Progress in Industrial Mathematics at ECMI 2016, P. Quintela, P. Barral, D. Gómez, F.J. Pena, J. Rodrígues, P. Salgado, M.E. VázquezMéndez, eds., 26 of Mathematics in Industry, Springer International Publishing AG, Cham, 2017, pp. 9198.

P. Farrell, Th. Koprucki, J. Fuhrmann, Comparison of consistent flux discretizations for drift diffusion beyond Boltzmann statistics, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 219220, DOI 10.1109/NUSOD.2017.8010070 .

M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Multiscale modelling and simulation of singlephoton sources on a device level, in: EuroTMCS II  Theory, Modelling & Computational Methods for Semiconductors, 7th  9th December 2016, Tyndall National Institute, University College Cork, Ireland, E. O'Reilly, S. Schulz, S. Tomic, eds., Tyndall National Institute, 2016, pp. 65.

M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Modeling and numerical simulation of electrically pumped singlephoton emitters, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. YuhRenn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 151152.

M. Kantner, U. Bandelow, Th. Koprucki, Multiscale modeling and simulation of singlephoton sources, in: Proceedings of iNOW 2015 (International NanoOptoelectronics Workshop) (PDF only), Y. Arakawa, F. Koyama, C. ChangHasnain, D. Bimberg, eds., pp. 129130.

D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, Th. Schröder, G. Capellini, Th. Koprucki, On device concepts for CMOScompatible edgeemitters based on strained germanium, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. YuhRenn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 129130.

A. Fischer, Th. Koprucki, A. Glitzky, M. Liero, K. Gärtner, J. Hauptmann, S. Reineke, D. Kasemann, B. Lüssem, K. Leo, R. Scholz, OLEDs: Lightemitting thin film thermistors revealing advanced selfheating effects, in: Organic Light Emitting Materials and Devices XIX, F. So, Ch. Adachi, J.J. Kim, eds., 9566 of Proc. SPIE, SPIE Digital Library, Bellingham, Washington, 2015, pp. 95661A/195661A/7.
Abstract
Large area OLEDs show pronounced Joule selfheating 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 selfheating, even allowing for 'switchedback' regions where the luminance finally decreases (Fischer et al., Adv. Funct. Mater. 2014, 24, 3367). By using a multiphysics 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. 
G. Capellini, M. Virgilio, Y. Yamamoto, L. Zimmermann, B. Tillack, D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, Th. Koprucki, Th. Schroeder, Modeling of an edgeemitting strainedGe laser, in: Advanced Solid State Lasers, OSA Technical Digest (online) (Optical Society of America, 2015), 2015, pp. ATu2A.19/1ATu2A.19/3.
Abstract
By using fullycoupled 2D optoelectronic simulations with embedded microscopic gain calculations, we study the optoelectronic performance of a monolithically integrated edgeemitting laser based on strained germanium microstrips fabricated using CMOS standard processes. 
TH. Koprucki, M. Kantner, J. Fuhrmann, K. Gärtner, On modifications of the ScharfetterGummel scheme for driftdiffusion equations with Fermilike statistical distribution functions, in: Proceedings of the 14th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2014, 14 September 2014, J. Piprek, J. Javaloyes, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2014, pp. 155156.

V. Mehrmann, A. Mielke, F. Schmidt, D  Electronic and photonic devices, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 229232.

TH. Koprucki, K. Gärtner, Generalization of the ScharfetterGummel scheme, in: Proceedings of the 13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013, 1922 August 2013, J. Piprek, L. Chrostowski, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2013, pp. 8586.

A. Glitzky, K. Gärtner, J. Fuhrmann, Th. Koprucki, A. Fischer, B. Lüssem, K. Leo, R. Scholz, Electrothermal modeling of organic semiconductors describing negative differential resistance induced by selfheating, in: Proceedings of the 13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013, 1922 August 2013, J. Piprek, L. Chrostowski, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2013, pp. 7778.

TH. Koprucki, K. Gärtner, Discretization scheme for driftdiffusion equations with strong diffusion enhancement, in: Proceedings of the 12th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD'12, J. Piprek, W. Lu, eds., IEEE Conference Publications Management Group, New Jersey, USA, 2012, pp. 103104.

U. Bandelow, Th. Koprucki, A. Wilms, A. Knorr, Multispecies modeling of quantum dot lasers with microscopic treatment of Coulomb scattering, in: Proceedings of the 10th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2010, J. Piprek, B. Klein, D. Yoder, eds., IEEE, Piscataway, NJ, USA, 2010, pp. 5960.

P.N. Racec, R. Racec, H. Neidhardt, Rmatrix formalism for electron scattering in two dimensions with applications to nanostructures with quantum dots, in: Trends in Nanophysics, A. Aldea, V. Bârsan, eds., Engineering Materials, Springer, Berlin/Heidelberg, 2010, pp. 149174.
Abstract
We investigate the scattering phenomena in two dimensions produced by a general finiterange nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the dimensionality of the scattering problem new processes as the scattering between conducting channels and the scattering from conducting to evanescent channels are allowed. For certain values of the energy, called resonance energy, the transmission through the scattering region changes dramatically in comparison with an onedimensional problem. If the potential has an attractive character even the evanescent channels can be seen as dips of the total transmission. The multichannel current scattering matrix is determined using its representation in terms of the Rmatrix. The resonant transmission peaks are characterized quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances. Our formalism is applied to a quantum dot in a two dimensional electron gas and a conical quantum dot embedded inside a nanowire. 
S. Ahmed, M. Usman, C. Heitzinger, R. Rahman, A. Schliwa, G. Klimeck, Symmetry breaking and fine structure splitting in zincblende quantum dots: Atomistic simulations of longrange strain and piezoelectric field, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 849850.

J. Behrndt, H. Neidhardt, J. Rehberg, Block matrices, optical potentials, trace class perturbations and scattering, in: Operator Theory in Inner Product Spaces, K.H. Förster, P. Jonas, H. Langer, C. Trunk, eds., 175 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2007, pp. 3349.

C. Cornet, M. Hayne, A. Schliwa, F. Doré, C. Labbé, H. Folliot, J. Even, D. Bimberg, Theory and experiment of InAs/InP quantum dots: From calculations to laser emission, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 779780.

F. Doré, C. Cornet, A. Schliwa, N. Bertru, O. Dehaese, I. Alghoraibi, H. Folliot, R. Piron, A. Le Corre, A theoretical and experimental study of $>2 mu$m luminescence of quantum dots on InP substrate, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 889890.

U. Wulf, P.N. Racec, H. Richter, Quantentransport in Nanotransistoren, in: vol. 90 (2007) of Sitzungsberichte der LeibnizSozietät, traem fo verlag dr. wolfgang weist, Berlin, pp. 121137.

A. Glitzky, Energy models where the equations are defined on different domains, in: GAMM Annual Meeting 2006  Berlin, Special Issue (Vol. 6, Issue 1) of PAMM (Proceedings of Applied Mathematics and Mechanics), WileyVCH Verlag, Weinheim, 2006, pp. 629630.

H. Gajewski, H.Chr. Kaiser, H. Langmach, R. Nürnberg, R.H. Richter, Mathematical modelling and numerical simulation of semiconductor detectors, in: Mathematics  Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 355364.

R. Hünlich, G. Albinus, H. Gajewski, A. Glitzky, W. Röpke, J. Knopke, Modelling and simulation of power devices for highvoltage integrated circuits, in: Mathematics  Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 401412.

H.Chr. Kaiser, U. Bandelow, Th. Koprucki, J. Rehberg, Modelling and simulation of strained quantum wells in semiconductor lasers, in: Mathematics  Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 377390.

U. Bandelow, H. Gajewski, H.Chr. Kaiser, Modeling combined effects of carrier injection, photon dynamics and heating in Strained MultiQuantumWell Laser, in: Physics and Simulation of Optoelectronic Devices VIII, R.H. Binder, P. Blood, M. Osinski, eds., 3944 of Proceedings of SPIE, SPIE, Bellingham, WA, 2000, pp. 301310.

R. Hünlich, A. Glitzky, On energy estimates for electrodiffusion equations arising in semiconductor technology, in: Partial differential equations. Theory and numerical solution, W. Jäger, J. Nečas, O. John, K. Najzar, eds., 406 of Chapman & Hall Research Notes in Mathematics, Chapman & Hall, Boca Raton, FL, 2000, pp. 158174.

H.Chr. Kaiser, J. Rehberg, About some mathematical questions concerning the embedding of SchrödingerPoisson systems into the driftdiffusion model of semiconductor devices, in: EQUADIFF 99: International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels, eds., 2, World Scientific, Singapore [u. a.], 2000, pp. 13281333.

M. Kantner, Generalized ScharfetterGummel schemes for electrothermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient, Preprint no. 2605, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2605 .
Abstract, PDF (7347 kByte)
Many challenges faced in today's semiconductor devices are related to selfheating phenomena. The optimization of device designs can be assisted by numerical simulations using the nonisothermal driftdiffusion system, where the magnitude of the thermoelectric cross effects is controlled by the Seebeck coefficient. We show that the model equations take a remarkably simple form when assuming the socalled Kelvin formula for the Seebeck coefficient. The corresponding heat generation rate involves exactly the three classically known selfheating effects, namely Joule, recombination and ThomsonPeltier heating, without any further (transient) contributions. Moreover, the thermal driving force in the electrical current density expressions can be entirely absorbed in the (nonlinear) diffusion coefficient via a generalized Einstein relation. The efficient numerical simulation relies on an accurate and robust discretization technique for the fluxes (finite volume ScharfetterGummel method), which allows to cope with the typically stiff solutions of the semiconductor device equations. We derive two nonisothermal generalizations of the ScharfetterGummel scheme for degenerate semiconductors (FermiDirac statistics) obeying the Kelvin formula. The approaches differ in the treatment of degeneration effects: The first is based on an approximation of the discrete generalized Einstein relation implying a specifically modified thermal voltage, whereas the second scheme follows the conventionally used approach employing a modified electric field. We present a detailed analysis and comparison of both schemes, indicating a superior performance of the modified thermal voltage scheme. 
A. Glitzky, M. Liero, G. Nika, An existence result for a class of electrothermal driftdiffusion models with GaussFermi statistics for organic semiconductors, Preprint no. 2593, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2593 .
Abstract, PDF (387 kByte)
This work is concerned with the analysis of a driftdiffusion model for the electrothermal behavior of organic semiconductor devices. A "generalized Van Roosbroeck” system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like GaussFermi statistics and mobilities functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder's fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that selfheating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal driftdiffusion model for organic semiconductors on a sound analytical basis. 
M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, Preprint no. 2575, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2575 .
Abstract, PDF (3500 kByte)
We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantumclassical model that selfconsistently couples van Roosbroeck's driftdiffusion system for classical charge transport with a Lindbladtype quantum master equation. The coupling is shown to obey fundamental principles of nonequilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of socalled GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy. 
R. Schlundt, A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices, Preprint no. 2556, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2556 .
Abstract, PDF (318 kByte)
This paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. The blockdiagonal matrices are decomposed by an incomplete LDL^{T} factorization with the BunchKaufman pivoting method. Using the example of Maxwell's equations the generality of the approach is demonstrated. 
D.H. Doan, A. Glitzky, M. Liero, Driftdiffusion modeling, analysis and simulation of organic semiconductor devices, Preprint no. 2493, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2493 .
Abstract, PDF (563 kByte)
We discuss driftdiffusion models for chargecarrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to socalled GaussFermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the stateoftheart modeling of the transport processes and provide a first existence result for the stationary driftdiffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder's fixedpoint theorem. Finally, we discuss the numerical discretization of the model using finitevolume methods and a generalized ScharfetterGummel scheme for the GaussFermi statistics. 
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A. Glitzky, $p(x)$Laplace thermistor models for electrothermal feedback in organic semiconductor devices, 9th European Conference on Elliptic and Parabolic Problems, May 23  27, 2016, University of Zurich, Institute of Mathematics, Gaeta, Italy, May 23, 2016.

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P. Farrell, ScharfetterGummel schemes for NonBoltzmann statistics, Conference on Scientific Computing (ALGORITMY 2016), March 14  18, 2016, Slovak University of Technology, Department of Mathematics and Descriptive Geometry, Podbanské, Slovakia, March 17, 2016.

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M. Kantner, Multiscale modeling and simulation of electrically pumped singlephoton sources, International NanoOptoelectronics Workshop (iNOW 2015), Tokio, Japan, August 3  7, 2015.

TH. Koprucki, On device concepts for CMOScompatible edgeemitters based on strained germanium, Symposium ``Alternative Semiconductor Integration in Si Microelectronics: Materials, Techniques and Applications'' of the EMRS Fall Meeting 2015, September 15  18, 2015, Warsaw University of Technology, Krakow, Poland, September 18, 2015.

TH. Koprucki, On device concepts for CMOScompatible edgeemitters based on strained germanium, 15th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2015), September 7  11, 2015, National Taiwan University, Taipeh, Taiwan, Province Of China, September 8, 2015.

M. Liero, Electrothermal modeling of largearea OLEDs, sc Matheon Center Days, April 20  21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

M. Liero, OLEDs  eine heiße Sache?, Organische Leuchtdioden, Workshop im Handlungsfeld Lichttechnik, OpTec Berlin Brandenburg e.V., Berlin, May 18, 2015.

M. Liero, On $p(x)$Laplace thermistor models describing electrothermal feedback in organic semiconductor devices, Theory of Applications of Partial Differential Equations (PDE 2015), November 30  December 4, 2015, WIAS Berlin, Berlin, December 3, 2015.

M. Liero, On a PDE thermistor system for largearea OLEDs, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2015), March 11  13, 2015, WIAS Berlin, Berlin, March 12, 2015.

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M. Thomas, Analysis for edgeemitting semiconductor heterostructures, Minisymposium ``Numerical and Analytical Aspects in Semiconductor Theory'' of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), August 10  14, 2015, International Council for Industrial and Applied Mathematics, Beijing, China, August 10, 2015.

M. Thomas, Modeling of edgeemitting lasers based on tensile strained germanium microstripes, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2015), March 11  13, 2015, WIAS Berlin, Berlin, March 11, 2015.

D.H. Doan, On modifications of the ScharfetterGummel scheme for driftdiffusion equations with Fermilike distribution functions, KickOff Meeting of the ECMI Special Interest Group ``Sustainable Energy'' on Nanostructures for Photovoltaics and Energy Storage, December 8  9, 2014, Technische Universität Berlin, Institut für Mathematik, December 8, 2014.

TH. Koprucki, DeviceSimulation: Mathematische Fragestellungen und Numerik, BlockSeminar des SFB 787 ``Nanophotonik'', May 21  23, 2014, Technische Universität Berlin, GraalMüritz, May 23, 2014.

TH. Koprucki, On modifications of the ScharfetterGummel scheme for driftdiffusion equations with Fermilike statistical distribution functions, 14th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2014), September 1  5, 2014, Palma de Mallorca, Spain, September 3, 2014.

M. Liero, Electrothermical modeling of largearea OLEDs, KickOff Meeting of the ECMI Special Interest Group ``Sustainable Energy'' on Nanostructures for Photovoltaics and Energy Storage, December 8  9, 2014, Technische Universität Berlin, Institut für Mathematik, December 8, 2014.

A. Glitzky, Driftdiffusion models for heterostructures in photovoltaics, 8th European Conference on Elliptic and Parabolic Problems, Minisymposium ``Qualitative Properties of Nonlinear Elliptic and Parabolic Equations'', May 26  30, 2014, Universität Zürich, Institut für Mathematik, organized in Gaeta, Italy, May 27, 2014.

H. Neidhardt, LandauerBütikker formula applied to photon emitting and absorbing system, Workshop ``Mathematical Challenge of Quantum Transport in Nanosystems'' (Pierre Duclos Workshop), September 23  26, 2014, Saint Petersburg National Research University of Informational Technologies, Mechanics, and Optics, Russian Federation, September 24, 2014.

TH. Koprucki, Generalization of the ScharfetterGummel scheme, Organic Photovoltaics Workshop 2013, December 10  11, 2013, University of Oxford, Mathematical Insitute, UK, December 10, 2013.

TH. Koprucki, SelbstaufheizungsEffekte in Halbleitern, negativer differentieller Widerstand und Bistabilität, Doktorandenseminar des SFB 787 Nanophotonik, Technische Universität Berlin, Institut für Physik, November 29, 2013.

TH. Koprucki, Discretization scheme for driftdiffusion equations with a generalized Einstein relation, scshape Matheon Workshop ``6th Annual Meeting Photonic Devices'', February 21  22, 2013, KonradZuseZentrum für Informationstechnik Berlin, February 22, 2013.

M. Liero, Gradient structures and geodesic convexity for reactiondiffusion system, SIAM Conference on Mathematical Aspects of Materials Science (MS13), Minisymposium ``Material Modelling and Gradient Flows'' (MS100), June 9  12, 2013, Philadelphia, USA, June 12, 2013.

M. Liero, On gradient structures and geodesic convexity for reactiondiffusion systems, Research Seminar, Westfälische WilhelmsUniversität Münster, Institut für Numerische und Angewandte Mathematik, April 17, 2013.

A. Glitzky, Electrothermal modeling of organic semiconductors describing negative differential resistance induced by selfheating, 13th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2013), August 19  22, 2013, Vancouver, Canada, August 20, 2013.

A. Glitzky, Nonlinear electrothermal feedback in organic semiconductors, Organic Photovoltaics Workshop 2013, December 10  11, 2013, University of Oxford, Mathematical Insitute, UK, December 10, 2013.

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A. Mielke, Analysis, modeling, and simulation of semiconductor devices, Kolloquium Simulation Technology, Universität Stuttgart, SRC Simulation Technology, May 14, 2013.

A. Mielke, Mathematische und thermodynamische Modellierung von Halbleiterstrukturen, BlockSeminar des SFB 787 ``Nanophotonik'', May 6  8, 2013, Technische Universität Berlin, GraalMüritz, May 8, 2013.

A. Mielke, Thermodynamic modeling of the MaxwellBloch and the semiconductor equations via GENERIC, Modeling, Analysis and Simulation of Optical Modes in Photonic Devices (MASOMO 13), April 10  12, 2013, WIAS Berlin, April 10, 2013.

TH. Koprucki, A. Glitzky, A. Fischer, Electronic and thermal effects in organic semiconductors, Organic Photovoltaics Workshop, Oxford University, Mathematical Institute, UK, April 2, 2012.

TH. Koprucki, K. Gärtner, A. Wilms, U. Bandelow, A. Mielke, Multidimensional modeling and simulation of quantumdot lasers, Fachtagung LeibnizNano (1. NanotechnologieWorkshop der LeibnizGemeinschaft), Berlin, January 30  31, 2012.

TH. Koprucki, Discretization scheme for driftdiffusion equations with strong diffusion enhancement, 12th International Conference on Numerical Simulation of Optoelectronic Devices NUSOD'12, August 28  31, 2012, Chinese Academy of Science, Shanghai Institute for Technical Physics, August 29, 2012.

TH. Koprucki, On coupling of optical models with electronic models for simulation of quantumdot VCSELs, 5th Annual Meeting Photonic Devices, February 23  24, 2012, KonradZuseZentrum für Informationstechnik, Berlin, February 24, 2012.

TH. Koprucki, Semiclassical modeling of quantum dot lasers with microscopic treatment of Coulomb scattering, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 24, 2012.

M. Liero, Interfaces in reactiondiffusion systems, Seminar ``Dünne Schichten'', Technische Universität Berlin, Institut für Mathematik, February 9, 2012.

M. Liero, Interfaces in solar cells, 5th Annual Meeting Photonic Devices, February 23, 2012, KonradZuseZentrum für Informationstechnik, Berlin, February 24, 2012.

M. Liero, WIASTeSCA simulations in photovoltaics for a point contact concept of heterojunction thin film solar cells, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 25, 2012.

A. Glitzky, An electronic model for solar cells taking into account active interfaces, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 27, 2012.

A. Glitzky, Mathematische Modellierung und Simulation organischer Halbleiterbauelemente, Senatsausschuss Wettbewerb (SAW), Sektion D der LeibnizGemeinschaft, LeibnizInstitut für Analytische Wissenschaften (ISAS), Dortmund, September 14, 2012.

K. Gärtner, A. Glitzky, Mathematics and simulation of the charge transport in semiconductor sensors, Fachtagung LeibnizNano (1. NanotechnologieWorkshop der LeibnizGemeinschaft), Berlin, January 30  31, 2012.

A. Mielke, Multidimensional modeling and simulation of optoelectronic devices, Challenge Workshop ``Modeling, Simulation and Optimisation Tools'', September 24  26, 2012, Technische Universität Berlin, September 24, 2012.

A. Mielke, Using gradient structures for modeling semiconductors, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 24, 2012.

H. Neidhardt, On the abstract LandauerBuettiker formula and applications, Workshop on Spectral Theory and Differential Operators, August 27  31, 2012, Technische Universität Graz, Institut für Numerische Mathematik, Austria, August 30, 2012.

P.N. Racec, H. Neidhardt, H.Chr. Kaiser, R. Racec, Electronic quantum transport in semiconductor nanostructures, Fachtagung LeibnizNano (1. NanotechnologieWorkshop der LeibnizGemeinschaft), Berlin, January 30  31, 2012.

P.N. Racec, Finite volume discretization and Rmatrix formalism for cylindrical nanowire heterostructures, Seminar Laboratory 30 ``Nanoscale Condensed Matter Laboratory'', National Institute of Materials Physics, Bucharest, Romania, October 9, 2012.

P.N. Racec, Quantum transport and the Rmatrix formalism for cylindrical nanowire heterostructures, Technische Universität Graz, Institut für Theoretische Physik, Austria, September 13, 2012.

P.N. Racec, Quantum transport in cylindrical nanowires with constrictions, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), MiniSymposium ``Scattering problems for quantum, electromagnetic, and acoustic waveguides'', September 10  14, 2012, Universität Wien, Austria, September 10, 2012.

P.N. Racec, Quantum transport in semiconductor nanoheterostructures, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 28, 2012.

A. Glitzky, An electronic model for solar cells including active interfaces, Workshop ``Mathematical Modelling of Organic Photovoltaic Devices'', University of Cambridge, Department of Applied Mathematics and Theoretical Physics, UK, June 9, 2011.

A. Mielke, Thermodynamical modeling of bulkinterface interaction in reactiondiffusion systems, Interfaces and Discontinuities in Solids, Liquids and Crystals (INDI2011), June 20  23, 2011, Gargnano (Brescia), Italy, June 20, 2011.

P.N. Racec, Rmatrix and finite volume method for cylindrical nanowire heterostructures, Mathematical Challenges of Quantum Transport in NanoOptoelectronic Systems, February 4  5, 2011, WIAS, February 4, 2011.

A. Mielke, Mathematical approaches to thermodynamic modeling, Autumn School on Mathematical Principles for and Advances in Continuum Mechanics, November 7  12, 2011, Centro di Ricerca Matematica ``Ennio De Giorgi'', Pisa, Italy.

TH. Koprucki, Multispecies modeling of quantum dot lasers with microscopic treatment of Coulomb scattering, 10th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) 2010, September 6  9, 2010, Georgia Institute of Technology, Atlanta, USA, September 7, 2010.

A. Glitzky, Existence of bounded steady state solutions to spinpolarized driftdiffusion systems, Workshop on Drift Diffusion Systems and Related Problems: Analysis, Algorithms and Computations, WIAS, Research Group ``Numerical Mathematics and Scientific Computing'', March 25, 2010.

J.A. Griepentrog, Maximal regularity for nonsmooth parabolic boundary value problems in SobolevMorrey spaces, International Conference on Elliptic and Parabolic Equations, November 30  December 4, 2009, WIAS, December 1, 2009.

P.N. Racec, Quantum transport in cylindrical nanowire heterostructures: The scattering problem, PaulDrudeInstitut für Festkörperelektronik, Abteilung Epitaxie, Berlin, May 13, 2009.

M. Ehrhardt, A high order finite element method for waves in periodic structures, 9th International Conference on Spectral and High Order Methods (ICOSAHOM09), Minisymposium ``Highorder Methods for Linear and Nonlinear Wave Equations'', June 22  26, 2009, Norwegian University of Science and Technology, Trondheim, June 24, 2009.

K. Gärtner, J.A. Griepentrog, H. Langmach, The van Roosbroeck system, its mathematical properties, and detector simulation examples, 11th European Symposium on Semiconductor Detectors, Wildbad Kreuth, June 7  11, 2009.

K. Gärtner, Charge explosion studies, 5th Meeting of the Detector Advisory Committee for the European XFEL, April 28  29, 2009, European XDAC, Hamburg, April 28, 2009.

H.Chr. Kaiser, Transient KohnSham theory, Jubiläumssymposium ``Licht  Materialien  Modelle'' (100 Jahre Innovation aus Adlershof), BerlinAdlershof, September 7  8, 2009.

J. Rehberg, Functional analytic properties of the quantum mechanical particle density operator, International Workshop on Quantum Systems and Semiconductor Devices: Analysis, Simulations, Applications, April 20  24, 2009, Peking University, School of Mathematical Sciences, Beijing, China, April 21, 2009.

P.N. Racec, Modeling of nanowire transistor, May 7  14, 2008, National Institute of Materials Physics, Bucharest, Romania, May 8, 2008.

A. Glitzky, Analysis of spinpolarized driftdiffusion models, 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2008), session ``Applied Analysis'', March 31  April 4, 2008, University of Bremen, April 1, 2008.

H.Chr. Kaiser, A driftdiffusion model for semiconductors with internal interfaces, Annual Meeting of the Deutsche MathematikerVereinigung 2008, Minisymposium ``Analysis of ReactionDiffusion Systems with Internal Interfaces'', September 15  19, 2008, FriedrichAlexanderUniversität ErlangenNürnberg, September 15, 2008.

H.Chr. Kaiser, A thermodynamic approach to transient KohnSham theory, 100th Statistical Mechanics Conference, December 13  18, 2008, Rutgers, The State University of New Jersey, New Brunswick, USA, December 16, 2008.

H.Chr. Kaiser, On driftdiffusion KohnSham theory, 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2008), session ``Applied Analysis'', March 31  April 4, 2008, University of Bremen, April 1, 2008.

P.N. Racec, Modelling of nanowire transistors in LandauerBüttiker formalism, Spring Meeting of the Condensed Matter Division of the Deutsche Physikalische Gesellschaft, Berlin, February 25  29, 2008.

P.N. Racec, Quantum transport in cylindrical nanowire heterostructures, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, December 4  7, 2008, Dublin Institute for Advanced Studies, School of Theoretical Physics, Ireland, December 6, 2008.

H.Chr. Kaiser, A driftdiffusion model of transient KohnSham theory, First Joint International Meeting between the American Mathematical Society and the Polish Mathematical Society, Special Session ``Mathematics of Large Quantum Systems'', July 31  August 3, 2007, University of Warsaw, Poland, August 3, 2007.

J. Rehberg, An elliptic model problem including mixed boundary conditions and material heterogeneities, Fifth Singular Days, April 23  27, 2007, International Center for Mathematical Meetings, Luminy, France, April 26, 2007.

J. Rehberg, On SchrödingerPoisson systems, International Conference ``Nonlinear Partial Differential Equations'' (NPDE 2007), September 10  15, 2007, Institute of Applied Mathematics and Mechanics of NASU, Yalta, Ukraine, September 13, 2007.

J. Rehberg, Operator functions inherit monotonicity, MiniWorkshop on PDE's and Quantum Transport, March 12  16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 14, 2007.

J. Rehberg, Über SchrödingerPoissonSysteme, Chemnitzer Mathematisches Colloquium, Technische Universität Chemnitz, Fakultät für Mathematik, May 24, 2007.

F. Schmid, An evolution model in contact mechanics with dry friction, 6th International Congress on Industrial and Applied Mathematics (ICIAM), July 16  20, 2007, ETH Zürich, Switzerland, July 19, 2007.

K. Gärtner, A. Glitzky, Th. Koprucki, Analysis and simulation of spinpolarized driftdiffusion models, Evaluation Colloquium of the DFG Priority Program SPP 1285 ``Semiconductor Spintronics'', Bad Honnef, December 14  15, 2006.

A. Glitzky, R. Nürnberg, U. Bandelow, ttfamily WIASTeSCA: Simulation of semiconductor lasers, LaserOptikBerlin, March 23  24, 2006.

A. Glitzky, Energy models where the equations are defined on different domains, GAMM Annual Meeting 2006, March 27  31, 2006, Technische Universität Berlin, March 29, 2006.

J. Rehberg, Existence and uniqueness for van Roosbroeck's system in Lebesque spaces, Conference ``Recent Advances in Nonlinear Partial Differential Equations and Applications'', Toledo, Spain, June 7  10, 2006.

J. Rehberg, Regularity for nonsmooth elliptic problems, Crimean Autumn Mathematical School, September 20  25, 2006, Vernadskiy Tavricheskiy National University, Laspi, Ukraine, September 21, 2006.

J. Rehberg, The SchrödingerPoisson system, Colloquium in Honor of Prof. Demuth, September 10  11, 2006, Universität Clausthal, September 10, 2006.

A. Glitzky, An application of the Implicit Function Theorem to stationary energy models for semiconductor devices, International Workshop ``Regularity for nonlinear and linear PDEs in nonsmooth domains'', September 4  7, 2005, Universität Stuttgart, Hirschegg, Austria, September 5, 2005.

A. Glitzky, Stationary energy models for semicoductor devices with incompletely ionized impurities, 2nd Joint Meeting of AMS, DMV, ÖMG, June 16  19, 2005, Johannes Gutenberg Universität, Mainz, June 19, 2005.

J. Rehberg, Elliptische und parabolische Probleme aus Anwendungen, Kolloquium im Fachbereich Mathematik, Universität Darmstadt, May 18, 2005.

J. Rehberg, Existence, uniqeness and regularity for quasilinear parabolic systems, International Conference ``Nonlinear Partial Differential Equations'', September 17  24, 2005, Institute of Applied Mathematics and Mechanics Donetsk, Alushta, Ukraine, September 18, 2005.

J. Rehberg, H$^1,q$regularity for linear, elliptic boundary value problems, Regularity for nonlinear and linear PDEs in nonsmooth domains  Analysis, simulation and application, September 5  7, 2005, Universität Stuttgart, Deutsche Forschungsgemeinschaft (SFB 404), Hirschegg, Austria, September 6, 2005.

J. Rehberg, Regularität für elliptische Probleme mit unglatten Daten, Oberseminar Prof. Escher/Prof. Schrohe, Technische Universität Hannover, December 13, 2005.

J. Rehberg, Some analytical ideas concerning the quantumdriftdiffusion systems, Workshop ``Problèmes spectraux nonlinéaires et modèles de champs moyens'', April 4  8, 2005, Institut Henri Poincaré, Paris, France, April 5, 2005.

J. Rehberg, Analysis of macroscopic and quantum mechanical semiconductor models, International Visitor Program ``Nonlinear Parabolic Problems'', August 8  November 18, 2005, Finnish Mathematical Society (FMS), University of Helsinki, and Helsinki University of Technology, Finland, November 1, 2005.

J. Rehberg, Existence, uniqueness and regularity for quasilinear parabolic systems, Conference ``Nonlinear Parabolic Problems'', October 17  21, 2005, Finnish Mathematical Society (FMS), University of Helsinki, and Helsinki University of Technology, Finland, October 20, 2005.

J. Fuhrmann, H.Chr. Kaiser, Th. Koprucki, G. Schmidt, Electronic states in semiconductor nanostructures and upscaling to semiclassical models, Evaluation Colloquium of the DFG Priority Program ``Analysis, Modeling and Simulation of Multiscale Problems'', Bad Honnef, May 20  21, 2004.

H. Gajewski, Zur Numerik des Ladungsträgertransports in Halbleiterbauelementen, Technische Universität München, Institut fär Technische Elektrophysik, February 5, 2004.

J. Rehberg, Elliptische und parabolische Probleme mit unglatten Daten, Technische Universität Darmstadt, Fachbereich Mathematik, December 14, 2004.

J. Rehberg, Quasilinear parabolic equations in $L^p$, Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann, June 28  30, 2004, Universität Zürich, Institut für Mathematik, Switzerland, June 29, 2004.

J. Rehberg, The twodimensional van Roosbroeck system has solutions in $L^p$, Workshop ``Advances in Mathematical Semiconductor Modelling: Devices and Circuits'', March 2  6, 2004, ChineseGerman Centre for Science Promotion, Beijing, China, March 5, 2004.

M. Baro, H. Gajewski, R. Hünlich, H.Chr. Kaiser, Optoelektronische Bauelemente: mikroskopische & makroskopische Modelle, MathInside  Überall ist Mathematik, event of the DFG Research Center ``Mathematics for Key Technologies'' on the occasion of the Open Day of Urania, Berlin, September 13, 2003  December 3, 2004.

H.Chr. Kaiser, Classical solutions of van Roosbroeck's equations with discontinuous coefficients and mixed boundary conditions on twodimensional space domains, 19th GAMM Seminar Leipzig on Highdimensional problems  Numerical treatment and applications, January 23  25, 2003, MaxPlanckInstitut für Mathematik in den Naturwissenschaften, Leipzig, January 25, 2003.

J. Rehberg, A combined quantum mechanical and macroscopic model for semiconductors, Workshop on Multiscale problems in quantum mechanics and averaging techniques, December 11  12, 2003, MaxPlanckInstitut für Mathematik in den Naturwissenschaften, Leipzig, December 12, 2003.

J. Rehberg, Solvability and regularity for parabolic equations with nonsmooth data, International Conference ``Nonlinear Partial Differential Equations'', September 15  21, 2003, National Academy of Sciences of Ukraine, Institute of Applied Mathematics and Mechanics, Alushta, September 17, 2003.

M. Baro, M. Demuth, E. Giere, Stable continuous spectra for differential operators of arbitrary order, Preprint no. 6, Technische Universität Clausthal, Institut für Mathematik, 2002.
Highlights
Organic semiconductor devices
In close cooperation with our partners from the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP, TU Dresden) we model and simulate organic semiconductor devices such as organic transistors (OPBTs, VOFETs) as well as organic lightemitting diodes (OLEDs). One crucial feature of organic devices is the temperatureactivated hopping transport of charge carriers. In connection with Joule selfheating this leads to a complex interplay that eventually results in Sshaped currentvoltage characteristics and can lead to brightness inhomogeneities in largearea OLEDs.
Together with the IAPP we derived an empirical PDE thermistor model. It is based on a p(x)Laplace operator that takes the nonOhmic behavior of the organic layers into account and an Arrhenius law whose activation energy describes the energetic disorder in organic materials. The model was implemented in a simulation tool capable of simulating the electrothermal interplay in largearea OLEDs including Sshaped characteristics with regions of negative differential resistance.
Mathematical optimization of optoelectronic device designs
Silicon photonics has become a rapidly developing new field with a high potential for lowcost solutions to problems ranging from highspeed data transfer for optical onchip communication to biosensing. However, for optoelectronic applications, the missing piece in silicon photonics is a monolithically integrated light source. For this, a promising candidate is germanium, since its optical properties can be influenced and enhanced by applying a mechanical strain and electronical doping.
To understand their potential in performance, in close collaboration with IHP (Innovations for High Performance microelectronics, Frankfurt Oder), we model, simulate, and optimize the design of germaniumonsilicon microstrips to enable sufficient light emission. To determine the influence of the macroscopic mechanical strain and the doping on the optoelectronic properties of the device, we developed a multiscale model, see IEEE Photonics (DOI:10.1109/JPHOT.2015.2427093).
Using this model, we carried out exemplary robustness studies, see OQE (DOI:10.1007/s1108201603944). The model is also the basis for the development of mathematical tools for a systematic topology and doping optimization based on second order methods for the underlying PDE systems, e.g. see Journal of Computational and Theoretical Transport (DOI:10.1080/23324309.2016.1189940). An overview to this approach is also given in the WIAS Annual Research Report 2015.
Publications
Monographs
Articles in Refereed Journals
Contributions to Collected Editions
Preprints, Reports, Technical Reports
Talks, Poster
External Preprints
Contact
Mathematical Context
 Algorithms for the generation of 3D boundary conforming Delaunay meshes
 Analysis of Partial Differential Equations and Evolutionary Equations
 Numerical Methods for PDEs with Stochastic Data
 Numerical methods for coupled systems in computational fluid dynamics
 Systems of partial differential equations: modeling, numerical analysis and simulation
Projects/Grants
 Datadriven electronic structure calculation for nanostructures
 Hybrid models for the electrothermal behavior of organic semiconductor devices
 Modelbased geometry reconstruction from TEM images
 Models for heat and charge carrier flow in organic electronics
 Multidimensional modeling and simulation of electrically pumped semiconductorbased emitters
 Pattern formation in systems with multiple scales