Moderne Halbleiter-Bauelemente und optoelektronische Bauelemente wie Halbleiterlaser oder Solarzellen basieren auf Halbleiterstrukturen, die z.B. durch Dotierungsprofile, Heterostrukturen oder Nanostrukturen gegeben sein können. Um das Verhalten dieser Bauelemente qualitativ und quantitativ zu beschreiben und zu optimieren, ist die mathematische Modellierung und Simulation der funktionsbestimmenden bzw. -limitierenden Ladungstransportvorgänge notwendig.

Von großem Interesse ist auch die Steigerung der Energieeffizienz neuer Bauteile sowie die Entwicklung neuer Technologien für Anwendungen in den Feldern Erneuerbare Energie, Kommunikation, Beleuchtung. Dieses Thema, das unter dem Begriff Green Photonics zusammengefasst wird, ist eine der wesentlichen technologischen Herausforderungen der kommenden Jahre. Das WIAS beteiligt sich aktiv an der Grundlagen- und anwendungsorientierten Forschung und Entwicklung neuer Lösungen.

Zur Beschreibung des Ladungsträgertransports in Halbleiter-Bauelementen haben sich Drift-Diffusions-Modelle etabliert. Das van Roosbroeck-System ist das grundlegende Modell für diese Klasse von Modellen. Es beschreibt die Bewegung von negativen und positiven Ladungsträgern (Elektronen und Löcher) in einem selbstkonsistenten elektrischen Feld aufgrund von Drift und Diffusion.

Die Forschungen in diesem Anwendungsfeld konzentrieren sich zum einen auf die Entwicklung und Untersuchung von mathematischen Modellansätzen zur Berücksichtigung weiterer wichtiger physikalischer Effekte. Zum anderen steht die Entwicklung schneller und robuster numerischer Lösungsverfahren für die gekoppelten Modellgleichungen im Vordergrund. Die konkreten Zielsetzungen ergeben sich häufig aus den anspruchsvollen Fragestellungen unserer Kooperationspartner.

Das WIAS hat eine lange Tradition in der mathematischen Modellierung und der numerischen Simulation von Halbleitermaterialien. Viele analytische Resultate für die Systeme partieller Differentialgleichungen, die den Ladungsträgertransport beschreiben, wurden publiziert. Zusätzlich wurden verschiedene Software-Pakete entwickelt: WIAS-TeSCA, WIAS-QW, ddfermi.

Simulierte Löcherstromdichte in einer CIGS Solarzelle mit Pin-Kontaktierung.

Neue Technologien unterliegen jedoch stetigem Wandel, sodass neue Methoden und Ansätze benötigt werden. Das WIAS verfolgt dabei folgende Aspekte:

  • Neue Werkzeuge für die mathematische Analysis wie z.B. Gradientenstrukturen
  • Weitere analytische Resultate für gekoppelte Modelle, z.B. Kopplung von Transportgleichungen und Quantenmechanischen Systemen
  • Neue mathematische Modelle für neuartige Materialien, z.B. organische Halbleiter (siehe Matheon-Projekt SE2)
  • Untersuchung verschiedener Diskretisierungsschemata für spezifische physikalische Situationen, wie z.B kryogenische Temperaturen
  • Entwicklung einer neuen Simulationssoftware: ddfermi
  • Dotierungs- und Topologieoptimierung (siehe Matheon-Projekt OT1)

Obere Reihe: Berechnete Bandkanten und Quasi-Fermi-Potentiale für eine GaAs p-i-n-Diode bei verschiedene angelegten Spannungen. (a) Thermodynamisches Gleichgewicht (Off-Zustand, 0V), (b) U = 1.5V (Flachband), (c) U = 3.0 V. Das Bauteil hat eine Länge von 10 μm (1 μm n-dotiert mit ND = 1016 cm-3, 8 μm intrinsisch, 1 μm p-dotiert mit NA = 1017 cm-3. Untere Reihe: (d) Elektrondichte durchgezogen, Lochdichte gestrichelt. (e) Strom-Spannungs-Kennlinien für das gleiche Bauteil mit verschiedenen Werten der Donatordichte ND.

Höhepunkte

Organische Halbleiterbauelemente

In enger Zusammenarbeit mit unseren Partnern vom Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP, TU Dresden) modellieren und simulieren wir organische Halbleiterbauteile, wie z.B. organische Transistoren (OPBTs, VOFETs) sowie organische Leuchtdioden (OLEDs). Eine besondere Eigenheit organischer Halbleitermaterialien ist der temperatur- aktivierte Hüpftransport der Ladungsträger. In Verbindung mit Joule'scher Selbstaufheizung führt dies auf ein komplexes Wechselspiel und kann letztendlich in S-förmigen Strom-Spannungs-Kennlinien resultieren. Dies kann wiederum zu ungewollten Inhomogenitäten der Luminanz z.B. in großflächigen organischen Leuchtdioden führen.

Links: S-förmige Strom-Spannungs-Kennlinien mit Bereichen negativen differentiellen Widerstands simuliert für kleinflächige organische nin-Struktur. Rechts: Inhomogene Stromdichte in OLED hervorgerufen durch Selbstaufheizungseffekten.

Zusammen mit dem IAPP haben wir ein empirisches Thermistormodel entwickelt, dass auf einem p(x)-Laplace-Operator und einem Arrheniusgesetz basiert. Ersterer modelliert das nicht-Ohm'sche Verhalten der organischen Schichten, während die Aktivierungsenergie in dem Arrheniusgesetz die energetische Unordung in organischen Materialien widerspiegelt. Das Model wurde in einem Software-Tool implementiert, das in der Lage ist das elektrothermische Wechselspiel in OLEDs inklusive S-förmiger Charakteristiken mit Bereichen negativen differentiellen Widerstands zu simulieren.

Simulationsstudie eines organischen Permeable-Base-Transistors hergestellt von unseren Partnern am IAPP.

Mathematische Optimierung optoelektronischer Bauteile

Silizium Photonik ist ein sich rasant entwickelndes, neues Feld mit hohem Potenzial für kostengünstige Lösungen im Bereich von Hochgeschwindigkeits-Datenübertragung oder Bio-sensing. Für Anwendungen in der Optoelektronik fehlt jedoch eine monolithisch integrierbare Lichtquelle. Germanium ist hierfür ein vielversprechender Kandidat, da seine optischen Eigenschaften durch eine mechanische Verspannung oder elektronische Dotierung beeinflusst und verbessert werden können.

Um das Anwendungspotential dieser Technologie zu verstehen, modellieren, simulieren und optimieren wir in enger Zusammenarbeit mit dem IHP (Innovationen für Hochleistungs-Mikroelektronik, Frankfurt Oder) das Design von Germanium-Silizium-Mikrostreifen, um eine ausreichende Lichtemission zu ermöglichen. Um den Einfluss der makroskopischen, mechanischen Verspannung und der elektronischen Dotierung auf die optoelektronischen Eigenschaften des Bauteils zu bestimmen, wurde ein Multiskalenmodell entwickelt IEEE Photonics (DOI:10.1109/JPHOT.2015.2427093).
Querschnitt durch einen Germanium Kantenemitter mit Löcherstrom (Farbe und Vektorfeld) und optische Mode (rote Isolinien) in der optisch aktiven Germaniumschicht

Mit diesem Modell führten wir an Beispielbauteilen Robustheitsuntersuchungen durch, siehe Journal of Computational and Theoretical Transport (DOI:10.1080/23324309.2016.1189940). Einen Übersichtsartikel zu diesem Thema findet man auch im WIAS Annual Research Report 2015.

Publikationen

  Monografien

  • 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).
    Abstract
    HAGs von Christoph bestätigen lassen

  • A. Zisowsky, A. Arnold, M. Ehrhardt, Th. Koprucki, Chapter 7: Transient Simulation of k$cdot$p-Schrödinger Systems Using Discrete Transparent Boundary Conditions, in: Multi-Band 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. 247--272, (Chapter Published).

  • D. Klindworth, M. Ehrhardt, Th. Koprucki, Chapter 8: Discrete Transparent Boundary Conditions for Multi-band Effective Mass Approximations, in: Multi-Band 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. 273--318, (Chapter Published).

  • M. Ehrhardt, Th. Koprucki, eds., Multi-Band 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: Fabry--Perot Lasers: Thermodynamics-based Modeling, in: Optoelectronic Devices --- Advanced Simulation and Analysis, J. Piprek, ed., Springer, New York, 2005, pp. 63-85, (Chapter Published).

  Artikel in Referierten Journalen

  • P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on unstructured 1D grids for a singularly perturbed advection-diffusion equation and some multidimensional extensions, Journal of Scientific Computing, 72 (2017), pp. 373--395, DOI 10.1007/s10915-017-0361-7 .
    Abstract
    The accurate and efficient discretization of singularly perturbed advection-diffusion 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 advection-diffusion 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 one-dimensional 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.

  • O. Marquardt, Th. Krause, V. Kaganer, J. Martin-Sánchez, M. Hanke, O. Brandt, Influence of strain relaxation in axial $In_xGa_1-xN/GaN$ nanowire heterostructures on their electronic properties, Nanotechnology, 28 (2017), pp. 215204/1--215204/6, DOI 10.1088/1361-6528/aa6b73 .
    Abstract
    We present a systematic theoretical study of the influence of elastic strain relaxation on the built-in electrostatic potentials and the electronic properties of axial InxGa1-xN/GaN nanowire (NW) heterostructures. Our simulations reveal that for a sufficiently large ratio between the thickness of the InxGa1-xN disk and the diameter of the NW, the elastic relaxation leads to a significant reduction of the built-in 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 built-in electrostatic potentials. We show that the structures under consideration are by no means field-free, and the built-in 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. 245309/1--245309/8, DOI 10.1103/PhysRevB.95.245309 .
    Abstract
    We study the electronic properties of GaAs nanowires composed of both the zinc-blende and wurtzite modifications using a ten-band k-p 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 zinc-blende/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 non-negligible 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 zinc-blende 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. 205--233, DOI 10.1007/s10955-017-1756-4 .
    Abstract
    We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional 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.

  • 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. 536--562.
    Abstract
    We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring non-Ohmic current-voltage laws and self-heating effects. The coupled system consists of the current-flow equation for the electrostatic potential and the heat equation with Joule heating term as source. The self-heating in the device is modeled by an Arrhenius-like temperature dependency of the electrical conductivity. Moreover, the non-Ohmic 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 $p(x)$-Laplace-type problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the two-dimensional 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 Caccioppoli-type estimates, Poincaré inequalities, and a Gehring-type Lemma for the $p(x)$-Laplacian. Finally, Schauder's fixed-point 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 one-dimensional blood flow models using experimental data, International Journal of Numerical Methods in Biomedical Engineering, 33 (2017), pp. 1--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 one-dimensional 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. 497--513, 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 Scharfetter--Gummel scheme to non-Boltzmann (e.g. Fermi--Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

  • 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, 330 (2017), DOI DOI 10.1007/s11082-017-1167-4 .
    Abstract
    Organic semiconductor devices show a pronounced interplay between temperature-activated conductivity and self-heating which in particular causes inhomogeneities in the brightness of large-area OLEDs at high power. We consider a 3D thermistor model based on partial differential equations for the electrothermal behavior of organic devices and introduce an extension to multiple layers with nonlinear conductivity laws, which also take the diode-like behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finite-volume approximation of this model. The appearance of S-shaped current-voltage characteristics with regions of negative differential resistance in a measured device can be quantitatively reproduced. Furthermore, this simulation study reveals a propagation of spatial zones of negative differential resistance in the electron and hole transport layers toward the contact.

  • M. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Optical and Quantum Electronics, 48 (2016), pp. 543/1--543/7.
    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 one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased 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 oxide-confined pn-diodes, IEEE Transactions on Electron Devices, 63 (2016), pp. 2036--2042.
    Abstract
    Current injection into single quantum dots embedded in vertical pn-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. Experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional pin-design. By an alternative design employing p-doping up to the oxide aperture the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.

  • 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 edge-emitting lasers based on strained germanium, Optical and Quantum Electronics, 48 (2016), pp. 156/1--156/7.
    Abstract
    We consider a device concept for edge-emitting lasers based on strained germanium microstrips. The device features an inhomogeneous tensile strain distribution generated by a SiN stressor deposited on top of the Ge microstrip. This geometry requires a lateral contact scheme and hence a full two-dimensional description. The two-dimensional simulations of the carrier transport and of the optical field, carried out in a cross section of the device orthogonal to the optical cavity, use microscopic calculations of the strained Ge material gain as an input. In this paper we study laser performance and robustness against Shockley-Read-Hall lifetime variations and device sensitivity to different strain distributions.

  • D. Peschka, N. Rotundo, M. Thomas, Towards doping optimization of semiconductor lasers, Journal of Computational and Theoretical Transport, 45 (2016), pp. 410--423.
    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 quantum-well 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. Lux-Steiner, M. Liero, Point contacts at the copper-indium-gallium-selenide interface -- A theoretical outlook, Journal of Applied Physics, 119 (2016), pp. 155304/1--155304/7, DOI 10.1063/1.4947267 .
    Abstract
    For a long time, it has been assumed that recombination in the space-charge 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 point-contact junction may call this into question. In this work a theoretical outlook is made using three-dimensional 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. 094501/1--094501/8.

  • TH. Koprucki, N. Rotundo, P. Farrell, D.H. Doan, J. Fuhrmann, On thermodynamic consistency of a Scharfetter--Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement, Optical and Quantum Electronics, 47 (2015), pp. 1327--1332.
    Abstract
    Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with arbitrary statistical distribution functions. This requires numerical schemes that preserve qualitative properties of the solutions, such as positivity of densities, dissipativity and consistency with thermodynamic equilibrium. An extension of the Scharfetter-Gummel scheme guaranteeing consistency with thermodynamic equilibrium is studied. It is derived by replacing the thermal voltage with an averaged diffusion enhancement for which we provide a new explicit formula. This approach avoids solving the costly local nonlinear equations defining the current for generalized Scharfetter-Gummel schemes.

  • M. Liero, Th. Koprucki, A. Fischer, R. Scholz, A. Glitzky, p-Laplace 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. 2957--2977.
    Abstract
    In large-area Organic Light-Emitting Diodes (OLEDs) spatially inhomogeneous luminance at high power due to inhomogeneous current flow and electrothermal feedback can be observed. To describe these self-heating effects in organic semiconductors we present a stationary thermistor model based on the heat equation for the temperature coupled to a p-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p-Laplacian describes the non-Ohmic electrical behavior of the organic material. Moreover, an Arrhenius-like temperature dependency of the electrical conductivity is considered. We introduce a finite-volume scheme for the system and discuss its relation to recent network models for OLEDs. In two spatial dimensions we derive a priori estimates for the temperature and the electrostatic potential and prove the existence of a weak solution by Schauder's fixed point theorem.

  • D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, G. Capellini, Th. Koprucki, Th. Schröder, Modeling of edge-emitting lasers based on tensile strained germanium microstrips, IEEE Photonics Journal, 7 (2015), pp. 1502115/1--1502115/15, DOI 10.1109/JPHOT.2015.2427093 .
    Abstract
    In this paper we present a thorough modeling of an edge-emitting 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 two-dimensional 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, Index-2 elliptic partial differential-algebraic models for circuits and devices, Journal of Mathematical Analysis and Applications, 423 (2015), pp. 1348--1369.

  • 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, Non-equilibrium current via geometric scatterers, Journal of Physics. A. Mathematical and General, 47 (2014), pp. 395301/1--395301/16.

  • 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. 3367--3374.
    Abstract
    For lighting applications, Organic light-emitting diodes (OLED) need much higher brightness than for displays, leading to self-heating. Due to the temperature-activated transport in organic semiconductors, this can result in brightness inhomogeneities and catastrophic failure. Here, we show that due to the strong electrothermal feedback of OLEDs, the common spatial current and voltage distribution is completely changed, requiring advanced device modeling and operation concepts. Our study clearly demonstrates the effect of negative differential resistance (NDR) in OLEDs induced by self-heating. As a consequence, for increasing voltage, regions with declining voltages are propagating through the device, and even more interestingly, a part of these regions show even decreasing currents, leading to strong local variation in luminance. The expected breakthrough of OLED lighting technology will require an improved price performance ratio, and the realization of modules with very high brightness but untainted appearance is considered to be an essential step into this direction. Thus, a deeper understanding of the control of electrothermal feedback will help to make OLEDs in lighting more competitive.

  • TH. Koprucki, K. Gärtner, Discretization scheme for drift-diffusion equations with strong diffusion enhancement, Optical and Quantum Electronics, 45 (2013), pp. 791--796.
    Abstract
    Inspired by organic semiconductor models based on hopping transport introducing Gauss-Fermi integrals a nonlinear generalization of the classical Scharfetter-Gummel scheme is derived for the distribution function F(η)=1/(exp(-η)+γ). This function provides an approximation of the Fermi-Dirac integrals of different order and restricted argument ranges. The scheme requires the solution of a nonlinear equation per edge and continuity equation to calculate the edge currents. In the current formula the density-dependent diffusion enhancement factor, resulting from the generalized Einstein relation, shows up as a weighting factor. Additionally the current modifies the argument of the Bernoulli functions.

  • M. Liero, A. Mielke, Gradient structures and geodesic convexity for reaction-diffusion systems, Philosophical Transactions of the Royal Society A : Mathematical, Physical & Engineering Sciences, 371 (2013), pp. 20120346/1--20120346/28.
    Abstract
    We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory. We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion 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, Self-heating, bistability, and thermal switching in organic semiconductors, Physical Review Letters, 110 (2013), pp. 126601/1--126601/5.
    Abstract
    We demonstrate electric bistability induced by the positive feedback of self-heating onto the thermally activated conductivity in a two-terminal device based on the organic semiconductor C60. The central undoped layer with a thickness of 200 nm is embedded between thinner n-doped layers adjacent to the contacts minimizing injection barriers. The observed current-voltage characteristics follow the general theory for thermistors described by an Arrhenius-like 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 reaction-diffusion 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. 29--52.
    Abstract
    We derive gradient-flow formulations for systems describing drift-diffusion processes of a finite number of species which undergo mass-action 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 electro-reaction-diffusion systems with active interfaces permitting drift-diffusion 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 self-consistent 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 Wigner--Eisenbud problem for a cylindrical nanowire within finite volume method, Journal of Computational Physics, 252 (2013), pp. 52--64.
    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 double-barriers 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, Self-heating effects in organic semiconductor crossbar structures with small active area, Organic Electronics, 13 (2012), pp. 2461--2468.
    Abstract
    We studied the influence of heating effects in an organic device containing a layer sequence of n-doped / intrinsic / n-doped C60 between crossbar metal electrodes. A strong positive feedback between current and temperature occurs at high current densities beyond 100 A/cm2, 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 C60 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 three-dimensional effects have a strong impact on a device with seemingly one-dimensional 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. 3874--3900.
    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 generation-recombination 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. 777--783.
    Abstract
    We present a spatially resolved semiclassical model for the simulation of semiconductor quantum-dot lasers including a multi-species 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. 1980--1998.
    Abstract
    We introduce an electronic model for solar cells including energy resolved defect densities. The resulting drift-diffusion 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. 341--375.
    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 Sobolev-Morrey 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. 809--828.
    Abstract
    We present a microscopic theory describing the charge carrier and light emission dynamics in quantum dot (QD) light emitters. The theory covers non-classical 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 electron-phonon scattering rates between bound QD, continuous wetting layer (WL) and bulk states. In the low carrier density limit, multi-phonon 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) time-resolved 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 vertical-cavity surface-emitting lasers (VCSELs) at high injection currents.

  • A. Glitzky, J.A. Griepentrog, Discrete Sobolev--Poincaré inequalities for Voronoi finite volume approximations, SIAM Journal on Numerical Analysis, 48 (2010), pp. 372--391.
    Abstract
    We prove a discrete Sobolev-Poincare 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 spin-polarized drift-diffusion systems, SIAM Journal on Mathematical Analysis, 41 (2010), pp. 2489--2513.
    Abstract
    We study a stationary spin-polarized drift-diffusion 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 Scharfetter-Gummel 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. 749--771.
    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 non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional 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. 155305/1--155305/14.
    Abstract
    We investigate the scattering phenomena produced by a general finite range non-separable potential in a multi-channel two-probe cylindrical nanowire heterostructure. The multi-channel current scattering matrix is efficiently computed using the R-matrix 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 non-uniform 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 nano-cylinder.

  • R. Haller-Dintelmann, 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. 397--428.
    Abstract
    The well known De Giorgi result on Hölder continuity for solutions of the Dirichlet problem is re-established 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. Haller-Dintelmann, J. Rehberg, Maximal parabolic regularity for divergence operators including mixed boundary conditions, Journal of Differential Equations, 247 (2009), pp. 1354--1396.
    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 non-smooth and $A$ is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth 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. 1347--1362.
    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 Scharfetter-Gummel-scheme. 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 electro-reaction-diffusion systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 70 (2009), pp. 788--805.
    Abstract
    We consider electro-reaction-diffusion 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 electro-reaction-diffusion 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 electro-reaction-diffusion systems with partly fast kinetics, Discrete and Continuous Dynamical Systems, 25 (2009), pp. 159--174.
    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 electro--reaction--diffusion 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 discrete-time 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 drift-diffusion equations for semiconductor devices: The 2D case, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 71 (2009), pp. 1584--1605.
    Abstract
    We regard drift-diffusion 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 quasi-linear 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 non-smooth 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. 179--185.
    Abstract
    An elementary proof of the anti-monotonicity 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 Kohn--Sham system at zero temperature, Journal of Physics. A. Mathematical and General, 41 (2008), pp. 385304/1--385304/21.
    Abstract
    An one-dimensional Kohn-Sham 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 Kohn-Sham 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 exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.

  • R. Haller-Dintelmann, H.-Chr. Kaiser, J. Rehberg, Elliptic model problems including mixed boundary conditions and material heterogeneities, Journal de Mathématiques Pures et Appliquées, 89 (2008), pp. 25--48.

  • M. Hieber, J. Rehberg, Quasilinear parabolic systems with mixed boundary conditions on nonsmooth domains, SIAM Journal on Mathematical Analysis, 40 (2008), pp. 292--305.
    Abstract
    In this paper we investigate quasilinear systems of reaction-diffusion equations with mixed Dirichlet-Neumann bondary conditions on non smooth domains. Using techniques from maximal regularity and heat-kernel 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. 1676--1693.
    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 two-dimensional 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 spin-polarized drift-diffusion model, Advances in Mathematical Sciences and Applications, 18 (2008), pp. 401--427.
    Abstract
    We introduce a spin-polarized drift-diffusion 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 electro-reaction-diffusion systems, Nonlinearity, 21 (2008), pp. 1989--2009.
    Abstract
    Our focus are electro-reaction-diffusion 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 electro-reaction-diffusion 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 Sobolev--Morrey spaces, Advances in Differential Equations, 12 (2007), pp. 1031--1078.
    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 SOBOLEV-MORREY 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, Sobolev--Morrey spaces associated with evolution equations, Advances in Differential Equations, 12 (2007), pp. 781--840.
    Abstract
    In this text we introduce new classes of SOBOLEV-MORREY 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 SOBOLEV-MORREY 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. 136--142.

  • 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. 122112/1--122112/3.

  • 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. 242109/1--242109/3.

  • 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. 205308/1--205308/9.

  • M. Winkelnkemper, R. Seguin, S. Rodt, A. Schliwa, L. Reimann, A. Strittmatter, A. Hoffmann, D. Bimberg, Polarized emission lines from A- and B-type excitonic complexes in single InGaN/GaN quantum dots, Journal of Applied Physics, 101 (2007), pp. 113708/1--113708/4.

  • U. Wulf, P.N. Racec, E.R. Racec, Admittance of planar two-terminal quantum systems, Phys. Rev. B., 75 (2007), pp. 075320/1--075320/9.

  • 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. 593--615.

  • 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. 233--252.
    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. 2215--2232.
    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 one-dimensional Schrödinger-type operators, Integral Equations and Operator Theory, 58 (2007), pp. 407--431.
    Abstract
    The paper is devoted to Schroedinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the Lax-Phillips 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 Birman-Krein formula are verified directly. The results are used for dissipative Schroedinger-Poisson systems.

  • P.N. Racec, U. Wulf, Small-signal circuit elements of MIS-type nanostructures, Solid State Phenomena, 121--123 (2007), pp. 549--552.

  • 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. 287-310.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Convexity of trace functionals and Schrödinger operators, Journal of Functional Analysis, 234 (2006), pp. 45--69.

  • M. Baro, N. Ben Abdallah, P. Degond, A. El Ayyadi, A 1D coupled Schrödinger drift-diffusion model including collisions, Journal of Computational Physics, 203 (2005), pp. 129-153.

  • M. Baro, H. Neidhardt, J. Rehberg, Current coupling of drift-diffusion models and dissipative Schrödinger--Poisson systems: Dissipative hybrid models, SIAM Journal on Mathematical Analysis, 37 (2005), pp. 941--981.

  • M. Baro, M. Demuth, E. Giere, Stable continuous spectra for differential operators of arbitrary order, Analysis and Applications, 3 (2005), pp. 223-250.

  • 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. 181911/1--181911/3.

  • H. Neidhardt, J. Rehberg, Uniqueness for dissipative Schrödinger--Poisson systems, Journal of Mathematical Physics, 46 (2005), pp. 113513/1--113513/28.

  • A. Glitzky, R. Hünlich, Global existence result for pair diffusion models, SIAM Journal on Mathematical Analysis, 36 (2005), pp. 1200--1225.

  • A. Glitzky, R. Hünlich, Stationary energy models for semiconductor devices with incompletely ionized impurities, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 85 (2005), pp. 778--792.

  • J. Rehberg, Quasilinear parabolic equations in $L^p$, Progress in Nonlinear Differential Equations and their Applications, 64 (2005), pp. 413-419.

  • M. Baro, H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, A quantum transmitting Schrödinger-Poisson system, Reviews in Mathematical Physics. A Journal for Both Review and Original Research Papers in the Field of Mathematical Physics, 16 (2004), pp. 281--330.

  • M. Baro, H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Dissipative Schrödinger--Poisson systems, Journal of Mathematical Physics, 45 (2004), pp. 21--43.

  • 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. 219--262.

  • A. Glitzky, W. Merz, Single dopant diffusion in semiconductor technology, Mathematical Methods in the Applied Sciences, 27 (2004), pp. 133--154.

  • A. Glitzky, R. Hünlich, Stationary solutions of two-dimensional heterogeneous energy models with multiple species, Banach Center Publications, 66 (2004), pp. 135-151.

  • A. Glitzky, Electro-reaction-diffusion systems with nonlocal constraints, Mathematische Nachrichten, 277 (2004), pp. 14--46.

  • M. Baro, H. Neidhardt, Dissipative Schrödinger-type operator as a model for generation and recombination, Journal of Mathematical Physics, 44 (2003), pp. 2373--2401.

  • H. Gajewski, I.V. Skrypnik, On the uniqueness of solutions for nonlinear elliptic-parabolic equations, Journal of Evolution Equations, 3 (2003), pp. 247--281.

  • 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. 291--304.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Macroscopic current induced boundary conditions for Schrödinger-type operators, Integral Equations and Operator Theory, 45 (2003), pp. 39--63.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, On 1-dimensional dissipative Schrödinger-type operators, their dilations and eigenfunction expansions, Mathematische Nachrichten, 252 (2003), pp. 51--69.

  • G. Albinus, H. Gajewski, R. Hünlich, Thermodynamic design of energy models of semiconductor devices, Nonlinearity, 15 (2002), pp. 367--383.

  • 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. 110--120.

  • J.A. Griepentrog, Linear elliptic boundary value problems with non-smooth data: Campanato spaces of functionals, Mathematische Nachrichten, 243 (2002), pp. 19--42.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Density and current of a dissipative Schrödinger operator, Journal of Mathematical Physics, 43 (2002), pp. 5325--5350.

  • A. Glitzky, R. Hünlich, Global properties of pair diffusion models, Advances in Mathematical Sciences and Applications, 11 (2001), pp. 293--321.

  • 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. 87--112.

  • 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. 541-567.

  • 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. 28--32.

  • J.A. Griepentrog, L. Recke, Linear elliptic boundary value problems with non-smooth data: Normal solvability on Sobolev-Campanato spaces, Mathematische Nachrichten, 225 (2001), pp. 39--74.

  • 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. 379--409.

  • A. Glitzky, R. Hünlich, Electro-reaction-diffusion systems including cluster reactions of higher order, Mathematische Nachrichten, 216 (2000), pp. 95--118.

  • H.-Chr. Kaiser, J. Rehberg, About a stationary Schrödinger-Poisson system with Kohn-Sham potential in a bounded two- or three-dimensional domain, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 41 (2000), pp. 33--72.

  • 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. 43--51.
    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 drift-diffusion 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 Sobolev-Campanato spaces.

  Beiträge zu Sammelwerken

  • M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, Modeling and simulation of electrothermal feedback in large-area organic leds, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 105--106, DOI 10.1109/NUSOD.2017.8010013 .

  • M. Bulíček, A. Glitzky, M. Liero, Thermistor systems of p(x)-Laplace-type with discontinuous exponents via entropy solutions, in: PDE 2015: Theory and Applications of Partial Differential Equations (PDE 2015), 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, American Institute of Mathematical Sciences, Springfield, 2017, pp. 697--713.
    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 current-flow equation is of p(x)-Laplacian-type 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 L1 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. Cances, P. Omnes, eds., 199 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 303--310.

  • 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'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 219--220, DOI 10.1109/NUSOD.2017.8010070 .

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Multi-scale modelling and simulation of single-photon sources on a device level, in: Euro-TMCS 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.

  • P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, Th. Koprucki, Numerical methods for drift-diffusion models, in: Handbook of Optoelectronic Device Modeling and Simulation (Two-Volume Set), J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press Taylor & Francis Group, 2017.
    Abstract
    The van Roosbroeck system describes the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation. It became the standard model to describe the current flow in semiconductor devices at macroscopic scale. Typical devices modeled by these equations range from diodes, transistors, LEDs, solar cells and lasers to quantum nanostructures and organic semiconductors. The report provides an introduction into numerical methods for the van Roosbroeck system. The main focus lies on the Scharfetter-Gummel finite volume discretization scheme and recent efforts to generalize this approach to general statistical distribution functions.

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Modeling and numerical simulation of electrically pumped single-photon emitters, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. Yuh-Renn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 151--152.

  • M. Kantner, U. Bandelow, Th. Koprucki, Multi-scale modeling and simulation of single-photon sources, in: Proceedings of iNOW 2015 (International Nano-Optoelectronics Workshop) (PDF only), Y. Arakawa, F. Koyama, C. Chang-Hasnain, D. Bimberg, eds., pp. 129-130.

  • D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, Th. Schröder, G. Capellini, Th. Koprucki, On device concepts for CMOS-compatible edge-emitters based on strained germanium, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. Yuh-Renn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 129--130.

  • A. Fischer, Th. Koprucki, A. Glitzky, M. Liero, K. Gärtner, J. Hauptmann, S. Reineke, D. Kasemann, B. Lüssem, K. Leo, R. Scholz, OLEDs: Light-emitting thin film thermistors revealing advanced self-heating 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/1--95661A/7.
    Abstract
    Large area OLEDs show pronounced Joule self-heating at high brightness. This heating induces brightness inhomogeneities, drastically increasing beyond a certain current level. We discuss this behavior considering 'S'-shaped negative differential resistance upon self-heating, even allowing for 'switched-back' regions where the luminance finally decreases (Fischer et al., Adv. Funct. Mater. 2014, 24, 3367). By using a multi-physics simulation the device characteristics can be modeled, resulting in a comprehensive understanding of the problem. Here, we present results for an OLED lighting panel considered for commercial application. It turns out that the strong electrothermal feedback in OLEDs prevents high luminance combined with a high degree of homogeneity unless new optimization strategies are considered.

  • 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 edge-emitting strained-Ge laser, in: Advanced Solid State Lasers, OSA Technical Digest (online) (Optical Society of America, 2015), 2015, pp. ATu2A.19/1--ATu2A.19/3.
    Abstract
    By using fully-coupled 2D optoelectronic simulations with embedded microscopic gain calculations, we study the optoelectronic performance of a monolithically integrated edge-emitting laser based on strained germanium microstrips fabricated using CMOS standard processes.

  • TH. Koprucki, M. Kantner, J. Fuhrmann, K. Gärtner, On modifications of the Scharfetter--Gummel scheme for drift-diffusion equations with Fermi-like statistical distribution functions, in: Proceedings of the 14th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2014, 1--4 September 2014, J. Piprek, J. Javaloyes, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2014, pp. 155--156.

  • 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. 229--232.

  • TH. Koprucki, K. Gärtner, Generalization of the Scharfetter--Gummel scheme, in: Proceedings of the 13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013, 19--22 August 2013, J. Piprek, L. Chrostowski, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2013, pp. 85--86.

  • A. Glitzky, K. Gärtner, J. Fuhrmann, Th. Koprucki, A. Fischer, B. Lüssem, K. Leo, R. Scholz, Electro-thermal modeling of organic semiconductors describing negative differential resistance induced by self-heating, in: Proceedings of the 13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013, 19--22 August 2013, J. Piprek, L. Chrostowski, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2013, pp. 77--78.

  • TH. Koprucki, K. Gärtner, Discretization scheme for drift-diffusion 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. 103--104.

  • U. Bandelow, Th. Koprucki, A. Wilms, A. Knorr, Multi-species 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. 59--60.

  • P.N. Racec, R. Racec, H. Neidhardt, R-matrix 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. 149--174.
    Abstract
    We investigate the scattering phenomena in two dimensions produced by a general finite-range 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 one-dimensional problem. If the potential has an attractive character even the evanescent channels can be seen as dips of the total transmission. The multi-channel current scattering matrix is determined using its representation in terms of the R-matrix. 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 long-range strain and piezoelectric field, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 849--850.

  • 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. 33--49.

  • 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. 779--780.

  • 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. 889--890.

  • U. Wulf, P.N. Racec, H. Richter, Quantentransport in Nanotransistoren, in: vol. 90 (2007) of Sitzungsberichte der Leibniz-Sozietät, traem fo verlag dr. wolfgang weist, Berlin, pp. 121--137.

  • 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), Wiley-VCH Verlag, Weinheim, 2006, pp. 629--630.

  • 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. 355--364.

  • R. Hünlich, G. Albinus, H. Gajewski, A. Glitzky, W. Röpke, J. Knopke, Modelling and simulation of power devices for high-voltage 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. 401--412.

  • 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. 377--390.

  • U. Bandelow, H. Gajewski, H.-Chr. Kaiser, Modeling combined effects of carrier injection, photon dynamics and heating in Strained Multi-Quantum-Well 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. 301--310.

  • R. Hünlich, A. Glitzky, On energy estimates for electro-diffusion 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. 158--174.

  • H.-Chr. Kaiser, J. Rehberg, About some mathematical questions concerning the embedding of Schrödinger-Poisson systems into the drift-diffusion 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. 1328--1333.

  Preprints, Reports, Technical Reports

  • P. Farrell, M. Patriarca, J. Fuhrmann, Th. Koprucki, Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi--Dirac and Gauss--Fermi statistics, Preprint no. 2424, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2424 .
    Abstract, PDF (1572 kByte)
    We compare three thermodynamically consistent Scharfetter--Gummel schemes for different distribution functions for the carrier densities, including the Fermi--Dirac integral of order 1/2 and the Gauss--Fermi integral. The most accurate (but unfortunately also most costly) generalized Scharfetter--Gummel 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 Fermi--Dirac and Gauss--Fermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) Scharfetter--Gummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017).

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantum-classical modeling of quantum dot devices, Preprint no. 2412, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2412 .
    Abstract, PDF (5602 kByte)
    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 well-established fields of semi-classical 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 quantum-classical 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 single-photon source based on a single quantum dot in the stationary and transient operation regime.

  • A. Mielke, D. Peschka, N. Rotundo, M. Thomas, Gradient structure for optoelectronic models of semiconductors, Preprint no. 2317, WIAS, Berlin, 2016.
    Abstract, PDF (178 kByte)
    We derive an optoelectronic model based on a gradient formulation for the relaxation of electron-, hole- and photon- densities to their equilibrium state. This leads to a coupled system of partial and ordinary differential equations, for which we discuss the isothermal and the non-isothermal scenario separately

  • M. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Preprint no. 2296, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2296 .
    Abstract, PDF (1445 kByte)
    At cryogenic temperatures the electron-hole plasma in semiconductor materials 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 one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased devices as they appear e.g. in optoelectronic applications.

  • 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 one-dimensional blood flow models using experimental data, Preprint no. 2248, WIAS, Berlin, 2016.
    Abstract, PDF (8646 kByte)
    This work presents a detailed investigation of a parameter estimation approach based on the reduced order unscented Kalman filter (ROUKF) in the context of one-dimensional 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.

  • J. Haskovec, S. Hittmeir, P. Markowich, A. Mielke, Decay to equilibrium for energy-reaction-diffusion systems, Preprint no. 2233, WIAS, Berlin, 2016.
    Abstract, PDF (436 kByte)
    We derive thermodynamically consistent models of reaction-diffusion 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 diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitely calculable constants and establish the convergence to thermodynamical equilibrium, at first in entropy and further in L1 using Cziszar-Kullback-Pinsker type inequalities.

  Vorträge, Poster

  • M. Liero, Modeling and simulation of electrothermal feedback in large-area organic LEDs, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Light-Emitting Diodes'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 25, 2017.

  • D. Peschka, Doping optimization for optoelectronic devices, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), Post-Deadline session, July 27 - 28, 2017, Technical University, Lyngby Campus, Kopenhagen, Denmark, July 28, 2017.

  • A. Fischer, M. Liero, A. Glitzky, Th. Koprucki, K. Vandewal, S. Lenk, S. Reinicke, Predicting electrothermal behavior from lab-size OLEDs to large area lighting panels, MRS Spring Meeting, Phoenix, Arizona, USA, April 17 - 21, 2017.

  • A. Glitzky, Electrothermal description of organic semiconductor devices by $p(x)$-Laplace thermistor models, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6 - 10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 9, 2017.

  • M. Thomas, Mathematical modeling and analysis of evolution processes in solids and the influence of bulk-interface-interaction, Humboldt-Universität zu Berlin, Institut für Mathematik, October 20, 2017.

  • TH. Koprucki, Comparison of consistent flux discretizations for drift diffusion beyond Boltzmann statistics, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Numerical Methods'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 27, 2017.

  • TH. Koprucki, Halbleiter-Bauteilsimulation: Modelle und numerische Verfahren, Block-Seminar des SFB 787 ``Nanophotonik'', June 7 - 9, 2017, Technische Universität Berlin, Graal-Müritz, June 8, 2017.

  • TH. Koprucki, Mathematical knowledge management as a route to sustainability in mathematical modeling and simulation, 2nd Leibniz MMS Days 2017, February 22 - 24, 2017, Technische Informationsbibliothek (TIB), Hannover, February 22, 2017, DOI 10.5446/21908 .

  • TH. Koprucki, Mathematical models as research data in numerical simulation of opto-electronic devices, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Model Representation'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 27, 2017.

  • TH. Koprucki, On current injection into single quantum dots through oxide-confined pn-diodes, 10th Annual Meeting ``Photonic Devices'', February 9 - 10, 2017, Zuse Institute Berlin (ZIB), Berlin, February 9, 2017.

  • TH. Koprucki, On the Scharfetter-Gummel scheme for the discretization of drift-diffusion equations and its generalization beyond Boltzmann, Kolloquium Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, Insittut für Mathematik, May 30, 2017.

  • M. Liero, A. Glitzky, Th. Koprucki, J. Fuhrmann, 3D electrothermal simulations of organic LEDs showing negative differential resistance, Multiscale Modelling of Organic Semiconductors: From Elementary Processes to Devices, Grenoble, France, September 12 - 15, 2017.

  • A. Mielke, Mathematical modeling of semiconductors: From quantum mechanics to devices, CIM-WIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6 - 8, 2017, Centro de Matemática, Lisboa, Portugal.

  • M. Mittnenzweig, A variational approach to quantum master equations coupled to a semiconductor PDE, Variational Methods for Evolution, November 12 - 17, 2017, Mathematisches Forschungszentrum Oberwolfach, November 14, 2017.

  • M. Mittnenzweig, Variational methods for quantum master equations, Barcelona Graduate School of Mathematics Junior Meeting, October 9 - 10, 2017, Berlin Mathematical School, Spain, October 10, 2017.

  • N. Rotundo, Numerical methods for drift-diffusion models, Seminar ``Angewandte Mathematik'', Ernst Moritz Arndt Universität Greifswald, Institut für Mathematik und Informatik, June 28, 2016.

  • N. Rotundo, On some extension of energy-drift-diffusion models, The 19th European Conference on Mathematics for Industry (ECMI 2016), Minisymposium 34 ``Mathematical Modeling of Charge Transport in Graphene and Low Dimensional Structure'', June 13 - 18, 2016, Universidade de Santiago de Compostela, Spain, June 14, 2016.

  • N. Rotundo, Thermodynamic modeling of optoelectronic semiconductor devices, Mathematical Models for Quantum and Classical Mechanics (SEMODAY2016), November 17 - 18, 2016, Università degli Studi di Firenze, Dipartamento di Matematica, Florence, Italy, November 18, 2016.

  • M. Kantner, Multi-scale modeling and numerical simulation of single-photon emitters, Matheon Workshop--9th Annual Meeting ``Photonic Devices", Zuse Institut, Berlin, March 3, 2016.

  • M. Kantner, Multi-scale modelling and simulation of single-photon sources on a device level, Euro--TMCS II Theory, Modelling & Computational Methods for Semiconductors, Tyndall National Institute and University College Cork, Cork, Ireland, December 9, 2016.

  • M. Liero, OLEDs - a hot matter? Electrothermal modeling of OLEDs., sc Matheon Workshop, 9th Annual Meeting ``Photonic Devices'', March 3 - 4, 2016, Zuse Institute Berlin, Berlin, March 4, 2016.

  • M. Liero, On $p(x)$-Laplace thermistor models describing eletrothermal feedback in organic semiconductors, The 19th European Conference on Mathematics for Industry (ECMI 2016), Minisymposium 23 ``Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics'', June 13 - 17, 2016, Universidade de Santiago de Compostela, Spain, June 15, 2016.

  • M. Liero, On $p(x)$-Laplace thermistor models describing eletrothermal feedback in organic semiconductors, Joint Annual Meeting of DMV and GAMM, Section 14 ``Applied Analysis'', March 7 - 11, 2016, Technische Universität Braunschweig, Braunschweig, March 9, 2016.

  • M. Liero, On electrothermal feedback in organic light-emitting diodes, Berlin Dresden Prague Würzburg Workshop ``Mathematics of Continuum Mechanics'', Technische Universität Dresden, Fachbereich Mathematik, December 5, 2016.

  • M. Mittnenzweig, Gradient structures for Lindblad equations satisfying detailed balance, 3rd PhD Workshop, May 30 - 31, 2016, International Research Training Group of the Collaborative Research Center (SFB) 1114 ``Scaling Cascades in Complex Systems'', Güstrow, May 31, 2016.

  • D. Peschka, Towards the optimization of Ge micro bridges, The 19th European Conference on Mathematics for Industry (ECMI 2016), minisymposium ``Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics'', June 13 - 17, 2016, Universidade de Santiago de Compostela, Faculty of Mathematics, Santiago de Compostela, Spain, June 15, 2016.

  • D. Peschka, Towards the optimization of on-chip germanium lasers, sc Matheon Workshop, 9th Annual Meeting ``Photonic Devices'', March 3 - 4, 2016, Zuse Institute Berlin, Berlin, March 4, 2016.

  • A. Glitzky, $p(x)$-Laplace thermistor models for electrothermal effects in organic semiconductor devices, 7th European Congress of Mathematics (7ECM), Minisymposium 22 ``Mathematical Methods for Semiconductors'', July 18 - 22, 2016, Technische Universität Berlin, July 22, 2016.

  • 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.

  • M. Thomas, Analysis and optimization for edge-emitting semiconductor heterostructures, 7th European Congress of Mathematics (ECM), session CS-8-A, July 18 - 22, 2016, Technische Universität Berlin, Berlin, July 19, 2016.

  • M. Thomas, Analysis and optimization for edge-emitting semiconductor heterostructures, The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 2 ``Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equation'', July 1 - 5, 2016, The American Institute of Mathematical Sciences, Orlando (Florida), USA, July 3, 2016.

  • M. Thomas, Mathematische Modellierung, Analysis und Optimierung von Germanium-Lasern, Vortrag vor dem WGL-Präsidenten anlässlich seines WIAS-Besuchs, WIAS Berlin, Berlin, February 18, 2016.

  • D.H. Doan, Numerical methods in non-Boltzmann regimes, sc Matheon Workshop, 9th Annual Meeting ``Photonic Devices'', March 3 - 4, 2016, Zuse Institute Berlin, Berlin, March 4, 2016.

  • P. Farrell, Scharfetter--Gummel schemes for Non-Boltzmann 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.

  • P. Farrell, Scharfetter--Gummel schemes for non-Boltzmann statistics, The 19th European Conference on Mathematics for Industry (ECMI2016), Minisymposium 23 ``Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics'', June 13 - 17, 2016, Universidade de Santiago de Compostela, Spain, June 14, 2016.

  • TH. Koprucki, On current injection into single quantum dots through oxide-confined PN-diodes, 16th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2016), July 7 - 17, 2016, University of Sydney, Sydney, Australia, July 14, 2016.

  • E. Cinti, Quantitative flatness results for nonlocal minimal surfaces in low dimensions, Theory of Applications of Partial Differential Equations (PDE 2015), November 30 - December 4, 2015, WIAS Berlin, Berlin, December 2, 2015.

  • N. Rotundo, Analytical methods for doping optimization for semiconductor devices, 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.

  • N. Rotundo, Towards doping optimization of semiconductor lasers, 24th International Conference on Transport Theory, September 7 - 11, 2015, University of Catania, Taormina, Italy, September 9, 2015.

  • M. Kantner, Multi-scale modeling and simulation of electrically pumped single-photon sources, International Nano-Optoelectronics Workshop (iNOW 2015), Tokio, Japan, August 3 - 7, 2015.

  • TH. Koprucki, On device concepts for CMOS-compatible edge-emitters based on strained germanium, Symposium ``Alternative Semiconductor Integration in Si Microelectronics: Materials, Techniques and Applications'' of the E-MRS Fall Meeting 2015, September 15 - 18, 2015, Warsaw University of Technology, Krakow, Poland, September 18, 2015.

  • TH. Koprucki, On device concepts for CMOS-compatible edge-emitters 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 large-area 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 large-area OLEDs, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2015), March 11 - 13, 2015, WIAS Berlin, Berlin, March 12, 2015.

  • D. Peschka, Mathematical modeling, analysis, and optimization of strained germanium-microbridges, sc Matheon Center Days, April 20 - 21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

  • A. Glitzky, Analysis of $p(x)$-Laplace thermistor models for electrothermal feedback in organic semiconductor devices, 3rd Workshop of the GAMM Activity Group ``Analysis of Partial Differential Equations'', September 30 - October 2, 2015, Universität Kassel, Institut für Mathematik, Kassel, September 30, 2015.

  • M. Thomas, Analysis for edge-emitting 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 edge-emitting 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 Scharfetter--Gummel scheme for drift-diffusion equations with Fermi-like distribution functions, Kick-Off 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, Block-Seminar des SFB 787 ``Nanophotonik'', May 21 - 23, 2014, Technische Universität Berlin, Graal-Müritz, May 23, 2014.

  • TH. Koprucki, On modifications of the Scharfetter--Gummel scheme for drift-diffusion equations with Fermi-like 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 large-area OLEDs, Kick-Off 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, Drift-diffusion 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, Landauer--Bütikker 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 Scharfetter--Gummel scheme, Organic Photovoltaics Workshop 2013, December 10 - 11, 2013, University of Oxford, Mathematical Insitute, UK, December 10, 2013.

  • TH. Koprucki, Selbstaufheizungs-Effekte 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 drift-diffusion equations with a generalized Einstein relation, scshape Matheon Workshop ``6th Annual Meeting Photonic Devices'', February 21 - 22, 2013, Konrad-Zuse-Zentrum für Informationstechnik Berlin, February 22, 2013.

  • M. Liero, Gradient structures and geodesic convexity for reaction-diffusion 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 reaction-diffusion systems, Research Seminar, Westfälische Wilhelms-Universität Münster, Institut für Numerische und Angewandte Mathematik, April 17, 2013.

  • A. Glitzky, Electro-thermal modeling of organic semiconductors describing negative differential resistance induced by self-heating, 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.

  • M. Thomas, Mathematical modeling, analysis and optimization of strained germanium microbridges, sc Matheon Center Days, Technische Universität Berlin, November 5, 2013.

  • 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, Block-Seminar des SFB 787 ``Nanophotonik'', May 6 - 8, 2013, Technische Universität Berlin, Graal-Müritz, May 8, 2013.

  • A. Mielke, Thermodynamic modeling of the Maxwell--Bloch 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 quantum-dot lasers, Fachtagung Leibniz-Nano (1. Nanotechnologie-Workshop der Leibniz-Gemeinschaft), Berlin, January 30 - 31, 2012.

  • TH. Koprucki, Discretization scheme for drift-diffusion 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 quantum-dot VCSELs, 5th Annual Meeting Photonic Devices, February 23 - 24, 2012, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, February 24, 2012.

  • TH. Koprucki, Semi-classical 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 reaction-diffusion 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, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, February 24, 2012.

  • M. Liero, WIAS-TeSCA 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 Leibniz-Gemeinschaft, Leibniz-Institut für Analytische Wissenschaften (ISAS), Dortmund, September 14, 2012.

  • K. Gärtner, A. Glitzky, Mathematics and simulation of the charge transport in semiconductor sensors, Fachtagung Leibniz-Nano (1. Nanotechnologie-Workshop der Leibniz-Gemeinschaft), 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 Landauer--Buettiker 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 Leibniz-Nano (1. Nanotechnologie-Workshop der Leibniz-Gemeinschaft), Berlin, January 30 - 31, 2012.

  • P.N. Racec, Finite volume discretization and R-matrix 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 R-matrix 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), Mini-Symposium ``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 nano-heterostructures, 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 bulk-interface interaction in reaction-diffusion systems, Interfaces and Discontinuities in Solids, Liquids and Crystals (INDI2011), June 20 - 23, 2011, Gargnano (Brescia), Italy, June 20, 2011.

  • P.N. Racec, R-matrix and finite volume method for cylindrical nanowire heterostructures, Mathematical Challenges of Quantum Transport in Nano-Optoelectronic 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, Multi-species 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 spin-polarized drift-diffusion 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 Sobolev--Morrey 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, Paul-Drude-Institut 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 ``High-order 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 Kohn--Sham theory, Jubiläumssymposium ``Licht -- Materialien -- Modelle'' (100 Jahre Innovation aus Adlershof), Berlin-Adlershof, 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 spin-polarized drift-diffusion 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 drift-diffusion model for semiconductors with internal interfaces, Annual Meeting of the Deutsche Mathematiker-Vereinigung 2008, Minisymposium ``Analysis of Reaction-Diffusion Systems with Internal Interfaces'', September 15 - 19, 2008, Friedrich-Alexander-Universität Erlangen-Nürnberg, September 15, 2008.

  • H.-Chr. Kaiser, A thermodynamic approach to transient Kohn--Sham 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 drift-diffusion Kohn--Sham 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 Landauer--Büttiker 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 drift-diffusion model of transient Kohn--Sham 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 Schrödinger--Poisson 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, Mini-Workshop on PDE's and Quantum Transport, March 12 - 16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 14, 2007.

  • J. Rehberg, Über Schrödinger-Poisson-Systeme, 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 spin-polarized drift-diffusion 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 WIAS-TeSCA: Simulation of semiconductor lasers, Laser-Optik-Berlin, 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 Schrödinger--Poisson 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 quantum-drift-diffusion systems, Workshop ``Problèmes spectraux non-linéaires 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 semi-classical 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 two-dimensional van Roosbroeck system has solutions in $L^p$, Workshop ``Advances in Mathematical Semiconductor Modelling: Devices and Circuits'', March 2 - 6, 2004, Chinese-German 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 two-dimensional space domains, 19th GAMM Seminar Leipzig on High-dimensional problems --- Numerical treatment and applications, January 23 - 25, 2003, Max-Planck-Institut 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, Max-Planck-Institut 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.

  Preprints im Fremdverlag

  • 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.