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Author: Koprucki, Thomas × Subject: finite volume method ×

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Now showing 1 - 4 of 4
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    Highly accurate quadrature-based Scharfetter-Gummel schemes for charge transport in degenerate semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Patriarca, Matteo; Farrell, Patricio; Fuhrmann, Jürgen; Koprucki, Thomas
    We introduce a family of two point flux expressions for charge carrier transport described by drift-diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoi finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newtons method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter-Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed.
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    Multi-dimensional modeling and simulation of semiconductor nanophotonic devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Kantner, Markus; Höhne, Theresa; Koprucki, Thomas; Burger, Sven; Wünsche, Hans-Jürgen; Schmidt, Frank; Mielke, Alexander; Bandelow, Uwe
    Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.
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    Non-isothermal Scharfetter--Gummel scheme for electro-thermal transport simulation in degenerate semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Kantner, Markus; Koprucki, Thomas
    Electro-thermal transport phenomena in semiconductors are described by the non-isothermal drift-diffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, non-isothermal generalization of the Scharfetter--Gummel finite volume discretization for degenerate semiconductors obeying Fermi--Dirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor.
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    Self-heating effects in organic semiconductor devices enhanced by positive temperature feedback
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Fischer, Axel; Pahner, Paul; Lüssem, Björn; Leo, Karl; Scholz, Reinhard; Koprucki, Thomas; Fuhrmann, Jürgen; Gärtner, Klaus; Glitzky, Annegret
    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 200ʿ 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 ...