Convergence of a Finite Volume Scheme for a Corrosion Model

In this paper, we study the numerical approximation of a system of partial dif-ferential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In particular, we are interested in the convergence of a numerical scheme consisting in an implicit Euler scheme in time and a Scharfetter-Gummel finite volume scheme in space

量子ドット太陽電池とペロブスカイト太陽電池における界面エンジニアリングと界面電荷移動ダイナミクス

電気通信大学201

Phenomena Simulation for Heavy Doping and Surface Recombination Velocity

The theoretical models now available that characterize heavily doped (highly conducting) regions in silicon are survyed. Analytical and numerical approaches that determine the influence of such regions on the conversion efficiency of solar cells are examined. Although dilutely doped silicon is well characterized except for some disagreement about optical absorption coefficients, what exists now for heavily doped silicon and its interplay with adjoining regions is an incomplete theory in which not all contributers to transport, recombination, generation, and trapping are defined. Further, the parameters relating to these mechanisms and their values as determined by experiment are subject to various interpretations. The characterization of heavily doped silicon is treated not as a theory but rather as an imperfectly articulated and incompletely formalized body of experience. This view is intended to help point the way toward the attainment of a more complete of heavily doped silicon and thereby toward more informed designs of solar cells. Because computer programs constitute tools both for design and for estimating performance limits, the review includes some remarks pertinent to existing and developing programs

Opto-Electrical Interactions in Next Generation Semiconductor Thin Films and Devices

The processes by which optical and electrical energies are transduced are at the heart of many modern technologies such as solar cells, light emitting diodes, photodetectors, imaging systems and displays. The basic functional element of these ‘opto-electrical’ devices are semiconductors, and the underpinning physics of how they transduce light and electricity is well understood for conventional inorganic materials such as silicon and gallium arsenide. However, new semiconductors such as the organics and the organohalide perovskites present additional opto-electrical questions and challenges since they are molecular solids with varying degrees of disorder and crystallinity. The work described in this thesis addresses these new questions and challenges, particularly in relation to how existing solid-state physics concepts must be adapted to reliably predict and model material-and-device-level structure-property relationships and performance. Two basic technology platforms are examined in detail – solar cells and light emitting diodes, with particular reference to so-called reciprocity. A second focus of the discussion is accurate determination of optical constants for these new semiconductors – a challenging endeavour due to factors such as morphological heterogeneity. Transfer matrix and drift diffusion formalisms are relied heavily upon to model, simulate and explain multi-layer device performance, and ellipsometry and spectrophotometry are utilised as the primary analysis and characterisation methodologies. A new approach to optical constant determination is presented and validated, as is an adapted reciprocity framework for the linking of absorption, emission and charge transfer state characterisation in the presence of cavity interference. Several ‘difficult’ solar cell systems are analysed in detail – in particular the previously mysterious working principles of the so-called carbon-stack perovskite system are elucidated for the first time. These findings explain how an electrically non-selective contact can still function as an effective photovoltaic electrode dependent upon the local minority and majority carrier concentration profile. The research described herein advances our understanding of next generation semiconductor opto-electrical physics and provides more practical means for the community to analyse optical constants

Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion with drift. The microscopic setting is a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Four new features arise in the upscaled equations: (i) the effective ionic diffusivities and mobilities become tensors, related to the microstructure; (ii) the effective permittivity is also a tensor, depending on the electrolyte/matrix permittivity ratio and the ratio of the Debye screening length to the macroscopic length of the porous medium; (iii) the microscopic fluidic convection is replaced by a diffusion-dispersion correction in the effective diffusion tensor; and (iv) the surface charge per volume appears as a continuous "background charge density", as in classical membrane models. The coefficient tensors in the upscaled PNP equations can be calculated from periodic reference cell problems. For an insulating solid matrix, all gradients are corrected by the same tensor, and the Einstein relation holds at the macroscopic scale, which is not generally the case for a polarizable matrix, unless the permittivity and electric field are suitably defined. In the limit of thin double layers, Poisson's equation is replaced by macroscopic electroneutrality (balancing ionic and surface charges). The general form of the macroscopic PNP equations may also hold for concentrated solution theories, based on the local-density and mean-field approximations. These results have broad applicability to ion transport in porous electrodes, separators, membranes, ion-exchange resins, soils, porous rocks, and biological tissues

Mathematical Analysis of Charge and Heat Flow in Organic Semiconductor Devices

Organische Halbleiterbauelemente sind eine vielversprechende Technologie, die das Spektrum der optoelektronischen Halbleiterbauelemente erweitert und etablierte Technologien basierend auf anorganischen Halbleitermaterialien ersetzen kann. Für Display- und Beleuchtungsanwendungen werden sie z. B. als organische Leuchtdioden oder Transistoren verwendet. Eine entscheidende Eigenschaft organischer Halbleitermaterialien ist, dass die Ladungstransporteigenschaften stark von der Temperatur im Bauelement beeinflusst werden. Insbesondere nimmt die elektrische Leitfähigkeit mit der Temperatur zu, so dass Selbsterhitzungseffekte, einen großen Einfluss auf die Leistung der Bauelemente haben. Mit steigender Temperatur nimmt die elektrische Leitfähigkeit zu, was wiederum zu größeren Strömen führt. Dies führt jedoch zu noch höheren Temperaturen aufgrund von Joulescher Wärme oder Rekombinationswärme. Eine positive Rückkopplung liegt vor. Im schlimmsten Fall führt dieses Verhalten zum thermischen Durchgehen und zur Zerstörung des Bauteils. Aber auch ohne thermisches Durchgehen führen Selbsterhitzungseffekte zu interessanten nichtlinearen Phänomenen in organischen Bauelementen, wie z. B. die S-förmige Beziehung zwischen Strom und Spannung. In Regionen mit negativem differentiellen Widerstand führt eine Verringerung der Spannung über dem Bauelement zu einem Anstieg des Stroms durch das Bauelement. Diese Arbeit soll einen Beitrag zur mathematischen Modellierung, Analysis und numerischen Simulation von organischen Bauteilen leisten. Insbesondere wird das komplizierte Zusammenspiel zwischen dem Fluss von Ladungsträgern (Elektronen und Löchern) und Wärme diskutiert. Die zugrundeliegenden Modellgleichungen sind Thermistor- und Energie-Drift-Diffusion-Systeme. Die numerische Diskretisierung mit robusten hybriden Finite-Elemente-/Finite-Volumen-Methoden und Pfadverfolgungstechniken zur Erfassung der in Experimenten beobachteten S-förmigen Strom-Spannungs-Charakteristiken wird vorgestellt.Organic semiconductor devices are a promising technology to extend the range of optoelectronic semiconductor devices and to some extent replace established technologies based on inorganic semiconductor materials. For display and lighting applications, they are used as organic light-emitting diodes (OLEDs) or transistors. One crucial property of organic semiconductor materials is that charge-transport properties are heavily influenced by the temperature in the device. In particular, the electrical conductivity increases with temperature, such that self-heating effects caused by the high electric fields and strong recombination have a potent impact on the performance of devices. With increasing temperature, the electrical conductivity rises, which in turn leads to larger currents. This, however, results in even higher temperatures due to Joule or recombination heat, leading to a feedback loop. In the worst case, this loop leads to thermal runaway and the complete destruction of the device. However, even without thermal runaway, self-heating effects give rise to interesting nonlinear phenomena in organic devices, like the S-shaped relation between current and voltage resulting in regions where a decrease in voltage across the device results in an increase in current through it, commonly denoted as regions of negative differential resistance. This thesis aims to contribute to the mathematical modeling, analysis, and numerical simulation of organic semiconductor devices. In particular, the complicated interplay between the flow of charge carriers (electrons and holes) and heat is discussed. The underlying model equations are of thermistor and energy-drift-diffusion type. Moreover, the numerical approximation using robust hybrid finite-element/finite-volume methods and path-following techniques for capturing the S-shaped current-voltage characteristics observed in experiments are discussed

A Finite-Volume Scheme for a Spinorial Matrix Drift-Diffusion Model for Semiconductors

An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly coupled equations for the charge and spin-vector densities, coupled to the Poisson equation for the elec-tric potential. The equations are solved in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The charge and spin-vector fluxes are approximated by a Scharfetter-Gummel discretization. The main features of the numerical scheme are the preservation of positivity and L $\infty$ bounds and the dissipation of the discrete free energy. The existence of a bounded discrete solution and the monotonicity of the discrete free energy are proved. For undoped semiconductor materials, the numerical scheme is uncon-ditionally stable. The fundamental ideas are reformulations using spin-up and spin-down densities and certain projections of the spin-vector density, free energy estimates, and a discrete Moser iteration. Furthermore, numerical simulations of a simple ferromagnetic-layer field-effect transistor in two space dimensions are presented

Modeling and investigation of current transport phenomena in schottky structures

We have used a numerical method to describe the importance of the contribution of generation-recombination current to the I-V characteristics of Schottky barrier contacts. The current-voltage relationship is derived directly from the fundamental set of equations such as Poisson; current-density and continuity equations, without having to make many simplifications or approximations. The final result includes not only the thermionic emission or drift diffusion mechanisms of current flow, but also the generation recombination processes. The experimental devices used for this work are very common low barrier height Schottky structures, Al/T0.3W0.7/n-Si/A1 and Ti0.3W0.7/n-Si/Al. The comparison between the measured and simulated results strongly showed the effect of recombination current as an important factor for even relatively low barrier height devices in the low bias region. From derived expression of the I-V characteristics, we can accurately fit the experimental results just simply by adding the term for the recombination effects. A good estimation for the values of recombination current effect can be calculated from I-V expression used for this work