1,050 research outputs found
Solution Map Analysis of a Multiscale Drift-Diffusion Model for Organic Solar Cells
In this article we address the theoretical study of a multiscale
drift-diffusion (DD) model for the description of photoconversion mechanisms in
organic solar cells. The multiscale nature of the formulation is based on the
co-presence of light absorption, conversion and diffusion phenomena that occur
in the three-dimensional material bulk, of charge photoconversion phenomena
that occur at the two-dimensional material interface separating acceptor and
donor material phases, and of charge separation and subsequent charge transport
in each three-dimensional material phase to device terminals that are driven by
drift and diffusion electrical forces. The model accounts for the nonlinear
interaction among four species: excitons, polarons, electrons and holes, and
allows to quantitatively predict the electrical current collected at the device
contacts of the cell. Existence and uniqueness of weak solutions of the DD
system, as well as nonnegativity of all species concentrations, are proved in
the stationary regime via a solution map that is a variant of the Gummel
iteration commonly used in the treatment of the DD model for inorganic
semiconductors. The results are established upon assuming suitable restrictions
on the data and some regularity property on the mixed boundary value problem
for the Poisson equation. The theoretical conclusions are numerically validated
on the simulation of three-dimensional problems characterized by realistic
values of the physical parameters
Classical solutions of drift-diffusion equations for semiconductor devices: the 2d case
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
Numerical methods for drift-diffusion models
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
Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells
This article is an attempt to provide a self consistent picture, including
existence analysis and numerical solution algorithms, of the mathematical
problems arising from modeling photocurrent transients in Organic-polymer Solar
Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear
diffusion-reaction partial differential equations (PDEs) with electrostatic
convection, coupled to a kinetic ordinary differential equation (ODE). We
propose a suitable reformulation of the model that allows us to prove the
existence of a solution in both stationary and transient conditions and to
better highlight the role of exciton dynamics in determining the device turn-on
time. For the numerical treatment of the problem, we carry out a temporal
semi-discretization using an implicit adaptive method, and the resulting
sequence of differential subproblems is linearized using the Newton-Raphson
method with inexact evaluation of the Jacobian. Then, we use exponentially
fitted finite elements for the spatial discretization, and we carry out a
thorough validation of the computational model by extensively investigating the
impact of the model parameters on photocurrent transient times.Comment: 20 pages, 11 figure
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Numerical methods for drift-diffusion models
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
disretization scheme and recent efforts to generalize this approach to
general statistical distribution functions
Systematic derivation of a surface polarization model for planar perovskite solar cells
Increasing evidence suggests that the presence of mobile ions in perovskite
solar cells can cause a current-voltage curve hysteresis. Steady state and
transient current-voltage characteristics of a planar metal halide
CHNHPbI perovskite solar cell are analysed with a drift-diffusion
model that accounts for both charge transport and ion vacancy motion. The high
ion vacancy density within the perovskite layer gives rise to narrow Debye
layers (typical width 2nm), adjacent to the interfaces with the transport
layers, over which large drops in the electric potential occur and in which
significant charge is stored. Large disparities between (I) the width of the
Debye layers and that of the perovskite layer (600nm) and (II) the ion
vacancy density and the charge carrier densities motivate an asymptotic
approach to solving the model, while the stiffness of the equations renders
standard solution methods unreliable. We derive a simplified surface
polarisation model in which the slow ion dynamic are replaced by interfacial
(nonlinear) capacitances at the perovskite interfaces. Favourable comparison is
made between the results of the asymptotic approach and numerical solutions for
a realistic cell over a wide range of operating conditions of practical
interest.Comment: 32 pages, 7 figure
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
Designing a Simulator for an Electrically-Pumped Organic Laser Diode
Organic semiconductors provide an alternative set of basis materials to fabricate electronic devices like PN Junctions, LEDs, and FETs. These materials have several benefits over traditional inorganic semiconductors including their mechanical flexibility, reliance on renewable resources, and inexpensive large-scale manufacturability. Despite the contemporary device implementations with organic semiconductors, a solid-state electrically-pumped organic laser diode does not exist. However, organically-based lasers do exist by utilizing the organic material strictly for optical gain. The challenge occurs when charge carriers appear in the organic material. The charge carriers must reach a concentration such that population inversion occurs producing optical gain. However, between the overlapping emission and absorption spectra of the organic material and insufficient carrier concentrations, positive optical gain remains elusive in electrically-pumped organic diodes. Organic device simulation provides a faster method of testing organic materials and device structures for positive optical gain based on known organic physics. The results generated from simulation provide key information in development of physical organic devices. This project produces a simulator capable of modeling current density and optical density with the intent of testing various device structures that allow for lazing in organic materials
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