78A35 Motion of charged particles
We discuss drift-diffusion models for charge-carrier transport in organic semiconductor de- vices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The for- mer leads to so-called Gauss-Fermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlin- ear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift-diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder’s fixed-point theorem. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.
This paper deals with the analysis of an instationary drift-diffusion model for organic semicon- ductor devices including Gauss–Fermi statistics and application-specific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent ener- getic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength.
To prove the existence of global weak solutions, we consider a problem with (for small den- sities) regularized state equations on any arbitrarily chosen finite time interval. We ensure its solvability by time discretization and passage to the time-continuous limit. Positive lower a priori estimates for the densities of its solutions that are independent of the regularization level en- sure the existence of solutions to the original problem. Furthermore, we derive for these solutions global positive lower and upper bounds strictly below the density of transport states for the densi- ties. The estimates rely on Moser iteration techniques.
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.
In a strong constant electric field, a dielectric particle immersed in a weakly conducting fluid exhibits spontaneous rotations. This phenomenon is known under the name of the Quincke effect. In the original setup the particle was suspended on a silk thread and performed torsional oscillations of remarkably high amplitude. We derive the governing equations for this experiment, and ascertain
that onset of oscillations from the quiescent state corresponds to the supercritical Hopf bifurcation.
For the case of a soft thread, we characterize the regime of large-scale torsional relaxation oscillations:
explicit estimates are derived for their period and amplitude, effects of bifurcation delay are described. In a stronger electric field, these relaxation oscillations yield to small-scale erratic rotations of the pendulum.
An electronic model for solar cells including active interfaces and energy resolved defect densities
(2011)
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.
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.
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.