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Electronic Transport In Mesoscopic Systems

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new but have gained rapid popularity in numerical solutions of hyperbolic partial differential equations (PDEs) and other convection dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, nonoscillatory, and sharp discontinuity transitions. The schemes are thus especially suitable for problems containing both strong discontinuities and complex smooth solution features. WENO schemes are robust and do not require the user to tune parameters. At the heart of the WENO schemes is actually an approximation procedure not directly related to PDEs, hence the WENO procedure can also be used in many non-PDE applications. In this paper we review the history and basic formulation of WENO schemes, outline the main ideas in using WENO schemes to solve various hyperbolic PDEs and other convection dominated problems, and present a collection of applications in areas including computational fluid dynamics, computational astronomy and astrophysics, semiconductor device simulation, traffic flow models, computational biology, and some non-PDE applications. Finally, we mention a few topics concerning WENO schemes that are currently under investigation.

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

Electrons and Phonons

Organic field-effect transistors hold the promise of enabling low-cost and flexible electronics. Following its success in organic optoelectronics, the organic doping technology is also used increasingly in organic field-effect transistors. Doping not only increases device performance, but it also provides a way to fine-control the transistor behavior, to develop new transistor concepts, and even improve the stability of organic transistors. This Review summarizes the latest progress made in the understanding of the doping technology and its application to organic transistors. It presents the most successful doping models and an overview of the wide variety of materials used as dopants. Further, the influence of doping on charge transport in the most relevant polycrystalline organic semiconductors is reviewed, and a concise overview on the influence of doping on transistor behavior and performance is given. In particular, recent progress in the understanding of contact doping and channel doping is summarized.

Doped Organic Transistors.

There can be little doubt that the Monte Carlo method for semiconductor device simulation has enormous power as a research tool. It represents a detailed physical model of the semiconductor material(s), and provides a high degree of insight into the microscopic transport processes. However, if the authority ascribed to Monte Carlo models of devices at 1/spl mu/m feature size is to be maintained for devices below O.1/spl mu/m, modelling of the fundamental physics must be further improved. And if the Monte Carlo method is to be successful as a semiconductor device design tool, the device model must be made more realistic. Success in the industrial sector depends on this, but also on achieving fast run-times optimisation - where the scope and need for ingenuity is now greatest.

The Monte Carlo method for semiconductor device simulation

Recently, it has been shown by several groups that the electrical characteristics of organic thin-film transistors (OTFTs) can be significantly influenced by depositing self-assembled monolayers (SAMs) at the organic semiconductor/dielectric interface. In this work, the effect of such SAMs on the transfer characteristics and especially on the threshold voltage of OTFTs is investigated by means of two-dimensional drift-diffusion simulations. The impact of the SAM is modeled either by a permanent space charge layer that can result from chemical reactions with the active material, or by a dipole layer representing an array of ordered dipolar molecules. It is demonstrated that, in both model cases, the presence of the SAM significantly changes the transfer characteristics. In particular, it gives rise to a modified, effective gate voltage V eff that results in a rigid shift of the threshold voltage, ΔV th , relative to a SAM-free OTFT. The achievable amount of threshold voltage shift, however, strongly depends on the actual role of the SAM. While for the investigated device dimensions, an organic SAM acting as a dipole layer can realistically shift the threshold voltage only by a few volts, the changes in the threshold voltage can be more than an order of magnitude larger when the SAM leads to charges at the interface. Based on the analysis of the different cases, a route to experimentally discriminate between SAM-induced space charges and interface dipoles is proposed. The developed model allows for qualitative description of the behavior of organic transistors containing reactive interfacial layers; when incorporating rechargeable carrier trap states and a carrier density-dependent mobility, even a quantitative agreement between theory and recent experiments can be achieved.

Threshold Voltage Shifts in Organic Thin‐Film Transistors Due to Self‐Assembled Monolayers at the Dielectric Surface

The single graphene layer is a novel material consisting of a flat monolayer of carbon atoms packed in a two-dimensional honeycomb lattice, in which the electron dynamics is governed by the Dirac equation. A pseudo-spin phase-space approach based on the Wigner–Weyl formalism is used to describe the ballistic transport of electrons in graphene including quantum effects. Our two-band quantum mechanical representation of the particles reveals itself to be particularly close to the classical description of the particle motion. We analyze the Klein tunneling and correction to the total current in graphene induced by this phenomenon. The equations of motion are analytically investigated and some numerical tests are presented. The temporal evolution of the electron–hole pairs in the presence of an external electric field and rigid potential step is investigated. The connection of our formalism with the Berry phase approach is also discussed.

https://iopscience.iop.org/article/10.1088/1751-8113/44/26/265301/pdf

Wigner model for quantum transport in graphene

We examine the dynamics of three-dimensional cells with square planform in dissipative Rayleigh-Benard convection. By applying a triple Fourier series ansatz up to second order, we obtain a system of nine nonlinear ordinary differential equations from the governing hydrodynamic equations. Depending on two control parameters, namely the Rayleigh number and the Prandtl number, the asymptotic behaviour can be stationary, periodic, quasiperiodic or chaotic. A period-doubling cascade is identified as a route to chaos. Hereafter, the asymptotic behaviour progressively evolves towards a hyperchaotic attractor. For given values of control parameters beyond the accumulation point, we observe a low-dimensional chaotic attractor as is currently done for dissipative systems. Although the correlation dimension strongly suggests that this attractor could be embedded in a three-dimensional space, a topological characterization reveals that a higher-dimensional space must be used. Thus, we reconstruct a four-dimensional model which is found to be in agreement with the properties of the original dynamics. The nine-dimensional Lorenz model could therefore play a significant role in developing tools to characterize chaotic attractors embedded in phase space with a dimension greater than 3.

https://iopscience.iop.org/article/10.1088/0305-4470/31/34/015/pdf

A nine-dimensional Lorenz system to study high-dimensional chaos

The coupled dynamics of electrons and optical phonons in graphene is investigated. For this purpose, a kinetic model based on space-dependent Boltzmann transport equations for electrons and optical phonons is established. This system is solved by deterministic methods that provide efficiently accurate results by dynamically treating nonequilibrium phenomena. The numerical simulations clearly show the importance of this approach when calculating $I$--$V$ characteristics over a reasonable voltage range. Optical phonon occupations surpassing equilibrium values by factors of thousands were found which affect the charge carrier transport considerably in graphene.

High-field transport and optical phonon scattering in graphene

The contact resistance is known to severely hamper the performance of organic thin-film transistors, especially when dealing with large injection barriers, high mobility organic semiconductors, or short channel lengths. Here, the relative significance of how it is affected by materials-parameters (mobility and interfacial level-offsets) and geometric factors (bottom-contact vs top-contact geometries) is assessed. This is done using drift-diffusion-based simulations on idealized device structures aiming at a characterization of the “intrinsic” situation in the absence of traps, differences in the film morphology, or metal-atoms diffusing into the organic semiconductor. It is found that, in contrast to common wisdom, in such a situation the top-contact devices do not always outperform the bottom-contact ones. In fact, the observed ratio between the contact resistances of the two device structures changes by up to two orders of magnitude depending on the assumed materials parameters. The contact resistance is also shown to be strongly dependent on the hole mobility in the organic semiconductor and influenced by the chosen point of operation of the device.

Ferdinand Schürrer

Papers

Threshold Voltage Shifts in Organic Thin‐Film Transistors Due to Self‐Assembled Monolayers at the Dielectric Surface

Wigner model for quantum transport in graphene

A nine-dimensional Lorenz system to study high-dimensional chaos

High-field transport and optical phonon scattering in graphene

Impact of Materials versus Geometric Parameters on the Contact Resistance in Organic Thin‐Film Transistors