Ab-initio Modeling of CBRAM Cells: from Ballistic Transport Properties to Electro-Thermal Effects

We present atomistic simulations of conductive bridging random access memory (CBRAM) cells from first-principles combining density-functional theory and the Non-equilibrium Green's Function formalism. Realistic device structures with an atomic-scale filament connecting two metallic contacts have been constructed. Their transport properties have been studied in the ballistic limit and in the presence of electron-phonon scattering, showing good agreement with experimental data. It has been found that the relocation of few atoms is sufficient to change the resistance of the CBRAM by 6 orders of magnitude, that the electron trajectories strongly depend on the filament morphology, and that self-heating does not affect the device performance at currents below 1 $\mu$A.Comment: 6 figures, conferenc

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension

Accurate and Efficient Solution of the Smoluchowski Equation

The probability density function (PDF) of the relative position of molecules diffusing independently in three dimensional space according to Brownian motion and reacting with a certain probability when any two of them collide is given by the Smoluchowski equation. The PDF is used to sample particle positions in simulations of reaction-diffusion processes by particle-based simulation methods, like Green's Function Reaction Dynamics (GFRD) proposed by van Zon and ten Wolde. The GFRD algorithm is an event-driven algorithm, allowing the use of longer time steps, which is particularly efficient for simulating chemical reactions at low concentration in molecular biology. This study is based on the improved version of the GFRD algorithm developed by S. Hellander and P. Lötstedt, where the applicability of the algorithm is increased and computing the PDFs is simplified by using an operator splitting approach. The main idea is to split the spatial differential operator of the Smoluchowski equation into a radial part and an angular part, resulting in two one-dimensional time-dependent partial differential equations (PDEs) to be solved independently and sequentially. These equations can be solved analytically but the solutions are complicated and computationally expensive to evaluate. This thesis intends to compare the accuracy and efficiency of sampling the radial distance between two molecules and the relative angular position of the two molecules from directly evaluated exact PDFs or their finite difference approximations and interpolating the positions from precomputed tabulated data

Projections of Immersed Surfaces and Regular Homotopy

This thesis is based on U. Pinkall’s study of the classification of immersions of compact surfaces into R3 up to regular homotopy. The main idea of the classification is to associate to any immersion f a quadratic form qf on the first homology group of the underlying surface Σ with Z2 coefficients, whose associated bilinear form is the nondegenerate intersection form in H1(Σ,Z2), having the property that it depends only on the regular homotopy class of f. In the case of orientable surfaces qf turns out to be a Z2-quadratic form. In this thesis we construct the Z2-quadratic form using the notion of Spin - structure, and via D. Johnson’s correspondence between Spin - structures on a surface and Z2-quadratic forms on the first homology group of the surface. Then by studying the relation between surface immersions into 3-space and their projections to a 2-plane, we give a formula for computing the value of the quadratic form on any homology class c ∈ H1(Σ,Z2), which we will use to construct an example of two nonregularly homotopic immersions of the 2 - dimensional torus T2 into R3 with identical plane projections

Efficient algorithms for large-scale quantum transport calculations

ISSN:0021-9606ISSN:1089-769