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René Hammer

Publications and source records attributed to René Hammer.

9 recordsLinked to original sources

Towards predictive atomistic simulations of SiC crystal growth

Simulations of SiC crystal growth using molecular dynamics (MD) have become popular in recent years. They, however, simulate very fast deposition rates, to reduce computational costs. Therefore, they are more akin to surface sputtering, leading to abnormal growth effects, including thick amorphous layers and large defect densities. A recently developed method, called the minimum energy atomic deposition (MEAD), tries to overcome this problem by depositing the atoms directly at the minimum energy positions, increasing the time scale. We apply the MEAD method to simulate SiC crystal growth on stepped C-terminated 4H substrates with 4° and 8° off-cut angle. We explore relevant calculations settings, such as amount of equilibration steps between depositions and influence of simulation cell sizes and bench mark different interatomic potentials. The carefully calibrated methodology is able to replicate the stable step-flow growth, which was so far not possible using conventional MD simulations. Furthermore, the simulated crystals are evaluated in terms of their dislocations, surface roughness and atom mobility. Our methodology paves the way for future high fidelity investigations of surface phenomena in crystal growth.

cond-mat.mtrl-sci↗

STEM EBIC as a Quantitative Probe of Semiconductor Devices

Electron beam-induced current (EBIC) imaging in the scanning transmission electron microscope (STEM), STEM-EBIC, provides direct access to carrier transport at the nanoscale. While well established in bulk SEM geometries, its application to thin TEM lamellae remains largely unexplored. Here, we present a systematic STEM-EBIC study of silicon photodiode lamellae prepared by gallium and xenon focused ion beam (FIB) milling. We directly visualize the p-n junctions in thin cross sections and extract effective diffusion lengths for electrons and holes as a function of local thickness. The values are orders of magnitude smaller than those obtained by SEM-EBIC on bulk silicon, reflecting pronounced surface recombination and FIB-induced surface modifications. Current-voltage measurements further reveal severe deviations from the expected diode-like behavior, which we attribute to ohmic metal-semiconductor contacts in the emasurement setup. Our analysis establishes STEM-EBIC as a quantitative probe of carrier transport in nanoscale devices.

cond-mat.mes-hall↗

The worm-LBM, an algorithm for a high number of propagation directions on a lattice Boltzmann grid: the case of phonon transport

The lattice Boltzmann method (LBM) is a numerical approach to tackle problems described by a Boltzmann type-equation, where time, space, and velocities are discretized to describe scattering and advection. Even though the LBM executes advection along a lattice direction without numerical error, its usage in the high Knudsen number regime (ballistic) has been hindered by the ray effect problem (for dimensions greater than 1D). This problem has its origin in the low number of available propagation directions on standard LBM lattices. Here, to overcome this limitation, we propose the worm-lattice Boltzmann method (worm-LBM), which allows a high number of lattice directions by alternating in time the basic directions described within the next neighbor schemes. Additionally, to overcome the velocity anisotropy issue, which otherwise clearly manifests itself in the ballistic regime (e.g. the $\sqrt 2$ higher grid velocity of the D2Q8 scheme along the diagonal direction compared to the axial one), the time-adaptive scheme (TAS) is proposed. The TAS method makes use of pausing advection on the grid, allowing to impose not only isotropic propagation but also arbitrary direction-dependent grid velocity. Last but not least, we propose a grid-mean free path (grid-MFP) correction to correctly handle the aforementioned velocity issue in the diffusive limit, without affecting the ballistic one. We provide a detailed description of the TAS method and the worm-LBM algorithm, and verify their numerical accuracy by using several transient diffusive-ballistic phonon transport cases, including different initial and boundary conditions. Overall, the new, very accurate, and efficient worm-LBM algorithm, free of numerical smearing and false scattering, has the potential to be at the forefront of the numerical solvers to tackle the advective part of different equations in a wide field of applications.

physics.comp-ph↗

From flat to tilted: gradual interfaces in organic thin film growth

We investigate domain formation and local morphology of thin films of $α$-sexithiophene ($α$-6T) on Au(100) beyond monolayer coverage by combining high resolution scanning tunneling microscopy (STM) experiments with electronic structure theory calculations and computational structure search. We report a layerwise growth of highly-ordered enantiopure domains. For the second and third layer, we show that the molecular orbitals of individual $α$-6T molecules can be well resolved by STM, providing access to detailed information on the molecular orientation. We find that already in the second layer the molecules abandon the flat adsorption structure of the monolayer and adopt a tilted conformation. Although the observed tilted arrangement resembles the orientation of $α$-6T in the bulk, the observed morphology does not yet correspond to a well-defined surface of the $α$-6T bulk structure. A similar behavior is found for the third layer indicating a growth mechanism where the bulk structure is gradually adopted over several layers.

cond-mat.mtrl-sci↗

Single-cone real-space finite difference scheme for the time-dependent Dirac equation

A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to optimal linear scaling behavior for the computational effort per space-time grid-point. It allows for an easy and efficient parallelization. A functional for a norm on the grid is identified. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation is shown and exact stability conditions are derived. Finally, a single-cone scheme for the two-component (2+1)D Dirac equation, its properties, and a simulation of scattering at a Klein step are presented.

physics.comp-ph↗

Dynamics of domain-wall Dirac fermions on a topological insulator: a chiral fermion beam splitter

The intersection of two ferromagnetic domain walls placed on the surface of topological insulators provides a one-way beam splitter for domain-wall Dirac fermions. Based on an analytic expression for a static two-soliton magnetic texture we perform a systematic numerical study of the propagation of Dirac wave packets along such intersections. A single-cone staggered-grid finite difference lattice scheme is employed in the numerical analysis. It is shown that the angle of intersection plays a decisive role in determining the splitting ratio of the fermion beam. For a non-rectangular intersection, the width and, to a lesser extent, the type of domain walls, e.g. Bloch or N{é}el, determine the properties of the splitter. As the ratio between domain-wall width and transverse localization length of the Dirac fermion is increased its propagation behavior changes from quantum-mechanical (wave-like) to classical ballistic (particle-like). An electric gate placed near the intersection offers a dynamic external control knob for adjusting the splitting ratio.

cond-mat.mes-hall↗

Staggered grid leap-frog scheme for the (2+1)D Dirac equation

A numerical scheme utilizing a grid which is staggered in both space and time is proposed for the numerical solution of the (2+1)D Dirac equation in presence of an external electromagnetic potential. It preserves the linear dispersion relation of the free Weyl equation for wave vectors aligned with the grid and facilitates the implementation of open (absorbing) boundary conditions via an imaginary potential term. This explicit scheme has second order accuracy in space and time. A functional for the norm is derived and shown to be conserved. Stability conditions are derived. Several numerical examples, ranging from generic to specific to textured topological insulator surfaces, demonstrate the properties of the scheme which can handle general electromagnetic potential landscapes.

physics.comp-ph↗

A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in (1+1)D

A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and time-staggered leap-frog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Z-transform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semi-infinite exterior domains. Admitting only solutions in $l_2$ which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Z-transformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stability of the whole space-time scheme. An exactly preserved functional for the norm of the Dirac spinor on the staggered grid is presented. Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energy-momentum dispersion relation on a grid.

physics.comp-ph↗

Dirac fermion wave guide networks on topological insulator surfaces

Magnetic texturing on the surface of a topological insulator allows the design of wave guide networks and beam splitters for domain-wall Dirac fermions. Guided by simple analytic arguments we model a Dirac fermion interferometer consisting of two parallel pathways, whereby a newly developed staggered-grid leap-frog discretization scheme in 2+1 dimensions with absorbing boundary conditions is employed. The net transmission can be tuned between constructive to destructive interference, either by variation of the magnetization (path length) or an applied bias (wave length). Based on this principle, a Dirac fermion transistor is proposed. Extensions to more general networks are discussed.

cond-mat.mes-hall↗