The role of step edge diffusion in epitaxial crystal growth

The role of step edge diffusion (SED) in epitaxial growth is investigated. To this end we revisit and extend a recently introduced simple cubic solid-on-solid model, which exhibits the formation and coarsening of pyramid or mound like structures. By comparing the limiting cases of absent, very fast (significant), and slow SED we demonstrate how the details of this process control both the shape of the emerging structures as well as the scaling behavior. We find a sharp transition from significant SED to intermediate values of SED, and a continuous one for vanishing SED. We argue that one should be able to control these features of the surface in experiments by variation of the flux and substrate temperature.Comment: revised and enlarged version 12 pages, 5 figures, to appear in Surface Scienc

Adjoint-Based Error Estimation and Mesh Adaptation for Hybridized Discontinuous Galerkin Methods

We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations. Hybridization of finite element discretizations has the main advantage, that the resulting set of algebraic equations has globally coupled degrees of freedom only on the skeleton of the computational mesh. Consequently, solving for these degrees of freedom involves the solution of a potentially much smaller system. This not only reduces storage requirements, but also allows for a faster solution with iterative solvers. The mesh adaptation is driven by an error estimate obtained via a discrete adjoint approach. Furthermore, the computed target functional can be corrected with this error estimate to obtain an even more accurate value. The aim of this paper is twofold: Firstly, to show the superiority of adjoint-based mesh adaptation over uniform and residual-based mesh refinement, and secondly to investigate the efficiency of the global error estimate

Modeling Space-Charge Limited Currents in Organic Semiconductors: Extracting Trap Density and Mobility

We have developed and applied a mobility edge model that takes into account drift and diffusion currents to characterize the space charge limited current in organic semiconductors. The numerical solution of the drift-diffusion equation allows the utilization of asymmetric contacts to describe the built-in potential within the device. The model has been applied to extract information of the distribution of traps from experimental current-voltage measurements of a rubrene single crystal from Krellner et al. [Phys. Rev. B, 75(24), 245115] showing excellent agreement across several orders of magnitude of current. Although the two contacts are made of the same metal, an energy offset of 580 meV between them, ascribed to differences in the deposition techniques (lamination vs. evaporation) was essential to correctly interpret the shape of the current-voltage characteristics at low voltage. A band mobility 0.13 cm2/Vs for holes was estimated, which is consistent with transport along the long axis of the orthorhombic unit cell. The total density of traps deeper than 0.1 eV was 2.2\times1016 cm-3. The sensitivity analysis and error estimation in the obtained parameters shows that it is not possible to accurately resolve the shape of the trap distribution for energies deeper than 0.3 eV or shallower than 0.1 eV above the valence band edge. The total number of traps deeper than 0.3 eV however can be estimated. Contact asymmetry and the diffusion component of the current play an important role in the description of the device at low bias, and are required to obtain reliable information about the distribution of deep traps

Tissue fusion over non-adhering surfaces

Tissue fusion eliminates physical voids in a tissue to form a continuous structure and is central to many processes in development and repair. Fusion events in vivo, particularly in embryonic development, often involve the purse-string contraction of a pluricellular actomyosin cable at the free edge. However in vitro, adhesion of the cells to their substrate favors a closure mechanism mediated by lamellipodial protrusions, which has prevented a systematic study of the purse-string mechanism. Here, we show that monolayers can cover well-controlled mesoscopic non-adherent areas much larger than a cell size by purse-string closure and that active epithelial fluctuations are required for this process. We have formulated a simple stochastic model that includes purse-string contractility, tissue fluctuations and effective friction to qualitatively and quantitatively account for the dynamics of closure. Our data suggest that, in vivo, tissue fusion adapts to the local environment by coordinating lamellipodial protrusions and purse-string contractions

Distinguishing step relaxation mechanisms via pair correlation functions

Theoretical predictions of coupled step motion are tested by direct STM measurement of the fluctuations of near-neighbor pairs of steps on Si(111)-root3 x root3 R30 - Al at 970K. The average magnitude of the pair-correlation function is within one standard deviation of zero, consistent with uncorrelated near-neighbor step fluctuations. The time dependence of the pair-correlation function shows no statistically significant agreement with the predicted t^1/2 growth of pair correlations via rate-limiting atomic diffusion between adjacent steps. The physical considerations governing uncorrelated step fluctuations occurring via random attachment/detachment events at the step edge are discussed.Comment: 17 pages, 4 figure