Vesselin Tonchev

Scaling properties of step bunches induced by sublimation and related mechanisms

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.

Surface Properties of Squalene/Meibum Films and NMR Confirmation of Squalene in Tears

Squalene (SQ) possesses a wide range of pharmacological activities (antioxidant, drug carrier, detoxifier, hydrating, emollient) that can be of benefit to the ocular surface. It can come in contact with human meibum (hMGS; the most abundant component of the tear film lipid layer) as an endogenous tear lipid or from exogenous sources as eyelid sebum or pharmaceuticals. The aims of this study were to determine (i) if SQ is in tear lipids and (ii) its influence on the surface properties of hMGS films. Heteronuclear single quantum correlation NMR confirmed 7 mol % SQ in Schirmer’s strips extracts. The properties of SQ/hMGS pseudo-binary films at the air/water interface were studied with Langmuir surface balance, stress-relaxation dilatational rheology and Brewster angle microscopy. SQ does not possess surfactant properties. When mixed with hMGS squalene (i) localized over the layers’ thinner regions and (ii) did not affect the film pressure at high compression. Therefore, tear SQ is unlikely to instigate dry eye, and SQ can be used as a safe and “inert” ingredient in formulations to protect against dry eye. The layering of SQ over the thinner film regions in addition to its pharmacological properties could contribute to the protection of the ocular surface.

Time scaling relations for step bunches from models with step-step attractions (B1-type models)

The step bunching instability is studied in three models of step motion defined in terms of ordinary differential equations (ODE). The source of instability in these models is step-step attraction, it is opposed by step-step repulsion and the developing surface patterns reflect the balance between the two. The first model, TE2, is a generalization of the seminal model of Tersoff et al. (1995). The second one, LW2, is obtained from the model of Liu and Weeks (1998) using the repulsions term to construct the attractions one with retained possibility to change the parameters in the two independently. The third model, MM2, is a minimal one constructed ad hoc and in this article it plays a central role. New scheme for scaling the ODE in vicinal studies is applied towards deciphering the pre-factors in the time-scaling relations. In all these models the patterned surface is self-similar - only one length scale is necessary to describe its evolution (hence B1-type). The bunches form finite angles with the terraces. Integrating numerically the equations for step motion and changing systematically the parameters we obtain the overall dependence of time-scaling exponent \b{eta} on the power of step-step attractions p as \b{eta} = 1/(3+p) for MM2 and hypothesize based on restricted set of data that it is \b{eta} = 1/(5+p) for LW2 and TE2.

Unstable vicinal crystal growth from cellular automata

In order to study the unstable step motion on vicinal crystal surfaces we devise vicinal Cellular Automata. Each cell from the colony has value equal to its height in the vicinal, initially the steps are regularly distributed. Another array keeps the adatoms, initially distributed randomly over the surface. The growth rule defines that each adatom at right nearest neighbor position to a (multi-) step attaches to it. The update of whole colony is performed at once and then time increases. This execution of the growth rule is followed by compensation of the consumed particles and by diffusional update(s) of the adatom population. Two principal sources of instability are employed – biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). Since these factors are not opposed by step-step repulsion the formation of multi-steps is observed but in general the step bunches preserve a finite width. We monitor the developing surface patterns and quantify the observations by scaling laws with focus on ...

Design of atomic step networks on Si(111) through strain distribution control

We propose an alternative method to control atomic step networks on silicon for future wafer-scale integration of self-assembling nanostructures. The method is the strain-distribution-control method that we have recently proposed in [H. Omi, D. J. Bottomley, and T. Ogino, Appl. Phys. Lett. 80, 1073 (2002)], which we apply here to design atomic step networks on vicinal Si(111) wafer. Si(111) with its strain patterned by buried silicon oxide inclusions was annealed at 1230 °C in ultrahigh vacuum and observed by in situ secondary electron microscopy and ex situ atomic force microscopy. The images show that the method enables us to create the desired arrays of atomic step networks on an arbitrary area of planar silicon wafer. The arrays remain stable during the 1230 °C annealing.

Electromigration of si Adatoms on si Surfaces: A Key to Understanding Step Bunching Instabilities During Sublimation and Mbe Growth

Recent progress in understanding the mechanisms of step bunching induced by direct electric current heating is reviewed. Experiments on step bunching during sublimation and during growth of Si crystals manifest different mechanisms of instability on vicinal surfaces that operate in different temperature intervals. Measurements of the width L b of a bunch, consisting of a fixed number of steps, as a function of the temperature of the Si crystal provide a basis for determining the temperature dependence g(T) of the step interaction coefficient in the expression f(g) = f(0) + Kϱ + gϱ 3 for the free energy (per unit projected area) of a vicinal surface with a density of steps ϱ. We have evaluated g(T) in the high-temperature interval on the basis of the derived expression and the measured values of L b and I(T) during crystal-vapour equilibrium [I(T) is the electric current flowing through the Si crystal to keep it at a temperature T]. The experiments on the temperature dependence of the bunch width L b under non-equilibrium conditions (growth of the Si crystal) manifest a sharp peak (at T = 1230° C), which indicates a significant change of the structure of the Si(111) surface.

Electric Current Induced Asymmetry of Surface Diffusion - Instability of Vicinal Crystal Surfaces

We measured the width Lb, of a bunch, consisting of a fixed number of steps, as a function of the temperature of the Si crystal, heated by direct electric current. We carried out these measurements in three different regimes—during crystal-vapor equilibrium, during sublimation, and during crystal growth. The central result of this work is the experimentally-determined temperature-dependence g(T) of the step interaction coefficient in the expression f (ρ) = f(0) + κρ + gρ 3 for the surface free energy (per unit projected area) of a vicinal surface of Si(111) with a density of steps ρ. We evaluated g(T) in the high temperature interval on the basis of the derived expression \(\frac{{g(T)}} {{g(T_0 )}} = \frac{{L_b^3 (T)}} {{L_b^3 (T_0 )}}\frac{{1(T)}} {{1(T_0 )}}\) and the measured values of Lb and I(T) during crystal-vapour equilibrium (I(T) is the electric current, flowing through the Si crystal to keep it at a temperature T). The experiments on the temperature-dependence of the bunch width Lb under non-equilibrium conditions (growth of the Si crystal) manifest a sharp peak (at T = 1230° C), which indicates a significant change of the structure of the Si(111) surface.