Drift Of Adatoms Research Articles

Surface Modifications by Field Induced Diffusion

By applying a voltage pulse to a scanning tunneling microscope tip the surface under the tip will be modified. We have in this paper taken a closer look at the model of electric field induced surface diffusion of adatoms including the van der Waals force as a contribution in formations of a mound on a surface. The dipole moment of an adatom is the sum of the surface induced dipole moment (which is constant) and the dipole moment due to electric field polarisation which depends on the strength and polarity of the electric field. The electric field is analytically modelled by a point charge over an infinite conducting flat surface. From this we calculate the force that cause adatoms to migrate. The calculated force is small for voltage used, typical 1 pN, but due to thermal vibration adatoms are hopping on the surface and even a small net force can be significant in the drift of adatoms. In this way we obtain a novel formula for a polarity dependent threshold voltage for mound formation on the surface for positive tip. Knowing the voltage of the pulse we then can calculate the radius of the formed mound. A threshold electric field for mound formation of about 2 V/nm is calculated. In addition, we found that van der Waals force is of importance for shorter distances and its contribution to the radial force on the adatoms has to be considered for distances smaller than 1.5 nm for commonly used voltages.

Step wandering on Si(111) vicinal face near the1×1↔7×7transition temperature with drift of adatoms parallel to steps

On a Si(111) surface, which is covered with the 1 x 1 structure at high temperature, the 7 x 7 structure appears when temperature is lower than the structural transition temperature (860 degrees C) . On the vicinal face, the 7 x 7 structure spreads from the upper side of the step edge. The diffusion coefficient on the 1 x 1 structure is larger than that on the 7 x 7 structure. During growth, due to the difference in the diffusion coefficient, step wandering occurs and grooves perpendicular to the steps are formed. When the direct electric current is added parallel to the step, the grooves are tilted. In this paper, with taking account of the drift of adatoms caused by the direct current, we study the possibility of tilting of the grooves.

Effect of impingement and evaporation on drift-induced step instabilities on Si(111) vicinal face near transition temperature

Abstract Bearing the Si(1 1 1) vicinal face in mind, we study the effect of impingement and evaporation on drift-induced step instabilities. On a Si(1 1 1) face, transition between 1 × 1 structure and 7 × 7 structure occurs at 860 ∘ C . On the vicinal face near the transition temperature, the two structures coexist: the 1 × 1 structure is at the lower side of step and the 7 × 7 structure is at the upper side. On the 1 × 1 structure, the diffusion coefficient is larger than that on the 7 × 7 structure. When the difference in the diffusion coefficients is taken into account, step bunching occurs with drift of adatoms. In a conserved system with fast drift, separation and coalescence of steps occur repeatedly, and the bunches grow gradually. The motion of bunches changes when the impingement or evaporation is present. With the impingement, the separation of steps is suppressed and the bunches grow via coalescence of small ones with step-down drift, while the separation is more frequent than that in conserved system with step-up drift. With the evaporation, the relation is the opposite.

Motion of step pairs during drift-induced step bunching on a Si(0 0 1) vicinal face

By Monte Carlo simulation of a lattice model with the periodic boundary condition, we study the motion of step pairs during step bunching on a Si(0 0 1) vicinal face heated by direct electric current. When the anisotropy of the surface diffusion is taken into account, step bunching occurs with the drift of adatoms. When the system width along the steps is so large that bunches fluctuate widely, the bunches with step-up drift recombine with neighboring bunches more frequently and grow faster than those with step-down drift. When the system width along the steps is so small that bunches are straight, the recombination is suppressed irrespective of the drift direction. The bunches with step-up drift grow slower than those with step-down drift. With increasing the drift velocity, separation of the step pair from the bunch occurs. The separated step pairs recede with step-down drift and advances with step-up drift.

Evaporation and impingement effects on drift-induced step instabilities on a Si(001) vicinal face

We theoretically study the effect of evaporation and impingement of atoms on step wandering induced by the drift of adatoms. With a Si(001) vicinal face in mind, the anisotropy in diffusion coefficient is assumed to alternate on consecutive terraces. Without evaporation, steps wander in-phase with step-up drift and grooves perpendicular to the steps appear. The form of the wandering steps is sinusoidal with the width increasing in time as ${t}^{1∕2}$. Evaporation of adatoms suppresses the step wandering and introduces two surface diffusion lengths. When they are longer than the step distance, the step width still increases in proportion to ${t}^{1∕2}$, but with a smaller coefficient than that in the case without evaporation. When one of the surface diffusion lengths is comparable or shorter than the step distance, the saturation of the step width occurs. Impingement of atoms, on the other hand, changes the form of the wandering steps: their front becomes flat and wide and the grooves become steep and narrow. The growth rate of the step width becomes small, but the step width increases with the same exponent $1∕2$.

Drift-induced step instabilities due to the gap in the diffusion coefficient

On a Si(1 1 1) vicinal face near the structural transition temperature, the 1 × 1 structure and the 7 × 7 structure coexist in a terrace: the 1 × 1 structure is in the lower side of the step edge and the 7 × 7 structure in the upper side. The diffusion coefficient of adatoms is different in the two structures. Taking account of the gap in the diffusion coefficient at the step, we study the possibility of step wandering induced by drift of adatoms. A linear stability analysis shows that the step wandering always occurs with step-down drift if the diffusion coefficient has a gap at the step. Formation of straight grooves by the step wandering is expected from a nonlinear analysis. The stability analysis also shows that step bunching occurs irrespective of the drift direction if the diffusion in the lower side of the step is faster. The step bunching disturbs the formation of grooves. If step–step repulsion is strong, however, the step bunching is suppressed and the straight grooves appear. Monte Carlo simulation confirms these predictions.

Growth of Step Bunches on a Si(001) Vicinal Face with Drift of Adatoms

On a Si(001) vicinal face, where the direction of fast surface diffusion alternates on consecutive terraces, step bunching has been observed under direct current heating. By using a one-dimensional step model with drift of adatoms, we study growth laws of step bunches. If evaporation is negligible, the average number N of steps in a bunch increases with time as N ∝ t β with \(\beta \lessapprox 1/2\). The growth exponent β weakly depends on the repulsive interaction potential between steps. When steps at a distance l interact with the repulsive potential ζ∝1/ l ν , the average step distance in a bunch l b decreases as l b ∝ N -α with α≈3/2(ν+2). The exponents α and β are related as β≈1/(2+ α). The simulation results are consistent with experiment if we take account of both logarithmic and ν=2 potentials, which are expected in this system. The growth rate of the bunch size with step-down drift is faster than that with step-up drift. If evaporation of adatoms is significant, the difference of the growth rate...

Step Bunching with Alternation of Structural Parameters

By taking account of the alternation of structural parameters, we study bunching of impermeable steps induced by drift of adatoms on a vicinal face of Si(001). With the alternation of diffusion coefficient, the step bunching occurs irrespective of the direction of the drift if the step distance is large. Like the bunching of permeable steps, the type of large terraces is determined by the drift direction. With step-down drift, step bunches grows faster than those with step-up drift. The ratio of the growth rates is larger than the ratio of the diffusion coefficients. Evaporation of adatoms, which does not cause the step bunching, decreases the difference. If only the alternation of kinetic coefficient is taken into account, the step bunching occurs with step-down drift. In an early stage, the initial fluctuation of the step distance determines the type of large terraces, but in a late stage, the type of large terraces is opposite to the case of alternating diffusion coefficient.

Step wandering induced by the drift of adatoms in a conserved system

We study step wandering induced by the drift of adatoms in a conserved system. When steps are impermeable, in-phase wandering occurs with the step-down drift. The steps are unstable for long-wavelength fluctuations and the wavelength of the most unstable mode is determined by the competition between the drift and the step stiffness. When nonlinear effects are taken into account, the steps obey the same type of equation as that of the step wandering due to the Ehrlich-Schwoebel effect in growth without evaporation. We carry out Monte Carlo simulation and compare the results with the nonlinear evolution equation.

Ｓｉ（１１１）表面の高温におけるステップ・原子の振る舞い 吸着原子の流れによるステップのバンチングと蛇行の理論について

Ｓｉ（１１１）表面の高温におけるステップ・原子の振る舞い 吸着原子の流れによるステップのバンチングと蛇行の理論について

Step bunching induced by drift of adatoms with anisotropic surface diffusion

By means of Monte Calro simulation we study step bunching induced by the drift of adatoms with anisotropic surface diffusion. Like a vicinal face of Si(0 0 1), we suppose that two types of terraces appear alternately, and their directions of fast diffusion are parallel and perpendicular to the steps. When the drift is perpendicular to the steps, we found from stability analysis that the vicinal face is unstable for pairing instability with both step-up and step-down drift. In a late stage of bunching, large bunches appear irrespective of the drift direction, while formation process of the bunches is affected by the drift direction.

Growth of permeable step bunches formed by drift of adatoms

We study bunching of permeable steps induced by drift of adatoms. In contrast to impermeable steps, bunching may occur with step-up drift. When diffusion length is short, terrace width between the bunches increases as L∝tβ with β≈1/2 through collision and coalescence. After the power law growth, the system reaches a steady state, where an array of similar bunches coexists with a few single steps on large terraces. If the diffusion length is long, the exponent β increases up to one.

Instabilities of Permeable Steps Induced by the Drift of Adatoms

We study the effect of permeability on the two types of step instabilities, bunching and wandering. When the step is permeable for adatom diffusion, the wandering instability occurs with step-down drift and the bunching instability occurs with step-up drift. In contrast, when the step is impermeable for adatom diffusion, both the wandering and the bunching instabilities occur with step-down drift. We derive the linear amplification rates of step fluctuation and the critical drift velocities to induce the instabilities. The results of the linear analysis are tested by Monte Carlo simulation.

Instabilities of steps induced by the drift of adatoms and effect of the step permeability

We theoretically study step wandering and step bunching induced by the drift of adatoms with attention to the permeability of steps. The critical drift velocity to induce the instability is calculated, and Monte Carlo simulation is performed to test the linear analysis. In sublimation, when the step distance is small in comparison with the surface diffusion length, the wandering and bunching of steps can occur simultaneously with the step-down drift if steps are impermeable. The instabilities do not occur simultaneously if steps are permeable: the bunching occurs with the step-up drift, and the wandering with the step-down drift. In growth, when the step distance is small, the bunching occurs with the step-down drift and the step wandering occurs with the step-up drift irrespective of the permeability, in agreement with M\'etois and Stoyanov [Surf. Sci. 440, 407 (1999)]. The change of the permeability with increasing temperature can explain the instabilities observed in Si(111) vicinal face [M. Degawa et al., Jpn. J. Appl. Phys 38, L308 (1999)].

Permeability of Steps and the Step Bunching Induced by Drift of Adatoms

Permeability of Steps and the Step Bunching Induced by Drift of Adatoms

Permeability of Steps and the Step Wandering Induced by Drift of Adatoms

Permeability of Steps and the Step Wandering Induced by Drift of Adatoms

Pattern formation in the instability of a vicinal surface by the drift of adatoms.

We study the behavior of steps in a vicinal face with drift of adsorbed atoms (adatoms) by an external field. When the drift is in the downhill direction and its velocity exceeds critical values, v(x)(c) and v(y)(c), the vicinal face is linearly unstable to long-wavelength fluctuations parallel and/or perpendicular to the steps. By taking the continuum limit of the step-flow model, we derive an anisotropic Kuramoto-Sivashinsky equation with propagative terms, which describes the motion of an unstable vicinal face. Its numerical solution shows ripples or a zigzag pattern expected from the linear analysis. Nonlinearity becomes important in the late stage and, depending on the condition, various patterns are formed: regular step bunches, a hill and valley structure tilted from the initial step direction, mounds, and a chaotic pattern.

Growth of step bunches formed by the drift of adatoms

We study power-law growth of step bunches produced by the drift of adatoms. When evaporation of the adatoms is neglected (conserved system), the terrace width between the bunches increases as L∝ t β with β≈1/2 through a hierarchical bunching. The time dependence of L is not affected by the form of step repulsion. When the adatoms evaporate to the atmosphere (non-conserved system), the motion of the steps changes drastically: isolated steps are always present in large terraces, and collision of the steps with the bunches is repeated. When the drift of adatoms is fast, the terrace width grows by ‘effective coalescence’ of the bunches as L∝ t 1/2, similarly to the bunching in the conserved system. When the drift of adatoms is slow, the bunches grow by ‘bunch size exchange’ with β smaller than 1/2 and the terrace width saturates in a late stage. The exponent β increases with increasing drift velocity and approaches β≈1/2.

22aC8 吸着原子のドリフト流による不安定化での微斜面のパターン(成長界面II)

22aC8 吸着原子のドリフト流による不安定化での微斜面のパターン(成長界面II)

Step Bunching Induced by the Drift of Adatoms.

Step Bunching Induced by the Drift of Adatoms.