Noriko Akutsu

Relationship between the anisotropic interface tension, the scaled interface width and the equilibrium shape in two dimensions

The formula which relates the scaled interface width to the anisotropic interface tension is generalised for an arbitrary orientation of the interface in two dimensions. The relationship between the scaled interface width and the curvature of the equilibrium crystal shape is also generalised.

Fluctuation of a Single Step on the Vicinal Surface-Universal and Non-Universal Behaviors

Mean-square fluctuation width of a single step on the vicinal surface, denoted by Δ 2 ( y ) ( y : distance along the step), is calculated based on the terrace-step-kink picture. For systems with only short-range step-step interactions, both the free-fermion approach and the capillary-wave approach are taken to derive the universal asymptotic behavior Δ 2 ( y )∼ A log y with A =(πρ) -2 ,where ρ is the step density. We present a general relation between Δ 2 ( y ) and the surface height-height correlation function, which connects the universal behavior to the universal Gaussian curvature jump at the facet edge. For the case with long-range (inverse-square) step-step interactions, we combine the exact solution of the Sutherland model with the capillary-wave theory. We successfully derive the non-universal amplitude A = A (ρ, g ) as a function of the coupling constant g .

Statistical mechanical calculation of anisotropic step stiffness of a two-dimensional hexagonal lattice-gas model with next-nearest-neighbour interactions: application to Si(111) surface

We study a two-dimensional honeycomb lattice-gas model with both nearest- and next-nearest-neighbour interactions in a staggered field, which describes the surface of a stoichiometrically binary crystal. We calculate the anisotropic step tension, step stiffness and equilibrium island shape, by an extended random walk method. We apply the results to the Si(111) 7 × 7 reconstructed surface and the high-temperature Si(111) 1 × 1 surface. We also calculate the inter-step interaction coefficient.

Universal Behavior of the Equilibrium Crystal Shape near the Facet Edge. I. A Generalized Terrace-Step-Kink Model

A generalized version of the terrace-step-kink (TSK) model is introduced to study in detail the shape of a crystal near the facet edge. The model is analyzed by the transfer-matrix method combined with the lattice fermion approach. As a result, behavior of the curvature near the facet edge is found to have unexpected new features: finite Gaussian curvature jump with universal amplitude and vanishing transverse curvature with universal exponent.

Logarithmic Step Fluctuations in Vicinal Surface: A Monte Carlo Study

Based on the terrace-step-kink (TSK) picture, the fluctuation property of a single step on the vicinal surface is studied by the Monte Carlo method. Logarithmic behavior of the squared step width W 2 ( y )∼ A W ln y ( y : distance between two points on the same step) is confirmed for both the free-fermion TSK model and the non-free-fermion solid-on-solid (SOS) step model. The calculated amplitude A W as a function of the step density ρ verifies the universal form A W =1/(π 2 ρ 2 ) for the free-fermion TSK model. For the SOS step model, A W deviates from the universal form as ρ increases.

Step stiffness and equilibrium island shape of Si(100) surface: statistical—mechanical calculation by the imaginary path weight random-walk method

A step on a surface is well-modeled by an interface in the Ising model. We calculate anisotropic interface tension and interface stiffness for the square-lattice Ising model with both nearest-neighbor and next-nearest-neighbor interactions by an extended Feynman-Vdovichenkos random-walk method. The result gives a satisfactory explanation for experimentally measured step tension, step stiffness and island shape on the Si(100) surface.

Equilibrium Crystal Shape:Two Dimensions and Three Dimensions

We show that the two-dimensional (2D) equilibrium crystal shape (ECS) determined from the anisotropic step free energy gives the facet shape of the 3D ECS below the roughening temperature. This fact brings us a general and efficient method to obtain the essential feature of 3D ECS, by estimating the step free energy from the 1D solid-on-solid (SOS) model or the 2D Ising model. We apply the method to the body-centered-cubic solid-on-solid (BCSOS) model and obtain almost the exact facet shape for a wide range of temperatures.

Stiffening Transition in Vicinal Surfaces with Adsorption

We study the vicinal surface with adsorption below the roughening temperature, using a solid-on-solid model coupled with the Ising model. We calculate the step tension γ and the step-interaction coefficient B using the density matrix algorithm. We find a temperature Ts where B vanishes and that the surface free energy has the form f (p) � f (0) = γp + (const) p 5 +···, where p is the surface gradient.

Statistical properties of atomic-scale Si/SiO2 interface roughness studied by STM

Abstract Thermal-oxide stripped Si(001) surface topography is measured by scanning tunneling microscopy (STM) in UHV in order to analyze the statistical properties of the surface. A quantitative analysis implies that the autocovariance of the interface topography cannot be definitely fitted by a Gaussian or an exponential function. The fractal nature of the interface is studied in the sub-nanometer range for the first time and the roughness characteristic for a Gaussian random process might be observed. The rms fluctuation and correlation length of the surface are estimated to be 3.3 and 73A(Gaussian fit), respectively. The effects of UHV annealing on the statistical properties of the interface roughness are also studied.

Statistical mechanics of the vicinal surfaces with adsorption

We study the vicinal surface with adsorption below the roughening temperature, using the restricted solid-on-solid model coupled with the Ising model. By the product-wavefunction renormalization group method, we calculate the surface gradient p and the adsorption coverage Θ as a function of the Andreev field η which makes surface tilt. Combining Monte Carlo calculations, we show that there emerges effective attraction between the steps. This attractive interaction leads to instability against step bunching.