Patent ID: 8583403

Claim:
Non-transitory computer readable medium containing a numerical simulation program for causing a computer processor to perform measuring and processing an anisotropic surface diffusion tensor or surface energy anisotropies of a surface defined by a function z(x,y) dependent on two co-ordinates (x,y) along two orthogonal directions, the Fourier transform of this surface enabling it to be decomposed into a sum of moderate-amplitude perturbations of initial amplitude (a 0 ) and of wavelengths (λ x , λ y ), the amplitude/wavelength ratios (a 0 /λ x ; a 0 /λ y ) being less than about 0.3, comprising the following steps: a first measurement of the surface topology enabling the Fourier transform H(f x ,f y ,0) of this first topology to be determined at an instant t 0 =0, f x and f y being the spatial frequencies; a step in which said surface evolves by surface diffusion; a second measurement of the surface topology after evolution of said surface, enabling the Fourier transform H(f x ,f y ,t) of this second topology at an instant t to be determined, f x and f y being the spatial frequencies; the determination of the components of the diffusion tensor or of the second derivatives of the surface energy, or a combination of the components of the tensor and of the second derivatives of the surface energy, enabling a measurement (G) of the deviation between a quantity H(f x ,f y ,t) and a quantity H(f x ,f y ,0)·a(t) to be minimized, where a ⁡ ( t ) = a 0 1 + a 0 2 ⁢ α 2 ⁡ ( max ⁡ ( f x ; f y ) ) 2 · exp ⁡ ( 2 ⁢ ⁢ t τ therory ) - a 0 2 ⁢ α 2 ⁡ ( max ⁡ ( f x ; f y ) ) 2 1 + a 0 2 ⁢ α 2 ⁡ ( max ⁡ ( f x ; f y ) ) 2 α 2 being dependent on f x and f y , f x and f y being the spatial frequencies in the orthogonal directions associated with the co-ordinates x and y, and τ theory = 1 C ⁡ ( d x ⁢ f x 2 + d y ⁢ f y 2 ) ⁢ ( ( γ 0 + γ x ″ ) ⁢ f x 2 + ( γ 0 + γ y ″ ) ⁢ f y 2 ) and d x and d y are the components of the diffusion tensor relative to the diffusion anisotropy in the x and y directions, γ 0 is the surface energy and γ x ″ and γ y ″ are the second derivatives of the surface energy with respect to the orientation of the surface in the directions associated with the co-ordinates x and y; and the measurement of the deviation (G) satisfies the following formula: G = ∑ fx = fx_min fx_max ⁢ ⁢ ∑ fy = fy_min fy_max ⁢ ⁢ ( PSD ⁡ ( fx , fy , t ) - PSD ⁡ ( fx , fy , 0 ) · a ⁡ ( t ) 2 ) 2 where PSD (f x ,f y ,t) is the power spectral density corresponding to the square of the norm of the Fourier transform at time t and PSD(f x ,f y ,0) is the power spectral density at time t 0 ; and displaying the anisotropic surface diffusion tensor or the surface energy anisotropies of the surface material.