Method of Measuring an Anisotropic Surface Diffusion Tensor or Surface Energy Anisotropies

Method of measuring 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 (a0) and of wavelengths (λx, λy) the amplitude/wavelength ratios (a0/λx;

• a0/λy) being less than about 0.3, comprising the following steps:
• a first measurement of the surface topology enabling the Fourier transform H(fx,fy,0) of this first topology to be determined at an instant t0=0, fx and fy 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(fx,fy,t) of this second topology at an instant t to be determined, fx and fy being the spatial frequencies;
• and
• 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, G′) of the deviation between a quantity H(fx,fy,t) and a quantity H(fx,fy,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
• theory
• )
• -
• a
• 0
• 2
• 
• α
• 2
• 
• (
• max
• 
• (
• f
• x
• ;
• f
• y
• )
• )
• 2
• 1
• +
• a
• 0
• 2
• 
• α
• 2
• 
• (
• max
• 
• (
• f
• x
• ;
• f
• y
• )
• )
• 2
• α2 being dependent on fx and fy, fx and fy 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 dx and dy are the components of the diffusion tensor relative to the diffusion anisotropy in the x and y directions, γ0 is the surface energy and γx″ and γy″ 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.