Modeling Multilayer Pyramidal-Like Adsorbate Structures …
435
Fig. 4 Correlation function C 0 (r ) at different values of the deposition rate F and interaction
strength ε (a); and the correlation length ξ as a function of the interaction strength ε at F = 2. Here
h = =φ max − φ min measures the averaged height difference between lower φ min and upper φ max
points on the surface
disordered surface toward pyramidal patterns through the Gaussian surface. Hence,
an increase in the interaction energy of adsorbate results in a competition between
adsorption and desorption/diffusion processes: it leads to a formation of the surface
with Gaussian-like surface and finally to the surface with pyramidal-like structures
[48].
4 Effects of the Adsorbate Flux Fluctuations
By considering the process of adsorbate islands growth at epitaxy in real conditions,
one should take into account the fluctuation source. Previously, it was shown that the
multiplicative noise can be introduced into the system dynamics in an ad hoc form
[29, 36, 37]. In our case in order to study stochastic system next we assume that
the total lateral flux of adsorbate J tot is composed by the regular part and stochastic
component. In such a case, we can write
∂ x
∂t
= F −
x
τ s0
e
−εx
− ∇ · J tot ,
J tot = −D e f (x)∇x + ζ (x; r, t),
(10)
where D e f (x) = D(1 − εx(1 − x)); for the stochastic source ζ we assume Gaussian
properties: (x, r, t) = 0, (x, r, t)ζ (x, r
, t
) = 2 D e f (x)δ(r − r
)δ(t − t
),
is the noise intensity. By using the Stratonovich interpretation of the stochas-
435
Fig. 4 Correlation function C 0 (r ) at different values of the deposition rate F and interaction
strength ε (a); and the correlation length ξ as a function of the interaction strength ε at F = 2. Here
h = =φ max − φ min measures the averaged height difference between lower φ min and upper φ max
points on the surface
disordered surface toward pyramidal patterns through the Gaussian surface. Hence,
an increase in the interaction energy of adsorbate results in a competition between
adsorption and desorption/diffusion processes: it leads to a formation of the surface
with Gaussian-like surface and finally to the surface with pyramidal-like structures
[48].
4 Effects of the Adsorbate Flux Fluctuations
By considering the process of adsorbate islands growth at epitaxy in real conditions,
one should take into account the fluctuation source. Previously, it was shown that the
multiplicative noise can be introduced into the system dynamics in an ad hoc form
[29, 36, 37]. In our case in order to study stochastic system next we assume that
the total lateral flux of adsorbate J tot is composed by the regular part and stochastic
component. In such a case, we can write
∂ x
∂t
= F −
x
τ s0
e
−εx
− ∇ · J tot ,
J tot = −D e f (x)∇x + ζ (x; r, t),
(10)
where D e f (x) = D(1 − εx(1 − x)); for the stochastic source ζ we assume Gaussian
properties: (x, r, t) = 0, (x, r, t)ζ (x, r
, t
) = 2 D e f (x)δ(r − r
)δ(t − t
),
is the noise intensity. By using the Stratonovich interpretation of the stochas-