440
A. V. Dvornichenko and O. M. Shchokotova
realized. By comparing results for two different sets of parameters one can conclude that the decaying rate and the frequency of oscillations depends on the system
parameters.
6 Scaling and Universality
6.1 Scaling Properties of the Islands Growth Processes
Next, we aim to discuss the dynamics of adsorbate islands growth by monitoring
evolution of the mean size of adsorbate islands and their number. In order to calculate
the area occupied by each pyramidal island on any height level, we will exploit the
percolating clusters method. In the model under consideration, the height of the
surface constantly grows according to the law φ = Ft. Hence, the mean height
level also will grow with time and will be calculated at each simulation time step t i
in the standard manner. At each time instant t i , we define the current value of the
mean height of the growing surface φ(t i ) and calculate the full number of adsorbate
structures and their mean size (occupied area) on this mean height level.
Obtained results as temporal dependencies of the mean value of a full number
of adsorbate structures N and their mean size (area) s, counted in the value of
the square of diffusion length L d on the mean height level of the growing surface
φ(t i ) are shown in log–log plots in Fig. 9. Here, plots (a) and (b) show dependencies at fixed values of deposition flux F and interaction energy ε and different
values of the relaxation time of the temperature field ν; plots (c) and (d) correspond
to data obtained at fixed ν and different values of F and ε. Here we present results
for the stage of pyramidal islands growth, neglecting the initial stage of the islands
formation. In all plots, symbols correspond to numerical data and curves relate to
power-law approximations, N ∝ t
−γ and s ∝ t
δ with γ, δ > 0. From the dependencies N (t) shown in Fig.9a, c it is followed that initially formed ∼50 small
pyramidal islands emerge during exposing organized single pyramidal structure and
the number of islands decays in time in power law t
−γ . From the temporal dependencies of the mean islands size s(t) shown in Fig. 9b, d one sees, that at initial stages
the mean size is about 1% of a total computational grid; at late stages one pyramidal
island occupies around 40% of the whole grid on a mean height level. A decrease
in time of the mean adsorbate size relates well with the power law. By comparing
obtained data at different system parameters one gets that an increase in the relaxation
time of temperature field ν delays dynamics of the mean islands size growth. At large
values of the deposition flux F the dynamics of the islands growth accelerate. With
increase in the interaction strength ε the growth processes are delayed. According
to obtained data one finds that the relation δ/γ remains invariant to the variation in
main system parameters
A. V. Dvornichenko and O. M. Shchokotova
realized. By comparing results for two different sets of parameters one can conclude that the decaying rate and the frequency of oscillations depends on the system
parameters.
6 Scaling and Universality
6.1 Scaling Properties of the Islands Growth Processes
Next, we aim to discuss the dynamics of adsorbate islands growth by monitoring
evolution of the mean size of adsorbate islands and their number. In order to calculate
the area occupied by each pyramidal island on any height level, we will exploit the
percolating clusters method. In the model under consideration, the height of the
surface constantly grows according to the law φ = Ft. Hence, the mean height
level also will grow with time and will be calculated at each simulation time step t i
in the standard manner. At each time instant t i , we define the current value of the
mean height of the growing surface φ(t i ) and calculate the full number of adsorbate
structures and their mean size (occupied area) on this mean height level.
Obtained results as temporal dependencies of the mean value of a full number
of adsorbate structures N and their mean size (area) s, counted in the value of
the square of diffusion length L d on the mean height level of the growing surface
φ(t i ) are shown in log–log plots in Fig. 9. Here, plots (a) and (b) show dependencies at fixed values of deposition flux F and interaction energy ε and different
values of the relaxation time of the temperature field ν; plots (c) and (d) correspond
to data obtained at fixed ν and different values of F and ε. Here we present results
for the stage of pyramidal islands growth, neglecting the initial stage of the islands
formation. In all plots, symbols correspond to numerical data and curves relate to
power-law approximations, N ∝ t
−γ and s ∝ t
δ with γ, δ > 0. From the dependencies N (t) shown in Fig.9a, c it is followed that initially formed ∼50 small
pyramidal islands emerge during exposing organized single pyramidal structure and
the number of islands decays in time in power law t
−γ . From the temporal dependencies of the mean islands size s(t) shown in Fig. 9b, d one sees, that at initial stages
the mean size is about 1% of a total computational grid; at late stages one pyramidal
island occupies around 40% of the whole grid on a mean height level. A decrease
in time of the mean adsorbate size relates well with the power law. By comparing
obtained data at different system parameters one gets that an increase in the relaxation
time of temperature field ν delays dynamics of the mean islands size growth. At large
values of the deposition flux F the dynamics of the islands growth accelerate. With
increase in the interaction strength ε the growth processes are delayed. According
to obtained data one finds that the relation δ/γ remains invariant to the variation in
main system parameters