Modeling Multilayer Pyramidal-Like Adsorbate Structures …
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of adsorbate [27]. Hence, a simultaneous influence of these processes will lead to
local change in the surface temperature even on mesoscopic level of consideration.
It was shown before, that local variations in temperature have an important influence onto dynamics of crystal/aggregates formation [28]. It is known that spatially
extended dynamical systems are very sensitive to influence of fluctuating sources
representing multiplicative noise. An influence of external and internal fluctuations
onto dynamics of pattern formation was studied previously in systems described
by reaction-diffusion models with quasi-chemical reactions [29–33], by studying
adsorbate islands formation at condensation from gas phase [34], at modeling surface evolution at ion-beam sputtering [17]. It was shown that problems of pattern
formation fluctuations can play an important and/or crucial role. At the same time
by performing theoretical studies of surface morphology change, during epitaxial
growth one usually assumes that fluctuations are negligible.
In this chapter, we perform a theoretical study of adsorbate islands formation at
epitaxial growth processes in the framework of phase-field modeling by taking into
account the interaction of adatoms. We will show that at small values of interaction
energy the Gaussian-like surface will grow whereas well-organized pyramidal-like
adsorbate structures can be realized at elevated values of the interaction energy of
adatoms only. We will generalize the phase-field model by taking into account fluctuations in the total lateral flux of adsorbate and local changes in the surface temperature
in time at adsorption/desorption processes. We will consider the system dynamics in
the framework of mean field analysis and by using numerical simulations. The role of
fluctuations in process of adsorbate islands formation will be analyzed. We will set a
window for the system parameters (interaction strength of adsorbate and deposition
flux) when oscillatory regime of surface growth is realized. We will discuss an influence of the deposition flux, interaction strength of adsorbate, and relaxation time of
the temperature of the growing surface onto the morphology of the growing surface,
dynamics of the number of pyramidal islands and their mean size and distribution of
adsorbate islands over sizes.
The chapter is organized in the following manner. In the next section, we derive the
mathematical model, describing the formation of pyramidal-like adsorbate islands
on the substrate during deposition, by taking into account the interaction of adsorbate
and local changes in the surface temperature. In Sect. 3, we perform numerical simulations of pattern formation in the system, characterized by the constant temperature.
In Sect. 4, we introduce fluctuations of the total lateral flux of adsorbate and discuss
noise-induced effects at deposition. In Sect. 5, we study effects of the local variations
in the surface temperature caused by adsorption/desorption processes. Section 6 contains results of the scaling properties of the dynamics of pyramidal islands formation.
Main conclusions are collected in the last section.
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of adsorbate [27]. Hence, a simultaneous influence of these processes will lead to
local change in the surface temperature even on mesoscopic level of consideration.
It was shown before, that local variations in temperature have an important influence onto dynamics of crystal/aggregates formation [28]. It is known that spatially
extended dynamical systems are very sensitive to influence of fluctuating sources
representing multiplicative noise. An influence of external and internal fluctuations
onto dynamics of pattern formation was studied previously in systems described
by reaction-diffusion models with quasi-chemical reactions [29–33], by studying
adsorbate islands formation at condensation from gas phase [34], at modeling surface evolution at ion-beam sputtering [17]. It was shown that problems of pattern
formation fluctuations can play an important and/or crucial role. At the same time
by performing theoretical studies of surface morphology change, during epitaxial
growth one usually assumes that fluctuations are negligible.
In this chapter, we perform a theoretical study of adsorbate islands formation at
epitaxial growth processes in the framework of phase-field modeling by taking into
account the interaction of adatoms. We will show that at small values of interaction
energy the Gaussian-like surface will grow whereas well-organized pyramidal-like
adsorbate structures can be realized at elevated values of the interaction energy of
adatoms only. We will generalize the phase-field model by taking into account fluctuations in the total lateral flux of adsorbate and local changes in the surface temperature
in time at adsorption/desorption processes. We will consider the system dynamics in
the framework of mean field analysis and by using numerical simulations. The role of
fluctuations in process of adsorbate islands formation will be analyzed. We will set a
window for the system parameters (interaction strength of adsorbate and deposition
flux) when oscillatory regime of surface growth is realized. We will discuss an influence of the deposition flux, interaction strength of adsorbate, and relaxation time of
the temperature of the growing surface onto the morphology of the growing surface,
dynamics of the number of pyramidal islands and their mean size and distribution of
adsorbate islands over sizes.
The chapter is organized in the following manner. In the next section, we derive the
mathematical model, describing the formation of pyramidal-like adsorbate islands
on the substrate during deposition, by taking into account the interaction of adsorbate
and local changes in the surface temperature. In Sect. 3, we perform numerical simulations of pattern formation in the system, characterized by the constant temperature.
In Sect. 4, we introduce fluctuations of the total lateral flux of adsorbate and discuss
noise-induced effects at deposition. In Sect. 5, we study effects of the local variations
in the surface temperature caused by adsorption/desorption processes. Section 6 contains results of the scaling properties of the dynamics of pyramidal islands formation.
Main conclusions are collected in the last section.