Phase-field Modeling Of Epitaxial Film Growth With The Kinetic Effects

Epitaxial growth of films has been regarded as a complex nonequilibrium growth process with the coupling effects of growth regimes during various atomic motions,which are related to a series of equilibiurm thermodynamic,nonequilibrium thermodynamic,and kinetic problems,consisting of nucleation,surface diffusion,step flow,Ehrlich-Schwoebel barrier,edge diffusion,interaction of adatoms,and et.al..Investigations of processes and mechanisms of epitaxial growth have not only enabled the new findings of the traditional and fundamental subjects(Solid-State Physics,Thermodynamic & Statistical Physics,and their interdiscipline subjects),but also promoted the key discoveries and breakthoughs in the fields of Low Dimensional Material Physics,Spintronics,and many other front subjects.However,because the governing equations of epitaxial growth usually deal with the multi-scale,multi-field coupling,and nonlinear problems,one can only obtain the analytical solutions during a few of issues with the simple or simplified models.This limits the promotions and applications of epitaixial growth theories.The phase-field method,based on the Ginzberg-Landau theory of phase transitions,is known as a new multiscale simulation technique in studies of phase transition,dendritic growth,and alloy solidifications.Recently,due to the ability to directly reproduce the nucleation and deposition processes of microsotropic atoms at the complex boundaries,the phase-field method has become useful for describing step motions,exploring equilibrium and nonequilibrium processes,and investigating the submonolayer regime of islands in the field of film growth.In this thesis,we employed and developed the phase field models to perform quantitative simulations of epitaxial film growth under the kinetic effects by introducing the atomic motions of nucleation,Ehrlich-Schwoebel barrier,and attachment/detachment.Our work attempts to explore the intrinsic relations between the simulated paramters and the growth characteristics of epitaxial growth.Our purpose is to establish a new multi-scale simulation technique,in order to precisely reflect the sharp-interface models in the microsotropic scales and accurately predict the characteristics and morphologies of growing surfaces in the macrosotropic scales.Our studies are expected to provide a new idea for the quantitative modulations of expitaxial growth processes and microstural atomic motions by the kinetic parameters.The main conclutions are listed as follows:1.Thin interface analysis was carried out on the quantitative phase field model for epitaxial growth with nucleation and the Ehrlich-Schwoebel effect.Results show that once nucleation is introduced into the phase field model,it can change the equilibrium densities of interfaces to prevent the quantitative descriptions of step motions under the nucleation kinetic effect.Modification must be carried out to get rid of this external interfacial effect.The modified step exhibits the degenerate oscillation mode in step velocity with relatively larger growth rate.Considering the Ehrlich-Schwoebel effect,an irrational step motion arises due to the asymmetric diffusivity,hence modification with respect to the attachment time should be taken into account.Attributed to the modification,both the step velocity and the growth rate have been significantly slowed down with the oscillation well weakened in simulations.Our analysis and modifications explore the quantitative linking between atom motions and step dynamics.2.Different forms of mobility were introduced into a quantitative phase-field model to produce the arbitrary Ehrlich-Schwoebel(ES)effects.Convergence studies were carried out in the one-side step flow model,showing that the original mobility not only induces the ES effect,but also leads to larger numerical instability with increase of the step width.Thus,another modified form of ES barrier is proposed,and is found more suitable for the larger scale simulations.Model applications were carried on the wedding cake structure,coarsening and coalescing of islands and spiral growth.Results show that ES barrier exhibits more significance of kinetic effects at the larger deposition rate by limiting motions of atoms on upper steps,thus leading to aggregations on the top layers,as well as the roughening of growing surfaces.3.Phase-field simulations were carried out by to investigate nucleation regime of submonolayer growth via a quantitative phase-field model with the quantified nucleation term.Results show that the nucleation related coefficient and interfacial kinetics have changed the density of islands and critical sizes to modulate the nucleation regime.The scaling behavior of the island density can be agreed with the classical theory only when effects of modulations have been quantified.We expect to produce the quantitative descriptions of nucleation for submonolayer growth in phase-field models.4.A regularized equation including the modified gradient coefficient was employed to produce the facet hexagonal spiral growth.Results show that the highly anisotropic energy leads to the promotion of spiral growth.The larger rate of deposition enables the shorter spacing for both anisotropic and isotropic spirals.Both the larger values of anisotropic energy and the deposition rate contribute to the lower levels of convergence in the phase-field model with the higher values of simulated errors.For the kinetic effect,the growth dynamics of spirals can be modulated by changing the step spacings and the scaling exponents of spacings with the difffernt values of kinetic coefficients.Furthermore,the highly anisotropic energy leads to the weakened sensitivity of the spiral spacing to the kinetic effect.