Prediction Of Epitaxial Growth Process Using Phase Field Method

Computational modeling and simulation of epitaxial growth process is a frontier domain in the field of manufactory science and material science. Phase-field method as a powerful tool is used to describe complex phase transitions in non-equilibrium state. Based on time-dependent Ginzburg-Landau's equation, a phase-field model of pure substances is derived. The governing equations of phase-field and the temperature-field are discretized using the finite difference method, and Neumann boundary conditions are adopted. Corresponding numerical scheme is given and dendritic growth during epitaxial can be displayed by appling suitable post treatment method.In order to overcome the deficiency of explicit integral schemes, we construct a new efficient numerical method, which FFT (Fast Fourier Transform) algorithm is combined with the semi-implicit spectral methods. This method is introduced in numerically solutions of the governing equations of the phase field coupled with temperature field. The numerical results show that with the assurance of the computing accuracy, the semi-implicit spectral method can reduce the dependence on time length and the time step can be increased comparing with the finite difference method.By systematic numerical simulation, dendritic growth in the solidification process is studied and the competitive growth of the secondary arms in the free dendritic growth is realized. The size and shape of initial crystal core and Stefen number and other critical factors are specially studied. The selection of time and space length and so on is also discussed. The results indicate that with the increase of undercooling the dendritic's growing can be accelerated and the interface becomes unstable. In order to ensure the reasonable results, the interface thickness should be smaller, at the same time we must pay attention to the selection of parameters which should be consistent with the material's physical properties.On the above integrity study on the phase field model for dendritic growth, phase field method is applied to numerical study of epitaxial growth. A time-dependent Ginzburge-Landau-Like equation coupled to diffusive transport equation of adatoms is used to describe the motion of the step. Nucleation and growth of step in epitaxy on the three terraces is simulated. The evolution of the trapezoidal steps and the spiral steps in the epitaxial growth is numerically analyzed by this model. The numerical results show that, the method proposed here is able to completely reproduce the tendency of the step growth's evolution, and evolutionary tendency is consistent with the experiment observation. Finally we describe that how to introduce the elastic strain energy into the phase field function and associate the semi-implicit spectral method for the theoretically derived work of related aspects.