Numerical Simulation Study On The Dynamics Of Material Growth

In the process of material growth, the surfaces and interfaces can exhibit kinetic roughening phenomena, which will, to a great extent, affect the properties of the material. It is shown that the interfaces of material usually have self-affine structure and can be treated by scaling theory. From the point of microcosmic numerical simulation, the dynamic scaling behavior of the interfaces in material growth are investigated theoretically in this thesis, the main work are as follows:Firstly, in order to study the microcosmic mechanisms of roughness interfaces exhibiting the anomalous scaling behavior and test the local slope theory, the 1+1-dimensional Das Sarma-Tamborenea (DT) model and the 1+1-dimensional Wolf-Villain (WV) model, which describe the growth of molecular beam epitaxy, are simulated on large length and long time scale. The results show that the 1+1-dimensional DT model exhibits intrinsic anomalous dynamic scaling behavior, and the conclusion here confirms the analytical result of the local slope equation based on scaling analysis. However, the 1+1-dimensional WV model still shows intrinsic anomalous dynamic scaling behavior in the time and length simulation range of this thesis, which in fact is inconsistent with the analytical result of the local slope equation based on dynamic renormalization-group analysis.Secondly, the influences of the Step-edge Diffusion (SED) effect on the mound morphology of the 2+1-dimensional WV model are discussed. By means of using the noise reduction technique, the SED effect is enhanced effectively. The results show that the SED is indeed the mechanism leading to the mound pattern of the 2+1-dimensional WV model. The dynamic scaling exponents obtained from the surface width depend on the strength of the SED, while the exponent describing the average mound separation is independent on the strength of the SED and seems to be universal. By using the quantity of the average mound separation, the dynamic behavior of the mound on the 2+1-dimensional WV surface can be successfully described in the framework of Family-Vicsek scaling.Finally, the growth of the Family model and the Etching model on the fractal substrates are studied by means of numerical simulations so as to investigate the influence on the dynamic behavior of material growth interfaces by changing the structure of the substrates. It is shown that the structure of the substrates can affect the dynamic scaling properties of the surfaces and interfaces. Although the standard Family-Vicsek scaling is still valid in describing the scaling behavior of the growth on fractal substrates, the original continuum equations are invalid. Considering the lateral growth behavior affected by the change of the substrates, the generalized KPZ equation is proposed to describe the Etching growth on fractal substrates. The results of the generalized KPZ equation based on the scaling analysis agree well with the simulation results.The investigation of this thesis provide a deeper understanding about the microcosmic mechanisms of material growth interfaces exhibiting kinetic roughening, which is of important for improving the material qualities.