Computer Simulation of the Control of Electroplating

本文采用计算机模拟的方法研究了金属表面沉积薄膜的表面结构、薄膜内部缺陷的形成和表面生长的控制。作为溶液生长的模型，我们扩展了一个基本的固体对固体（SOS）模型，使薄膜在生长过程中产生空位，并对二维方形晶格进行了蒙特卡罗模拟。得到了以下结果：随着化学势（电沉积中的过电位）的增大，表面由层状结构变为粗糙结构，缺陷密度增大。当过电位较大时，表面到处都有形核，表面结构较细。这些结果与实验结果相符。当薄膜表面呈层状结构时，会出现点缺陷（单空位）。当表面变得粗糙时，会形成较大的空洞和点缺陷。当表面的空心部分被沉积的原子填满时，就会产生空缺。表面生长的历史反映在孔隙结构中。当表面有过孔时，就会产生空洞，并沿生长方向排列。这将在薄膜上产生针孔，导致耐腐蚀性下降。当初始表面有沟槽时，也会形成空洞，这与实验中的互连铜沉积相对应。并对热处理过程进行了模拟。温度高时，表面扩散增强，表面粗糙度降低。我们还研究了两种液体的混合（混沌混合），并采用重要采样方法开发了高效的蒙特卡罗模拟算法。

In this work, the surface structure of thin film deposited on a metal surface, the formation of defects within the film and the control of the surface growth have been studied using computer simulation methods. As a model of solution growth, we extended a basic Solid-on-Solid (SOS) model so that vacancies are created in the film during the growth and performed Monte Carlo simulations for a two-dimensional square lattice. Following results are obtained.1. The surface changes from a layer structure to a rough structure and the density of defects increases as the chemical potential (overpotential in electrodeposition) becomes large. For large overpotential, the nucleation occurs everywhere on the surface and the surface has a fine structure. These results correspond to experimental findings.2. Point defects (single vacancies) appear in the film when the surface has a layer structure. When the surface becomes rough, large voids are formed as well as point defects. The vacancies are created when hollow parts of the surface are filled with deposited atoms. The history of the surface growth is reflected in the void structure.3. When the surface has vias, voids are created and aligned in the direction of the growth. This will produce a pinhole in the film, resulting in the decrease in the corrosion resistance. Voids are also formed when the initial surface has trenches, corresponding to experimental copper deposition for interconnects.4. The simulations of heat treatment are also performed. The surface diffusion is enhanced when the temperature is high, and the roughness of the surface decreases.We also studied the mixing of two liquids (chaos mixing), and developed efficient Monte Carlo simulation algorithm by applying an importance sampling method.