Numerical techniques for surface diffusion with applications in microfabrication and dealloying

Abstract

Surface diffusion is a mechanism caused by atom migration along the surface driven by chemical potential gradients along the surface, which is especially significant at high temperature and small scale. This mechanism has recently been utilized for microfabrication. For example, surface diffusion has been successfully applied to the MEMS fabrication for achieving large released structures without traditional sacrificial etching or backside etching methods. It has been shown that buried cavities/microchannels can be self-assembled simply by annealing a prestructured silicon wafer at high temperature. This technique also allows monolithic integration of MEMS-CMOS, thus avoiding material- and process-incompatibility issues inherent in traditional integration schemes. The final structures are determined by the initial configurations. For the MEMS fabrication, the locations and sizes of the buried cavities have to be precisely controlled in order to achieve certain functionality, calling for careful design of the initial structures, which after the annealing process produces the desired final structures. Another example of surface diffusion can be found in the coarsening of nanoporous metals. The nano-scale dimensions and large surface-volume ration have provide this kind of structures remarkable functional properties. They have been widely used in various applications such as biocatalyst, supercapacitor, actuation, DNA sensors and so on. The chemical, optical and mechanical properties depend on the ligament sizes, which can be turned by coarsening under annealing. Thus, understanding the evolution of ligament size distribution of nanoporous metals under coarsening is very important. Another important property of nanoporous metals is the self-similarity. Self-similarity can provide a lot of benefits in applications and modelling. For example, the theoretical foundations of some scaling-laws are based on the self-similarity assumption and also in some modelling, we can use the smaller structures in the earlier coarsening stage instead of the larger ones in the late coarsening stage. Thus, investigating whether the coarsening process is self-similar or not is also very important. Since it is expensive to perform experiments, the numerical approach is very important in investigating the phenomena theoretically and providing guidance in the design process. In this thesis, efficient and accurate modelling and design tools are developed for surface diffusion. Morphology change due to coarsening is also investigated. For the modelling of surface diffusion, an improved phase-field method was developed and used to predict the structure evolved from surface diffusion for a given initial configuration. The improved phase-field method eliminates or reduces some adverse artificial effects such as shrinkage, coarsening and false merging that exist in the previous phase-field methods. Results obtained by our proposed improved model match quite well with experimental ones. The design part is the inverse process of the modelling one. Design problems, particularly those with complex constraints, are challenging problems to solve due to their non-uniqueness and the difficulty in incorporating the constraints into the conventional optimization methods, for example, the topological optimization method. In this thesis, we propose a method based on the recently developed machine learning method, Variational Autoencoder (VAE) for solving inverse design problems by utilizing its powerful learning ability. The performance of the method is demonstrated on two examples: inverse design of surface diffusion induced morphology change and inverse mask design for optical micro/nano lithography. To investigate the coarsening process of nanoporous metals, the evolution of three-dimensional two-phase structures using non-conserved and conserved dynamics is studied. Allen-Cahn equation is used to model non-conserved dynamics and Cahn-Hillard equations with constant and degenerate mobility are used to model conserved dynamics caused by bulk diffusion and surface diffusion, respectively. The morphologies of nanoporous structures are characterized by interfacial shape distribution and ligament size distribution. Results show that coarsening of nanoporous structures is self-similar in morphology for all the dynamics when the volume fraction is close to 50%. In addition, morphology observed in experiments is quite similar with that induced by non-conserved dynamics, while it is very different from that induced by conserved dynamics. Two possible reasons may lead to these differences: one is that the initial structures formed by spinodal decomposition are quite different from those by dealloying; the other is that some other effects, except for surface diffusion, may affect the coarsening procedure. Further studies are necessary to fully understand the coarsening mechanism. Keywords: Phase-field method; Cahn-Hilliard; Surface diffusion; Semi-implicit scheme; Spectral method; Artificial neural network; Inverse design; Nanoporous structure; Coarsening.

Date of Award	2018
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology