Numerical Techniques for Surface Diffusion with Applications in Microfabrication and Dealloying

Speaker :
Mr Yujie ZHANG
Department of Mechanical and Aerospace Engineering, HKUST
Date : 24 Aug 2018 (Fri)
Time : 4:00 pm
Venue : Room 2548, HKUST (2/F., Lift #27/28)


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-COMS, 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.  Morphology change by surface diffusion also finds its application in structural evolution of nanoporous metals during thermal coarsening. It affects material properties and performance and thus should be controlled if possible. 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, the phase-field model is chosen over the level-set based method and front-tracking method due to the conservation nature and its ability in handling complex topological changes naturally. In this thesis, 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. The desired final structures are to be achieved and the initial structures should be carefully designed. 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. We utilize the learning capability of the VAE to learn the constraints by providing training data that satisfies the constraints, and use the generative capability of the VAE to generate new design candidates that automatically satisfy all the constraints. In addition, we show that the VAE network is also capable of learning the underlying physics of the design problem, leading to an efficient design method that does not need any physical simulation once the network is constructed. 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.

For the coarsening of nanoporous structures, in the literature, some numerical simulations have been done using non-conserved dynamics and bulk-diffusion dominated conserved dynamics. However, the obtained morphology for the conserved dynamics is quite different from that obtained by experimental coarsening of np-Au. To explain this difference, further numerical investigation is necessary. In this thesis, the evolution of three-dimensional two-phase structures using non-conserved and conserved dynamics is studied. Allen-Cahn (AC) equation is used to model non-conserved dynamics. Cahn-Hillard (CH) 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 both non-conserved dynamics and conserved dynamics when the volume fraction is close to 50%. In addition, morphology induced by non-conserved dynamics is quite different from that by conserved dynamics, while morphology induced by conserved dynamics with constant and degenerate mobility is similar with each other, which is quite different from the observed experimental results for dealloying. 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.

(Supervisor: Prof. Wenjing Ye)