Modeling electrodeposition in LIGA micro-fabrication using an arbitrary Lagrangian-Eulerian formulation for moving-boundary tracking with repeated re-meshing

摘要

Electrodeposition is a key process in LIGA (Lithographic, Galvanoformung, Abformung - German words for lithography, electroplating and molding) microfabrication, which is increasingly demonstrated to be a viable technology for fabricating micro-devices or parts. LIGA Electrodeposition involves complex multi-physics phenomena: 1) diffusion, migration, and convection of charged species in a centimeter-scale electrolyte-bath region and in micron-scale feature-cavity or trench regions; 2) homogeneous and heterogeneous electrochemical reactions; and 3) moving deposition surface or surfaces on which metal ions (e.g., Ni~(2+)) are electrochemically reduced to form a pure metal or an alloy. In this paper we report efforts toward developing a predictive multidimensional computer model for simulating electrodeposition in LIGA microfabrication. A Poisson equation that explicitly describes electrolyte potential is derived by combining the species mass conservation equations and the electroneutrality constraint. Mesh-motion equations that employ an arbitrary Lagrangian-Eulerian formulation, and species-mass, charge and momentum conservation equations are solved using GOMA in parallel computations. GOMA is a multi-physics multi-dimensional finite-element computer code developed and being enhanced at Sandia National Laboratories. In the present work, homogeneous reactions are taken to be infinitely fast whereas metal-ion reduction reaction on the deposition surface is assumed to obey Butler-Volmer kinetics. Sample results are presented for electrolyte potential, species concentrations, flow field, and positions of the deposition surface for nickel electrodeposition in a two-dimensional trench. To handle the dramatic reduction of trench domains, re-meshing is repeatedly performed using a Sandia-developed mesh-generation toolkit, CUBIT, and re-mapping is done with Sandia's utility program, MAPVAR.