| Jack Judy and Paulo Motto have developed a modified electrodeposition process to fabricate very small metal structures on a substrate. Layers of metal of various shapes are placed on the substrate, then the substrate is placed in an electroplating solution. Some of the metal layers have power applied to them, while the rest of the metal layers are not connected to the power initially. Metal ions in the plating solution start plating the powered layers and a surface grows from the powered layers. As the surface grows, it may touch one of the metal layers that was not initially powered. This causes the initially unpowered metal layer to become powered, and it will start growing with the rest of the surface. The metal layers on the substrate are known as seed layer patterns, and different seed layer patterns can grow different shapes. In this paper, we model and simulate the growth of a surface from a seed layer pattern. A simple model of uniform growth in the direction normal to the surface is made, and the level set method is used to simulate the growth computationally in 2D and 3D. An inverse problem, which is to determine a seed layer pattern that would produce a given surface shape, is also addressed in 2D and 3D. Some given surface shapes may not be attainable by any seed layer pattern, and some conditions for attainable shapes are given. |
