Simulation of multiple etch fronts

We developed a series of algorithms, based on the string model, that simulate the inhomogeneous etching process of polymeric materials, which exhibit swelling during dissolution by an organic solvent, used in IC process fabrication. The swelling creates a gel layer between the solid (polymer) and the liquid (solvent) phases. Usually, simulations based on the string development model assume an abrupt solid-liquid interface. Our algorithms are capable of simulating two interrelated etch fronts, and may easily be extended to simulate n interrelated etch fronts. The speed with which the points of the gel-solid boundary advance depends on the distance of each point from the gel-liquid boundary. Considering the two boundaries as plane curves, one must deal with the problem of what we define as the “distance” of every point of the first curve from the second. The algorithm developed can deal with any pair of non-intersecting curves in two dimensions. Two pairs of curves were used to test the algorithm: the first with curves of a simple form, and the second with curves of a complicated form. Next we simulated the development process of an e-beam resist that exhibits swelling. The results were perfect for the minimum distance subalgorithm, and they predicted a longer development time for the e-beam resist compared with that required for a non-swelling resist.