A study on R-m -> R-1 maps: Application to a 0.16-mu m via etch process endpoint

We introduce several endpoint algorithms that map real-time, in situ process signals to a via etch process endpoint, Some of the mathematical techniques include: Andrews plots (Fourier series), Chebyshev polynomials, Legendre polynomials, wavelets, singular value decomposition, and neural networks. We show that many of the techniques work to varying degrees of success for a via etch process on 0.16-mum technology. Based on our observations from many lots of manufacturing wafers and experiments with all the endpoint methods, we believe the Chebyshev polynomial area-time curves perform the best, but this statement should be taken with a caveat. It is really best to empirically test the various methods for a given etch process to deduce the endpoint algorithm for that application.