Numerical ellipsometry: Real-time solutions using mapping onto the complex index plane

While in situ ellipsometry measurements can be made on growing films, real-time solutions for thickness and optical properties remain challenging. Numerical techniques are necessary because for practical material systems, the equations are not generally invertible. In the absorbing film on a known substrate problem, the typical real number unknowns (film n(1), k(1), and d) outnumber the real parameters (psi and Delta) obtained in a single measurement. Although it is known that two intersecting sets of n(1), k(1), and d values are established from two measurements, in the past these sets have not been well understood. The work here is a thorough investigation of such curves and explores all theoretically possible intersections for metals depositing onto an oxide substrate. Mathematical and material considerations identify the solution intersection in a few milliseconds for real-time monitoring and control. (C) 1996 American Vacuum Society.