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 n1, k1, and d) outnumber the real parameters (Ψ and Δ) obtained in a single measurement. Although it is known that two intersecting sets of n1, k1, 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.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 n1, k1, and d) outnumber the real parameters (Ψ and Δ) obtained in a single measurement. Although it is known that two intersecting sets of n1, k1, 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.