Real-time monitoring and growth control of Si-gradient-index structures by multiwavelength ellipsometry

Real-time monitoring and control of the growth of plasma-deposited gradient-index structures by multiwavelength phase-modulated ellipsometry are presented. An efficient method for estimating the optical parameters based on a least-squares fitting on the most recent recorded measurements is described. This method is used for real-time monitoring of the outerlayer refractive index and rate of deposition during deposition of inhomogeneous transparent films. An accurate integral expansion of the reflection coefficient, giving a continuous optical model describing inhomogeneous films, is used in the real-time modeling of the deposited structure. A variety of increasing complexities of the optical model is studied within inversion algorithms. Furthermore several ways of defining the optical parameters to be estimated are discussed. Inversion of simulated growth trajectories by using the described algorithms show what kind of information is available from the various approximations and in what conditions they are useful. Since real-time measurements during growth involves statistical noise and systematic errors, it becomes necessary to stabilize the fit. Various stabilizing functionals are discussed and implemented to solve this problem. Several plasma-deposited silicon oxynitride gradient-index structures where both rate of deposition and the refractive index are varied continuously are inverted in real time. As an example of application, a successful real-time control of the growth of a linear gradient index is demonstrated by using inversion algorithms. Inversion algorithms are extremely fast, with calculation times from less than a second (for the lowest-order approximation) to approximately 3 s.