(317e) Observability Analysis of Effective Medium Model and Its Application in Real-Time Sensing for Chemical Vapor Deposition

Real-time sensing for thin film deposition is important for process monitoring and feedback control. Currently optical sensors such as laser reflectometry and spectroscopic ellipsometry are the most commonly used because they are easy to implement and compatible with CVD processing environment. The typical approach to extract film properties from optical measurements is to assume constant growth rate and optical properties and then fit measurements to an optical sensor model by least squares fitting. This assumption may not be valid for the deposition processes with changing growth rate. Furthermore, due to the coupling between film properties there is a need to systematically address the observability of the sensor model, i.e. what film properties can be estimated and its associated uncertainty.

In this work we studied two optical models that describe light reflection on thin film with rough surface, light scattering model and effective medium model. The comparison between spectral reflectance measurement and model prediction indicated that effective medium model is better than light scattering model to describe roughness effect. Effective medium model is a highly nonlinear and complex model. In order to study the observability of such a model, some simple nonlinear examples were studied first. The results indicated that linearized observability does not guarantee the observability of the original nonlinear system. Due to the existence of local minimal the guess for the initial state is very important to determine whether the observer will converge. A moving horizon estimation technique was used to extract film thickness and surface roughness from the normal reflectance measurement. The deposition experiment was stopped at various times and the film was characterized offline. The estimated film properties were compared with offline characterization to evaluate the performance of the observer.