Nonlinear estimation with applications to in situ etch rate and film thickness measurements in reactive ion etching.

Abstract

Optical measurements, such as reflectometry and ellipsometry, are routinely used ex-situ to obtain measurements of the thickness and composition of thin films in microelectronics manufacturing. Recently there has been an effort to incorporate optical sensors onto processing platforms to obtain real-time in-situ measurements. The extraction of parameters from raw data becomes more challenging in this case, as the sensor observes a wafer surface which is dynamically changing during the etching process, and because of the need for real time data. Our investigations were in two parts. In the first part, the in-situ optical metrology problem was considered in detail, concentrating on reflectometry. We formulated the in-situ reflectometry problem as a nonlinear estimation problem, and we used extended Kalman filtering as an approximate solution. Several of the important features of the reflectometry nonlinear estimation problem, such as observability and model uncertainty, are discussed, as well as some methods for solving these problems. One of the interesting aspects of in-situ reflectometry was the possibility of drifting sensor gains due to clouding of the windows which gave access to the sample. This motivated the second part of this thesis, in which we were concerned with state estimation of a nominally linear system with time varying sensor gains. We formulated the problem of estimation in the face drifting sensor gains as a deterministic least squares problem, and developed several recursive algorithms which give approximate solutions as well as sufficient conditions for local exponential stability of the estimation errors.