The Cramer-Rao bound and adaptive estimation with applications to IC lithography

There are many situations where a finite number of parameters are estimated from an input waveform. Some examples are position estimation in radar and sonar, and lithographic alignment in integrate circuit (IC) fabrication. All of these examples involve position and/or amplitude estimation of a single pulse or a series of overlapping pulses. In this thesis lower bounds on the estimation error of amplitude and position are derived and algorithms are developed for position estimation in lithographic alignment.; The first part of this thesis concentrates on the use of the Cramer-Rao Bound (CRB) in pulse position and amplitude estimation. The CRB is a lower bound on the estimation error of a parameter that is independent of the algorithm used to estimate the parameter. A new description of the CRB is given in terms of the projection of a single vector onto a subspace formed by a set of other vectors. Simple intuitive approximations to the CRB in pulse position and amplitude estimation are derived. The effect on a given parameter of the pulse shape and the other unknown amplitudes and positions is clearly seen so that pulse shape optimization to minimize the effect of overlapping pulses is then possible. The CRB is also derived for edge position estimation and the effect of a finite observation window on the CRB is examined.; The second part of this thesis is concerned with the problem of alignment in IC fabrication. As the minimum feature size of ICs decreases there is a decrease in the maximum alignment error that can occur before circuit malfunction. Therefore more accurate alignment algorithms are required. However, lithography systems are becoming more expensive and high throughput is required from the alignment system. The algorithms described in this thesis have both high accuracy and high throughput. An adaptive alignment algorithm is described and shown to be robust and of low computational complexity. A multi-step approach to alignment is also presented that can reduce the computational complexity of a given alignment algorithm without degrading the alignment accuracy.