A gallery of seed profiles is constructed and the initial parameter values
associated with the profiles are selected using manufacturing process
knowledge of semiconductor devices. Manufacturing process knowledge may
also be used to select the best seed profile and the best set of initial
parameter values as the starting point of an optimization process whereby
data associated with parameter values of the profile predicted by a model
is compared to measured data in order to arrive at values of the
parameters. Film layers over or under the periodic structure may also be
taken into account. Different radiation parameters such as the
reflectivities R.sub.s, R.sub.p and ellipsometric parameters may be used
in measuring the diffracting structures and the associated films. Some of
the radiation parameters may be more sensitive to a change in the
parameter value of the profile or of the films then other radiation
parameters. One or more radiation parameters that are more sensitive to
such changes may be selected in the above-described optimization process
to arrive at a more accurate measurement. The above-described techniques
may be supplied to a track/stepper and etcher to control the lithographic
and etching processes in order to compensate for any errors in the
profile parameters.