Phenomenological modeling of the optical properties of semiconductors for process characterization and control.

Optical reflection measurement techniques such as ellipsometry and reflectometry are commonly used to determine thicknesses of layers deposited or etched during semiconductor wafer processing. In order for these methods to be effective, accurate optical properties of the materials need to be known a priori or must be modeled. In many cases the optical properties are highly dependent on the processing conditions, and so they can vary from wafer to wafer or lot to lot. In this work, a model for the dielectric function of semiconductors is presented and demonstrated. The model assumes that interband optical transitions are dominated by transitions at critical points in the bandstructure, and then uses the constants from the theoretical equations as free parameters to fit the theoretical model to experimental data. The model is used to fit the dielectric function data for InGaAsP semiconductors (lattice-matched to InP), GaAs at room temperature and at higher temperatures, and InAlAs nearly lattice-matched to InP. The difference between the modeled values and the data are typically less than 0.5% for every data point. Critical point energies can be found to within.01 eV by this model, are in good agreement with other published reports. The model is then modified, and composition- and temperature-dependent models for the dielectric function are generated. The accuracy of these models are then tested. The composition of a sample can be determined to within 1%, and temperatures can be found to within 2.3$\sp\circ$C, which is within the accuracy of the original data (3$\sp\circ$C). Once models for the dielectric function are established, they may be used for the original problem of extracting the thickness of a layer from the measured data. Applications for analysis of materials before and after plasma etch processes using reflectometry will be demonstrated. In addition, aIl algorithm for using reflectometry in situ for etch endpoint detection will be presented. The endpoint algorithm stops the etch of polysilicon on silicon dioxide with 36 A overetch into the oxide, with a standard deviation of 8.74 A.PhDApplied SciencesCondensed matter physicsElectrical engineeringPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130023/2/9711996.pd