OPTICAL DIFFRACTION AND INVERSE SCATTERING FROM FEATURES ON SILICON WAFERS

THE PURPOSE OF THIS RESEARCH IS TO DEVELOP A CAPABILITY FOR: (1) CALCULATING TWO-DIMENSIONAL OPTICAL DIFFRACTIONS FROM THE EDGES OF DIELECTRIC OR IMPERFECTLY CONDUCTING FEATURES ON LAYERED, SILICON-BASED SUBSTRATES; AND (2) UTILIZING DIFFRACTED TWO-DIMENSIONAL FIELDS IN AN INVERSION ALGORITHM FOR SHAPE RECONSTRUCTION OF LINEAR (LINE-LIKE) FEATURES ON SILICON WAFERS AND CHIPS FOR INTEGRATED CIRCUITS. THE RESEARCH IS FUNDAMENTALLY MATHEMATICAL IN NATURE AND IS DRIVEN BY CRITICAL PROBLEMS IN THE INTEGRATED CIRCUIT INDUSTRY, ALTHOUGH IT IS IMPORTANT TO A WIDER CLASS OF APPLICATIONS. THE RESEARCH OBJECTIVE FOR PHASE I IS: (1) TO IMPLEMENT A NEW THEORY OF VECTOR DIFFRACTION UTILIZING SELF-SIMILARITY AND VECTOR BOUNDARY VALUE PROBLEMS IM COMPLEX VARIABLE THEORY; AND (2) TO BEGIN PRELIMINARY STUDY OF THE INVERSE OPTICAL SCATTERING PROBLEM FOR METROLOGY OF EDGED FEATURES ON SILICON SUBSTRATES, CONSIDERING THE PROS AND CONS OF TIME DOMAIN AND FREQUENCY DOMAIN DATA, AND FEASIBILITY OF DATA ACQUISITION. IF SUCCESSFUL, THESE DIFFRACTION SOLUTIONS AND INVERSION METHODS WILL PROVE TECHNICALLY BENEFICIAL FOR A VARIETY OF APPLIED PROBLEMS. HOWEVER, THEIR GREATEST POTENTIAL MAY EVENTUALLY BE REACHED IN THE INTEGRATED CIRCUIT INDUSTRY IF THEY CAN CONTRIBUTE TO INCREASED YIELD BY MEANS OF AUTOMATEDMETROLOGY.