Abstract: A method and apparatus for determining optical mask corrections for photolithography. A plurality of grating patterns is printed onto a wafer utilizing a photomask having at least one grating. Each grating pattern within the plurality of grating patterns is associated with known photolithographic settings. Each grating pattern is illuminated independently with a light source, so that light is diffracted off each grating pattern. The diffracted light is measured utilizing scatterometry techniques to determine measured diffracted values. The measured diffracted values are compared to values in a library to determine a profile match. A 2-dimensional profile description is assigned to each grating pattern based on the profile match. A database is compiled of the profile descriptions for the plurality of grating patterns. Photomask design rules are then generated by accessing the database containing the 2-dimensional profile descriptions.

Abstract: The diffraction of electromagnetic radiation from periodic grating profiles is determined using rigorous coupled-wave analysis, with intermediate calculations cached to reduce computation time. To implement the calculation, the periodic grating is divided into layers, cross-sections of the ridges of the grating are discretized into rectangular sections, and the permittivity, electric fields and magnetic fields are written as harmonic expansions along the direction of periodicity of the grating. Application of Maxwell's equations to each intermediate layer, i.e., each layer except the atmospheric layer and the substrate layer, provides a matrix wave equation with a wave-vector matrix A coupling the harmonic amplitudes of the electric field to their partial second derivatives in the direction perpendicular to the plane of the grating, where the wave-vector matrix A is a function of intra-layer parameters and incident-radiation parameters.

Abstract: A method of generating a library of simulated-diffraction signals (simulated signals) of a periodic grating includes obtaining a measured-diffraction signal (measured signal). Hypothetical parameters are associated with a hypothetical profile. The hypothetical parameters are varied within a range to generate a set of hypothetical profiles. The range to vary the hypothetical parameters is adjusted based on the measured signal. A set of simulated signals is generated from the set of hypothetical profiles.

Abstract: The diffraction of electromagnetic radiation from periodic grating profiles is determined using rigorous coupled-wave analysis, with intermediate calculations cached to reduce computation time. To implement the calculation, the periodic grating is divided into layers, cross-sections of the ridges of the grating are discretized into rectangular sections, and the permittivity, electric fields and magnetic fields are written as harmonic expansions along the direction of periodicity of the grating. Application of Maxwell's equations to each intermediate layer, i.e., each layer except the atmospheric layer and the substrate layer, provides a matrix wave equation with a wave-vector matrix A coupling the harmonic amplitudes of the electric field to their partial second derivatives in the direction perpendicular to the plane of the grating, where the wave-vector matrix A is a function of intra-layer parameters and incident-radiation parameters.