Efficient characterization of symmetrically illuminated symmetric 2-D gratings
US7525672B1 · kind B1 · utility
Assignee
Inventors
Key dates
| Filing date | Dec 16, 2005 |
| Grant date | Apr 28, 2009 |
| Priority date | — |
| Expiry date | Mar 4, 2026 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG01N21/4788
- WIPO fieldMeasurement
- WIPO sectorInstruments
Abstract
Methods and apparatus for optical characterization based on symmetry-reduced 2-D RCWA calculations are provided. The invention is applicable to gratings having a grating reflection symmetry plane. A sample can be illuminated at normal incidence or at a non-zero angle of incidence such that the plane of incidence is parallel to or identical with the symmetry plane. The diffracted field components are either symmetric or anti-symmetric with respect to the grating symmetry plane. This symmetry is exploited to provide a symmetry-reduced 2-D RCWA having reduced matrix dimension (by about a factor of two) that is mathematically equivalent to a conventional 2-D RCWA. For normal incidence on a grating having two reflection symmetry planes, a symmetry-reduced 2-D RCWA having reduced matrix dimension (by about a factor of four) is provided. This normal incidence RCWA can be used to approximately characterize a sample illuminated at non-normal incidence. Approximation accuracy can be improved by modifying either the grating depth or the grating refractive index.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.