Semi-empirical model of light scattering from submicron pyramidal pits

Michael Jordan, Rodolfo Diaz, E. Dan Hirleman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Silicon wafers that are fabricated by the Czochralski technique contain pyramidal pits, which are referred to in more general terms as crystal-originated particles (COPs). Because wafer inspection systems now benefit from the predictability of scattering from particles of known size, shape, and composition, it is of interest to achieve the same level of predictability for surface breaking defects such as pits. A model, valid for s-polarization and a high incidence angle, is based on the Fraunhoffer approximation for the diffraction from a square aperture, and is enhanced by an empirically derived term that accounts for the scatter component attributed to facets. Measurements and the model show that (using the prescribed optics configuration) a characteristic peak occurs between 20 and 45 deg in the forward scatter region, which increases in magnitude and moves forward with increasing pit size. This kind of information can be used to improve an instrument’s ability to distinguish between surface particles and COPs by strategically positioning detectors accordingly. Furthermore, the model can be used as a check against numerical models that are designed to predict scatter from pyramidal pits that are of size equal to a wavelength or much smaller.

Original languageEnglish (US)
Pages (from-to)518-528
Number of pages11
JournalOptical Engineering
Issue number2
StatePublished - Feb 2002


  • Aperture
  • Crystal
  • Diffraction
  • Inspection
  • Optics
  • Particles
  • Pits

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • General Engineering


Dive into the research topics of 'Semi-empirical model of light scattering from submicron pyramidal pits'. Together they form a unique fingerprint.

Cite this