Analytical, first-order model of light scattering from submicron pyramidal pits

Michael Jordan, Rodolfo Diaz, E. Dan Hirleman

Research output: Contribution to journalArticlepeer-review


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, which neglects edge effects due to surface current accumulation at the periphery. Measurements and the model show that (using the prescribed optics configuration) a characteristic peak occurs between 20 and 45 degrees in the forward scatter region that increases in magnitude and moves forward with increasing pit size. Wafer inspection system designers can use this kind of information to improve their instruments' ability to distinguish between surface contaminants and COPs and to correctly gauge the size of COPs. Further work is underway to improve the fit between the model and the data and to extend its range of applicability.

Original languageEnglish (US)
Pages (from-to)138-146
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2001


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

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Analytical, first-order model of light scattering from submicron pyramidal pits'. Together they form a unique fingerprint.

Cite this