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Applied Optics

Applied Optics


  • Vol. 27, Iss. 3 — Feb. 1, 1988
  • pp: 500–504

Model for gradient formation in polycrystalline germanium–silicon alloy GRIN crystals via Czochralski crystal growing

Joseph J. Miceli, Jr. and Denis P. Naughton  »View Author Affiliations

Applied Optics, Vol. 27, Issue 3, pp. 500-504 (1988)

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A mathematical model has been developed which describes the silicon composition gradient produced in germanium–silicon alloy GRIN crystals formed via Czochralski crystal growing. This model is based on the naturally occurring segregation effect of silicon in germanium. The refractive index of the alloy is described in terms of its relation to the band gap energy, which is itself dependent on the silicon composition. A relationship between refractive index and silicon composition of the alloy is derived.

© 1988 Optical Society of America

Original Manuscript: June 17, 1987
Published: February 1, 1988

Joseph J. Miceli and Denis P. Naughton, "Model for gradient formation in polycrystalline germanium–silicon alloy GRIN crystals via Czochralski crystal growing," Appl. Opt. 27, 500-504 (1988)

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  1. J. Czochralski, “Measuring the Velocity of Crystallization of Metals,” Z. Phys. Chem. 92, 219 (1918).
  2. J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Ph.D. Thesis, U. Rochester (1982).
  3. D. P. Naughton, “Fabrication and Testing of Infrared Gradient Index Materials,” M. S. Thesis, U. Rochester (1986).
  4. E. R. Johnson, S. M. Christian, “Some Properties of Germanium-Silicon Alloys,” Phys. Rev. 95, 560 (1954). [CrossRef]
  5. J. J. Miceli, Ref. 2, p. 34.

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