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
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