Infrared Studies of Birefringence in Silicon

Abstract

Permanent and elastic strains in silicon crystals grown by the Czochralski technique have been studied by observing the crystal birefringence. These studies reveal that the presence of birefringence is related to (a) plastic deformation caused by severe thermal gradients which produce forces exceeding the crystal yield force and (b) work damage or externally applied forces. The first source of birefringence has been termed permanent strain since this appears in the crystal as grown and the birefringence pattern cannot be altered by changes in sample geometry. This characteristic is typical of a ``frozen‐in'' strain. A strain‐free sample may also be made birefringent, however, by a work damage such as surface abrasion or sand blasting. Such a birefringent pattern can be altered if the sample geometry is changed. This characteristic, of course, is typical of elastic strain. Studies made of samples both parallel and perpendicular to the direction of crystal growth revealed birefringence patterns similar to those of naturally anisotropic crystals such as calcite. The patterns indicate the formation of a pseudo‐optic axis in silicon coincident with the growth direction and is caused by the uneven temperature distribution which results in perdominantly uniaxial stress. Regions of tension and compression have been discovered and their respective magnitudes determined. The calculation of the ``frozen‐in'' tension and compression stresses are based upon experimental determination of the stress‐optic coefficient of silicon. Satisfactory agreement was obtained between frozen‐in stress calculations and measurements of yield stress at elevated temperatures.