A METHOD TO INTERPRET MICRO-RAMAN EXPERIMENTS MADE TO MEASURE NONUNIFORM STRESSES - APPLICATION TO LOCAL OXIDATION OF SILICON STRUCTURES

A method is described to calculate the Raman spectrum from a nonunifor mly strained sample taking into account the effects that arise due to finite depth of penetration and diameter of the laser beam. Both the p arallel and the focused beams are considered. The case of stress in. S i substrate decaying monotonically with depth z (rapidly near the inte rface and slowly at larger depths) is considered in detail. The predic ted Raman shifts are found to be sensitive to both the distribution of stress and to the absorption coefficient alpha for the laser light wa velength used. It is found that light scattered from distances much la rger than 1/alpha still contribute significantly to the observed Raman spectrum. The observed shift in the peak of the spectrum does not cor respond to the stress close to the interface. If the stress decays mor e rapidly than the light intensity, the Raman line that originates fro m the unstrained lower part of the substrate dominates. For transparen t material (alpha=0) and unfocused beam the Raman spectrum consists of only the unstrained Si line; the contribution to Raman line from the strained interface region is completely masked. For measurements of st resses near the interface short wavelength light with an absorption de pth of 5-10 nm is recommended. The calculated and observed Raman shift s in a local oxidation of silicon (a processing technique for isolatio n) with polysilicon buffer between the nitride stripe and the Si subst rate are compared. The agreement between the calculated and the observ ed Raman shifts is very good. The salient points of our approach which enabled us to obtain this agreement are: We took into account the eff ects of laser beam width, penetration depth, and focusing; we included the stresses in the polysilicon layer and near the polysilicon/silico n interface, and we included contributions from large depths. (C) 1998 American Institute of Physics. [S0021-8979(98)02415-3].