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 nonuniformly strained sample taking into account the effects that arise due to finite depth of penetration and diameter of the laser beam. Both the parallel and the focused beams are considered. The case of stress in. Si substrate decaying monotonically with depth z (rapidly near the interface and slowly at larger depths) is considered in detail. The predicted Raman shifts are found to be sensitive to both the distribution of stress and to the absorption coefficient alpha for the laser light wavelength used. It is found that light scattered from distances much larger than 1/alpha still contribute significantly to the observed Raman spectrum. The observed shift in the peak of the spectrum does not correspond to the stress close to the interface. If the stress decays more rapidly than the light intensity, the Raman line that originates from the unstrained lower part of the substrate dominates. For transparent 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 stresses near the interface short wavelength light with an absorption depth of 5-10 nm is recommended. The calculated and observed Raman shifts in a local oxidation of silicon (a processing technique for isolation) with polysilicon buffer between the nitride stripe and the Si substrate are compared. The agreement between the calculated and the observed Raman shifts is very good. The salient points of our approach which enabled us to obtain this agreement are: We took into account the effects of laser beam width, penetration depth, and focusing; we included the stresses in the polysilicon layer and near the polysilicon/silicon interface, and we included contributions from large depths. (C) 1998 American Institute of Physics. [S0021-8979(98)02415-3].