Abstract

Microcrystal sizes below 100 Å can in principle be easily measured from an analysis of the Raman-Stokes line shape. Richter et al.¹ have shown that the confinement of phonons inside silicon grains of spherical shape leads to downshifting, broadening, and asymmetrization of the Raman line. In their model, phonons with finite wave vectors contribute to the line through an uncertainty principle argument. For the phonon envelope function, Richter selected a Gaussian whose magnitude is one-half at the grain boundary. We have now calculated the Stokes line for various microcrystalline semi-conductors as a function of grain size, assuming different envelope functions, and in particular that predicted by a simple theory. In silicon, we obtain significant departures from the size which can be deduced from Richter’s calculations. This may explain the often observed discrepancy between Raman and TEM results.² In addition, we have calculated the Stokes line for various shapes, including columnar grains. These calculations are compared to measurements that we performed in various microcrystalline films having spherical or columnar grains. Finally, we discuss the influence of surface phonons, intragrain defects, and grain boundary material.

© 1985 Optical Society of America