화학공학소재연구정보센터
Journal of Materials Science, Vol.30, No.15, 3761-3767, 1995
3-Dimensional Analysis of Modulated Photoreflectance in a Silicon-Wafer
The effects of probe and pumping beam size and modulation frequency on photoreflectance were investigated for a silicon wafer by considering one- and three-dimensional generation and propagation of thermal and plasma waves, PR(1D) and PR(3D). The magnitude of PR(1D) decreased as the inverse square of the effective beam radius and that of PR(3D) was 100 times smaller than PR(1D) at 0.1 mu m effective beam radius and decreased with the effective beam radius. The phase shift of PR(1D) was nearly constant at 225 degrees, whereas that of PR(3D) increased with the effective beam radius from 0 degrees to 225 degrees. The magnitude and phase of PR(3D) become the same as those of PR(1D) by satisfying the equivalence conditions, where the probe and pumping beam radii are larger than the thermal and plasma wavelengths, when the effective beam radius was larger than 112 mu m. PR(1D) decreased with modulation frequency as omega(-1/2), whereas the magnitude of PR(3D) was nearly constant and 100 times smaller than that of PR(1D) at 1 kHz modulation frequency. The PR(1D) phase varied from 180 degrees to 225 degrees, but that of the PR(3D) increased from 0 degrees to that of PR(1D) with increase of the modulation frequency. As the modulation frequency increased, the magnitude and phase of PR(3D) approached to those of PR(1D) by approaching the equivalence conditions, owing to the decrease of the thermal and plasma wavelengths. The good agreements in the modulation frequency dependence of the magnitude and phase of PR(3D) with those measured, justified the three-dimensional analysis of the photoreflectance.