Symmetry analysis of theE2structures in Si by low-field electroreflectance

Abstract

The precise analysis of the $E_2$ transitions in Si is described. From the line-shape analysis using the low-field resonant function, we show that the $E_2$ structures consist of three critical points, $E_2\mathrm{}\left(1\right)\mathrm{}$, $E_2\mathrm{}\left(2\right)\mathrm{}$, and $E_2\mathrm{}\left(3\right)\mathrm{}$, of type $M_1$, $M_1$, and $M_2$, respectively. The symmetry (and the reduced-mass relation) of the critical points are determined from the polarization anisotropies and the line shapes of low-field electroreflectance spectra: The $E_2\mathrm{}\left(1\right)\mathrm{}$ critical point is assigned conclusively to the ${\Sigma }_2^{\nu }\to {\Sigma }_3^c$ transition ($\frac{1}{{\mu }_{T2\mathrm{}}}+\frac{1}{{\mu }_L}=\frac{4}{{\mu }_{T1\mathrm{}}}$, ${\mu }_{T1\mathrm{}}>0\mathrm{}$, and ${\mu }_{T2\mathrm{}}{\mu }_L<0\mathrm{}$) and the $E_2\mathrm{}\left(3\right)\mathrm{}$ critical point is probably to the ${\Delta }_5^{\nu }\to {\Delta }_1^c$ transition near the $X$ point (${\mu }_L\ll \left|{\mu }_T\right|$, ${\mu }_T<0\mathrm{}$, ${\mu }_L>0\mathrm{}$).