Symmetry analysis and uniaxial-stress effect on the low-field electroreflectance of Si from 3.0 to 4.0 eV

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Abstract
The low-field electroreflectance (ER) spectra of Si in the energy range from 3.0 to 4.0 eV have been measured and analyzed in the absence and in the presence of strain. In the absence of strain, the symmetry location K→0 of a critical point can be deduced from both the polarization anisotropies and the line shape of a low-field ER spectrum. Uniaxial-stress effects on a low-field ER spectrum are also described in the low-strain limit. These results are used to reveal the 3.4-eV complexities. The structures of the low-field ER spectrum of Si from 3.0 to 4.0 eV may arise from two critical points with different symmetries. First, the main structure in the higher-energy side is attributed conclusively to a high-symmetry critical point along the Λ axis (or at the L point) in the Brillouin zone [Λ3v→Λ1c (or L3′v→L1c) in Si]. The experimentally determined band-edge parameters are as follows: the critical-point energy Eg=3.412±0.005 eV (300 K); the phenomenological broadening energy Γ=0.060±0.005 eV (300 K); and the pair band deformation-potential parameters D11=−9.8±1.3 eV, D15=6.5±1.4 eV, D33=4.7±0.5 eV, and D35=3.0±1.7 eV (77 K). In addition, this critical point is three-dimensional M1 type and the relations between the assumed reduced masses μT and μL are μT≪|μL|, μT>0, and μL<0. From the mass relation, μT≪|μL|, the critical point may be nearly two-dimensional (M0 type). Second, for the weak structure in the lower-energy side the experimental results under uniaxial stress can not be explained by any high-symmetry critical point except the degenerate critical point in the Δ direction (Δ5v→Δ1c near Γ in Si). If we assume that this structure is attributed to the Δ critical point, the experimentally determined parameters are as follows: