Spin-orbit Splitting of Valence Band in Silicon Whiskers under Strain

Silicon whiskers with doping concentration of 2 × 1018 cm– 3 were chosen to investigate magnetoconductance in the range of 0-14 T at cryogenic temperatures under compressive strain up to – 2 × 10– 3 rel. un. The whiskers were doped with boron during the growth process by chemical vapor deposition method, and the concentration of charge carriers, according to Hall studies, was about 2 × 1018 cm– 3. The uniaxial strain of whiskers was carried out by fixing them to the substrates using thermal strain due to the difference between the coefficients of thermal expansion of the crystal and the substrate material. Longitudinal magnetoresistance for unstrained and strained Si whiskers was studied in the temperature range of 4.2 - 70 K. The unstrained whiskers have a quadratic dependence of the magnetoresistance on the magnetic field induction. The strain leads to the appearance of negative magnetoresistance with sufficiently large magnitude (up to 15 %). The possible reasons of the effect were discussed. The most probable reason of negative magnetoresistance appearance is weak localization (WL) of the charge carriers. According to calculations within the WL model, the coherence length Lso and spin-orbit length Lso are proportional to T− 0.53 and T− 0.45, respectively. The latter one is closed to T− 1/2 expected from the theoretical data for a two-dimensional system. This fact is the evidence of the conclusion that conductance in Si whiskers mostly occurs in the subsurface layers of crystals. Strain influence on spin-orbit splitting and the valence band spectrum was studied. As a result, the splitting of light and heavy hole branches was found under compressive strain according to the k-p-method. The spin splitting energy for sub-band of heavy holes ΔSO was found to be 1.8 meV.