Galvanomagnetic Effect for Holes and the Valence Band in (001) Silicon on Sapphire

Magnetoresistance (MR) anisotropy measurement previously performed at room temperature for 1–2 µm thick p-type (001) silicon on sapphire (SOS) has been extended down to 77 K. In order to explain these anisotropies, the valence band structure is numerically calculated by the k·p method along with deformation-potential-constant formalism assuming the lateral compressive strain (∼4 ×10 -3 ) in silicon. In the four <110 > directions for the upper strain-split m J =±3/2 band, the derivative (d E /d k 2 ) becomes very small at hole energies above ∼10 meV, resulting in a tetragonally-warped, constant-energy surface with four long <110 > protrusions, which may be responsible for room-temperature “four <110 >-ellipsoid-like” MR anisotropies. Although low-temperature MR anisotropies cannot be explained in terms of the low-energy ellipsoid, the high hole mobility which exceeds the electron one (A. C. Ipri: Appl. Phys. Lett. 22 (1973) 76) may be due to rapid decrease of hole effective mass to the ellipsoidal one.