Effects of a Tilted Magnetic Field on a Two-Dimensional Electron Gas

Abstract

$n$-type inverted silicon surfaces were studied to examine properties of a two-dimensional electron gas as well as those properties of silicon itself. The effect of a magnetic field tilted up to \ifmmode\pm\else\textpm\fi{}90\ifmmode^\circ\else\textdegree\fi{} from the normal to the (100) Si surfaces was measured between 1.3 and 4.2\ifmmode^\circ\else\textdegree\fi{}K and up to 90 kOe. The electric field associated with the $n$-type inversion layer quantizes the surface electrons and they behave as a two-dimensional electron gas. It was found that the oscillatory magnetoconductance, due to magnetic quantization into Landau levels, depends solely upon the normal component of the magnetic field with respect to the surface. The observed splitting due to spin appears to be determined by the total magnetic field. The parallel component of the magnetic field was found to have a negligible effect on the surface quantization. The cyclotron mass, measured from the temperature dependence of the oscillation amplitude, is equal to the transverse mass of the electron in silicon and is independent of the tilt angle. The spin splitting can be quantitatively identified at certain angles where the Landau splitting is twice that of the spin splitting. The Land\'e $g$ factor determined in this way was found to be substantially larger than 2 and decreases with the increasing surface electron density. The $g$ factor has values between 3.25 and 2.47 for a surface electron density ranging from 1\ifmmode\times\else\texttimes\fi{}${10}^{12}$ to 6\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}2}$.