Magnetoresistance in Heavily Dopedn-Type Silicon

Abstract

The magnetoresistance effect has been investigated in $n$-type silicon at 4.2, 77, and 300\ifmmode^\circ\else\textdegree\fi{}K. At 77 and 300\ifmmode^\circ\else\textdegree\fi{}K, the low-field magnetoresistance coefficients have been evaluated in the impurity concentration range from approximately 1\ifmmode\times\else\texttimes\fi{}${10}^{15}$ to 1\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. At 300\ifmmode^\circ\else\textdegree\fi{}K, the symmetry relation among the coefficients found in pure silicon is obeyed at all impurity concentrations, while at 77\ifmmode^\circ\else\textdegree\fi{}K, the symmetry relation is fulfilled only up to impurity concentrations of 1\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The mobility anisotropy has been evaluated from the low-field coefficients in the impurity concentration ranges where the symmetry relation is obeyed. At 4.2\ifmmode^\circ\else\textdegree\fi{}K, the magnetoresistance effect is negative and tends toward saturation with increasing magnetic field strength for impurity concentrations greater than 5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Below this concentration, a large positive magnetoresistance is observed and the change in sign is correlated with the appearance of an impurity ionization energy.