Saturation Magnetoresistance and Impurity Scattering Anisotropy in n -Type Silicon

In the classical strong-field region the magnetoresistance of semiconductors is expected to saturate. If one investigates the dependence of the saturation magnetoresistance upon impurity concentration, i.e., upon the strength of ionized-impurity scattering, quantitative conclusions may be drawn concerning the anisotropy of the relaxation time for such scattering. The strong-field longitudinal magnetoresistance and carrier mobility of phosphorus-doped silicon have been studied in dc magnetic fields to 90 kG at 78^∘{}K. Measurements were made on a series of [111]-oriented samples covering the doping range 2×{}10¹³-6×{}10¹⁶ phosphorus atoms /cm³. A quantitative analysis has been made involving Maxwellian averages over carrier energy and relaxation times that combine the impurity, intravalley, and intervalley scattering mechanisms. The strength of the impurity scattering in each sample was taken to be μLμ where μL is the known lattice scattering mobility and μ is the conductivity mobility determined from the measured value of R_∞ρ, the ratio of the strong field Hall coefficient to the resistivity. The data agree very well with the theory of Samoilovich, Korenblit, and Dakhovskii (SKD). In the more heavily doped samples, above 10¹⁶ phosphorus atoms/cm³, the effects of neutral impurity scattering are observed.