Magnetoresistance in a Multivalley Model with〈110〉-Ellipsoids of General Shape

Expressions are derived for the three weak-field magnetoresistance coefficients, $b$, $c$, and $d$, using a multivalley model having ellipsoids of general shape along the $〈110〉$ directions in $k$ space. The results are given in terms of statistical and scattering integrals and of the two mass ratios $K$ and $L$ needed to specify the relative values of the three effective-mass components characterizing the ellipsoids. The properties of $b$, $c$, and $d$ as functions of $K$ and $L$ are discussed, including in particular the fact that the symmetry conditions which are appropriate for each of the three ellipsoid-of-revolution models are satisfied along certain lines in the $K-L$ plane.