Magnetoresistance Effect in Cubic Semiconductors with Spheroidal Energy Surfaces

The collision frequency of electrons having a spheroidal energy surface with acoustical modes of vibration is calculated without neglecting phonon energy. Using an asymptotic form in which the collision frequency is proportional to the square root of their energy, the electronic current in a semiconductor in combined magnetic and weak electric fields can be calculated in a closed form by the formal theory of conductivity. The magnetoresistance effect in oriented single crystals of $n$- and $p$-type germanium observed by Pearson and Suhl may be discussed consistently at least semiquantitatively with this calculation in both weak and strong magnetic fields.