Transverse magnetoresistance of nondegenerate semiconductors in strong magnetic fields

The transverse magnetoresistance has been calculated for a nondegenerate semiconductor throughout the high-field region. The calculation has been performed taking into account the inelasticities in the electron-phonon scattering due to the finite energy of the phonons involved. The results are in agreement with previous calculations for the classical and quantum limits. However, our results are also valid in the intermediate region $\hslash {\omega }_c\sim k T$. Our results indicate that the classical limit is realized for $\frac{\hslash {\omega }_c}{k T}\le \frac{1}{4}$ while the quantum limit is obtained for $\frac{\hslash {\omega }_c}{k T}\ge 4$. We expect that these values are also valid for other scattering mechanisms.