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Anisotropic Effective Mass

In this work, we derive a three-dimensional effective mass that is suitable for treatment of electrons in anisotropic semiconductors. We show that it is possible to define a scalar anisotropic three-dimensional mass that reduces to a one-dimensional definition for isotropic materials. We extend the effective mass definition and apply it to electrons in non-parabolic semiconductors and demonstrate that the effective mass is generally dependent on particle energy. Finally, we show that the proposed definition of the effective mass is compatible with the experimentally measured cyclotron mass in isotropic materials while leading to a more accurate result in anisotropic semiconductors.