Effective mass

As an electron moves through a crystal it will undergo Coulomb scattering with other electrons and atomic nuclei. In free space, a force applied on an electron can be related to it's acceleration using Newton's 2nd Law, however due to coulomb scattering, the applied force is not the only force. The effective mass is the mass required for the electron to have an acceleration a with applied force F. It is calculated using h_bar^2/(d^2E/dk^2)