Effective Mass

• The electrons' "wave-particle" motion in a lattice is not the same as that for a free electron, because of the interaction with the periodic potential of the lattice.
• To still be able to treat these particles as "free", the rest mass has to be altered to take into account the influence of the lattice.
• The calculation of effective mass takes into account the shape of the energy bands in three-dimensional (3D) k-space, taking appropriate averages over the various energy bands.
• The effective mass of an electron in a band with a given (E,k) relation is given by

                               M^x = [h/(2π)]² / d²E/dk²