Effective Mass

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

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