A particle’s effective mass (often denoted m* is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. . [Source:Wikipedia]
Band Structure (E-k diagram)
Atoms are arranged periodically in a lattice. This has a periodic potential variation and in turn the probability of finding an electron should also vary periodically.
Band structure calculations take advantage of the periodic nature of a crystal lattice, exploiting its symmetry. If you plot the E vs k diagram of all the valid energy states , you get a periodic plot where a is the atomic distance between atoms in the crystal lattice. Here k is Boltzmann’s constant.
The movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modelling the behavior of a free particle with that mass. Consider a semiconductor is connected to an electric field. Since the crystal lattice has a periodic potential within it, every free electron also experiences an internal force, as well as a force due to the applied electric field.
F = Fexternal + Finternal
However, it is seen that crystal momentum only depends on the external force applied by the electric field, and the internal forces due to the lattice potential needn’t be taken into account. The electron can be modeled as responding to the external force as if it was a free particle with an effective mass that is different from the rest mass of the electron. It is specified as
h is reduced Plank’s constant.