# UGC NET: Effective Mass

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. 