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
= F_{external} + F_{internal}

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 neednâ€™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

Where ~~h~~ is reduced Plank’s constant.