Question

Describe in your own words, what is the PHYSICAL SIGNIFICANCE of effective mass?? (Don’t talk about the formulae)

Answer 1

In solids especially in crystalline materials, electrons move in a periodic potential of the lattice. The electrons respond to the externally applied voltages and move in a directional manner. In such cases the force acting on a single electron can be expressed as

where e is electron charge and E is externally applied electric field. We can apply Newtonian mechanics to describe the momentum evolution, i.e.,

Where mo is the rest mass of electron. But if you closely observe this equation, you will find that something is missing. We are ignoring one important additional force which acts on the electron in the solid. This additional force comes from the lattice potential and is considered as the internal force. Thus, the total force acting on the electron can be expressed as

Well…! We can not determine the internal force. But, until unless we determine that internal force we can’t explain the momentum. This problem can be overcome by the introduction of effective mass concept. The effective mass of electron critically depends on the lattice potential and it usually obtains from the curvature of energy bands present.

m∗=ℏ^2/(d^2E/dk^2)

The force equation now can be expressed as

Here m∗ is the effective mass of electron and it considers the internal lattice potential. Thus, the electrons respond to the applied voltages as if they have an effective mass m∗ which is different from the rest mass mo of the electron.

The effective mass is a quantity that is used to simplify band structures by constructing an analogy to the behavior of a free particle with that mass.

This concept is useful in determining the density of states as well as mobility of charge carriers in semiconductor devices.