Effective Mass Approximation

EFFECTIVE MASS APPROXIMATION

We know the energy of the electron in a uniform potential field is

............(1)

We know the effective mass of an electron moving in a periodic potential is

............(2)

Comparing equation (1) and (2), we can say that for an electron moving in constant potential field m* = m

But for an electron moving in a periodic potential m*≠m and therefore the electron in the crystal will behave as a particle with variable effective mass.

Thus when an electron is applied with periodic potential, the free electron mass (m) should be replaced by proper effective mass (m*) and this is called as effective mass approximation.

Therefore by replacing the value of m by m* in the energy value we can write the energy of an electron in a periodic potential as

............(3)

The concept of effective mass and its approximation is used for finding the high electronic specific heat of transition metals and their paramagnetic susceptibilities experimentally.