See also conductivity

Newton's second law says that F = ma, where F is the force on a particle, m is its mass, and a is its acceleration. When a charged particle is in a solid material in which an electric field is applied, the particle feels the force qE from the electric field (more generally an external force Fext ) and a force Fint from the nucleii and other particles in the solid. Luckily, if a solid is a crystal, the effect of the internal forces can be lumped into a new effective mass m*, and Fext = m*a. This is a nice concept since it eases analysis of the dynamics of electron and hole carrier transport in crystals.

It can be shown that m* = h2(d2E/dk2)-1, where E(k) vs. k is the energy vs. Bloch wavevector relationship of the energy band in which a carrier resides. For a free particle, E = h2k2/2m, so m* = m, as expected.

h is really "hbar," or Planck's constant over 2π.

Effective masses of electrons and holes (respectively) in semiconductors (in units of m*/mo where mo is the rest mass of an electron).

It is interesting to note that the effective masses of electrons in crystals are all smaller than the free electron masses.