**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 F_{ext} ) and a force F_{int} 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 F_{ext} = 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* = h^{2}(d^{2}E/dk^{2})^{-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 = h^{2}k^{2}/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*/m_{o} where m_{o} is the rest mass of an electron).

- Silicon (Si): 0.19-0.26, 0.50
- Germanium (Ge): 0.08-0.12, 0.28
- Gallium arsenide (GaAs): 0.07, 0.65
- Gallium phosphide (GaP): 0.35, 0.5
- Indium phosphide (InP): 0.08, 0.2
- Indium antimonide (InSb): 0.013, 0.18
- Indium arsenide (InAs): 0.02, 0.41
- Gallium antimonide (GaSb): 0.05, 0.4
- Cadmium selenide (CdSe): 0.14, 0.37
- Cadmium sulfide (CdS): 0.27, 0.07

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