**Effective mass** is an important concept in semiconductor physics. It can be shown that electrons and holes in a crystal respond to an electric field almost as if they were free particles in a vacuum, but with a different mass. This mass is usually stated in units of the ordinary mass of an electron *m _{e}* (9.11×10

Effective mass is defined by analogy with Newton's second law **F**=*m* **a**. Using quantum mechanics it can be shown that for an electron in an external electric field *E*:

*a*= (1 /~~h~~^{2}) (*d*^{2}ε /*dk*^{2})*qE*

- (1/
*m*^{*}) = (1 /~~h~~^{2}) (*d*^{2}ε /*dk*^{2})

In energy regions far away from a minimum, effective mass can be negative or even approach infinity. Effective mass is generally dependent on direction (with respect to the crystal axes), however for most calculations the various directions can be averaged out.

Effective mass should not be confused with reduced mass, which is a concept from Newtonian mechanics. Effective mass can only be understood with quantum mechanics.

Material | Electron effective mass | Hole effective mass |
---|---|---|

Silicon | 0.36 m _{e} |
0.81 m _{e} |

Gallium arsenide | 0.067 m_{e} |
0.45 m_{e} |

Germanium | 0.55 m_{e} |
0.37 m_{e} |