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).
- 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.