Effective mass

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* = 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*/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.