Effective Mass
A parameter that simplifies modeling electron and hole dynamics in a crystal lattice by treating them as free particles with a modified mass determined by energy band curvature.
Governing formula
m* = ℏ² / (d²E / dk²)
SI unit
kg or Fraction of Rest Mass m_e
In depth
When an electron moves through a periodic crystal potential, internal lattice forces alter its acceleration in response to external fields. Highly curved E(k) band dispersion curves correspond to a small effective mass m*, yielding high carrier mobility.
Examples in the real world
Conduction electrons in Gallium Arsenide having a small effective mass (m* ≈ 0.067 m_e), enabling high-speed radio frequency transistors.