Effective mass

Effective mass is a parameter that describes how a particle or excitation responds to forces in a medium. It captures the medium’s influence through motion that can differ from that of a free particle.

Energy band: An energy band is a range of allowed energies for electrons in a solid. Effective mass describes carrier dynamics within a solid’s allowed energy bands.
Dispersion relation: A dispersion relation specifies how a wave’s frequency or a particle’s energy depends on its momentum or wavevector. Effective mass is extracted from the curvature of an energy–momentum dispersion.
Electrical conductivity: Electrical conductivity measures how readily a material carries electric current in response to an electric field. Carrier effective mass helps set acceleration and conductivity alongside scattering and carrier density.
Reduced mass: Reduced mass is the mass parameter that converts a two-body relative-motion problem into an equivalent one-body problem. It arises from separating two free bodies, not from a medium’s effect on one excitation.
Band structure: Band structure is the dependence of allowed electron energies on crystal momentum in a periodic solid. The band structure supplies the energy–momentum relation from which band effective mass is calculated.
Group velocity: Group velocity is the speed at which a wave packet’s envelope and energy propagate. In a band, the slope of energy with momentum sets carrier group velocity.
Semiconductor: A semiconductor is a material whose electrical conductivity can be controlled by doping, temperature, light, or applied fields. Electron and hole effective masses help determine semiconductor transport and device response.
Phonon: A phonon is a quantized collective vibration of atoms in a solid. Phonon effective mass can describe lattice response, unlike the common electronic band-mass setting.
Crystal momentum: Crystal momentum is a wavevector-related quantity conserved in ideal periodic crystals, defined modulo reciprocal lattice vectors. Its change under applied forces connects band curvature to carrier acceleration.
Newton's second law: Newton's second law relates an object's acceleration to the net force acting on it. Effective mass is defined by how acceleration under force differs from the free-particle case.

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