Nonparabolic

Nonparabolic refers to the deviation of the energy–momentum relationship (E-k) for charge carriers from a simple parabolic form near a band edge in a solid. In the effective mass approximation, the conduction or valence band is often treated as E ≈ E0 + (ħ^2 k^2)/(2m*), a quadratic, or parabolic, relation. Real semiconductors, however, exhibit nonparabolicity because bands interact with each other and with higher-lying bands, especially at higher energies or in materials with strong band coupling. This nonlinearity affects how carrier energy relates to momentum, and consequently influences transport, optical transitions, and density of states.

The Kane model is the standard framework for describing nonparabolicity in semiconductors. It introduces a nonparabolic correction parameter, α, and yields a dispersion that can be written in a form such as E(1 + αE) = (ħ^2 k^2)/(2m0) for the conduction band. This leads to an energy-dependent effective mass, m*(E), and a departure from a purely quadratic band. The degree of nonparabolicity is material dependent and is particularly pronounced in narrow-gap or heavily mixed-band systems.

Nonparabolicity matters in device physics and materials characterization. It influences carrier mobility at high energies, optical absorption near the band edge, and the density of states used in simulations. It is important in the modeling of high-field transport, quantum wells and infrared detectors, and in the interpretation of experimental data from cyclotron resonance or optical spectroscopy. While many low-energy or wide-band-gap regimes can use a parabolic approximation, accurate descriptions of carrier dynamics often require nonparabolic models.