Nonparabolicity

Nonparabolicity is the deviation of the electron energy–momentum dispersion from a simple parabolic form near a band edge in crystalline solids. While parabolic models yield E = ħ^2 k^2 / (2 m*), real semiconductor bands arise from coupling between conduction and other bands, causing the dispersion to bend as energy increases. The effect is especially pronounced in narrow-gap materials and for states several hundred meV above the band edge.

To describe nonparabolicity, theories such as the Kane model introduce a nonparabolicity parameter α. They give relations like E(1 + α E) = (ħ^2 k^2) / (2 m0) for the conduction band, or an energy-dependent effective mass m*(E) that deviates from a constant value. In these frameworks, the effective mass often grows with energy, reflecting stronger band coupling at higher energies.

Nonparabolicity affects device properties by altering the density of states and by changing transport and optical response. In quantum wells, wires, and dots, subband energies and wavefunctions depend on the nonparabolic dispersion, shifting absorption edges and intersubband transitions and influencing carrier distributions at elevated energies. It is an important consideration in hot-electron transport and high-field operation.

Parameter values are obtained by fitting experimental data or via k·p calculations. Common probes include cyclotron resonance, infrared absorption, and photoluminescence excitation spectroscopy. Incorporating nonparabolicity is standard in semiconductor device simulations and nanostructure design.