deformationpotential

Deformation potential is a quantity in solid-state physics that describes how the electronic energy levels of a crystal shift in response to mechanical deformation, such as strain. It provides a simple way to parametrize the interaction between electrons and lattice vibrations (phonons) when the phonon wavelength is long compared with the lattice spacing.

In the simplest case of hydrostatic strain, the shift of a band edge is ΔE = Ξ ε_h, where Ξ is the deformation potential constant. For the conduction band this is often denoted Ξ_c and for the valence band Ξ_v. For general strain, the effect is tensorial and described by deformation-potential constants that relate energy shifts to components of the strain tensor. In cubic semiconductors a small set of independent constants suffices (for example, a_c, a_v, and additional shear-related constants such as b and d).

These constants enable calculation of electron-phonon scattering rates, particularly for long-wavelength acoustic phonons (acoustic deformation potential). In some materials, optical deformation potentials are also defined to describe coupling to optical phonons, contributing to carrier scattering in nonpolar or polar crystals.

Historically, the deformation potential concept emerged from work by Bardeen and Shockley and has become a standard tool for modeling carrier transport, enabling estimates of mobility and phonon-limited conductivity. It is widely used in semiconductors such as silicon, germanium, and various III–V compounds, often within the deformation-potential approximation or combined with k·p and tight-binding frameworks.

Limitations include neglect of short-range and nonuniform strain effects and reduced accuracy for large strains or high-q phonons. More complete treatments rely on full electron-phonon coupling calculations derived from first principles.