In polar semiconductors the electron-longitudinal optical (LO) phonon scattering is the dominant intersubband scattering mechanism for separations of the subbands less than the LO phonon energy [83]. Due to the polarization in polar semiconductor crystals induced by the optical vibration mode, the electrons are scattered through the interaction of the Coulomb field of the lattice polarization waves.

In optical vibrations the atoms in a lattice vibrate against each other, which can produce polarization
effects. For longitudinal optical vibrations there is an restoring force due to the polarization field
generated by the vibration. The lattice polarization P_{Lat} is proportional to the lattice displacement U
and the Fröhlich constant F_{c}

| (5.8) |

where F_{c } is given by [84]

| (5.9) |

Here, ϵ_{0 } is the vacuum dielectric constant, ε_{s} and ε_{∞} are the static dielectric permittivity and high
frequency dielectric permittivity.

An electric displacement D is generated by the charge distribution according to

| (5.10) |

The interaction potential ΔÛ between the external electric displacement and the lattice polarization reads

| (5.11) |

with

| (5.12) |

where â _{q } and â_{q}^{†} denote the annihilation and creation operators. The summation over all generated
dipoles result in the total interaction Hamiltonian, hence

| (5.13) |

An electron located at x generates a displacement at x^{′} according to

| (5.14) |

which yields an interaction Hamiltonian of the form

| (5.15) |

where the coupling coefficent is given by

| (5.16) |

The scattering rate for an electron initially in subband ν and stage λ to a final subband ν^{′} and stage
λ^{′ } , can be written as (see Appendix B.1)

| (5.18) |