Jump to content

Electron-longitudinal acoustic phonon interaction

From Wikipedia, the free encyclopedia

The electron-longitudinal acoustic phonon interaction is an interaction that can take place between an electron and a longitudinal acoustic (LA) phonon in a material such as a semiconductor.

Displacement operator of the LA phonon

[edit]

The equations of motion of the atoms of mass M which locates in the periodic lattice is

,

where is the displacement of the nth atom from their equilibrium positions.

Defining the displacement of the th atom by , where is the coordinates of the th atom and is the lattice constant,

the displacement is given by

Then using Fourier transform:

and

.

Since is a Hermite operator,

From the definition of the creation and annihilation operator

is written as

Then expressed as

Hence, using the continuum model, the displacement operator for the 3-dimensional case is

,

where is the unit vector along the displacement direction.

Interaction Hamiltonian

[edit]

The electron-longitudinal acoustic phonon interaction Hamiltonian is defined as

,

where is the deformation potential for electron scattering by acoustic phonons.[1]

Inserting the displacement vector to the Hamiltonian results to

Scattering probability

[edit]

The scattering probability for electrons from to states is

Replace the integral over the whole space with a summation of unit cell integrations

where , is the volume of a unit cell.

See also

[edit]

Notes

[edit]
  1. ^ Hamaguchi, Chihiro (2017). Basic Semiconductor Physics. Graduate Texts in Physics (3 ed.). Springer. p. 292. doi:10.1007/978-3-319-66860-4. ISBN 978-3-319-88329-8.

References

[edit]