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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.
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
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.
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
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.
![]() | This article has multiple issues. Please help
improve it or discuss these issues on the
talk page. (
Learn how and when to remove these template messages)
|
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.
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
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.
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
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.