|
|
Line 85: |
Line 85: |
|
|
|
|
|
==References== |
|
==References== |
|
*{{cite book | author=C. Hamaguchi | title=Basic Semiconductor Physics | publisher=Springer | year=2001 | pages= 183–239}} |
|
<!--* {{cite book | author=C. Hamaguchi | title=Basic Semiconductor Physics | publisher=Springer | year=2001 | pages= 183–239}}--> |
|
*{{cite book |author1=Yu, Peter Y. |author2=Cardona, Manuel | title=Fundamentals of Semiconductors | edition = 3rd | publisher=Springer | year=2005}} |
|
* {{cite book |last=Hamaguchi |first=Chihiro |date= |title=Basic Semiconductor Physics |edition=3 |url=https://www.springer.com/gp/book/9783319668598 |location= |publisher=Springer |page=265-363 |isbn=978-3-319-88329-8 |author-link= |doi=}} |
|
|
* {{cite book |author1=Yu, Peter Y. |author2=Cardona, Manuel | title=Fundamentals of Semiconductors | edition = 3rd | publisher=Springer | year=2005}} |
|
|
|
|
|
{{DEFAULTSORT:Electron-Longitudinal Acoustic Phonon Interaction}} |
|
{{DEFAULTSORT:Electron-Longitudinal Acoustic Phonon Interaction}} |
The electron-LA phonon interaction is an interaction that can take place between an electron and a longitudinal acoustic (LA) phonon.
Displacement operator of the LA phonon
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 nth 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
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
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.
Notes
- ^ Hamaguchi 2001, p. 208.
References