Intravalley scattering refers to processes where the initial and final valley of the scattered electron is the same. The scattering can take place through acoustic or optical phonons.
The scattering by acoustic phonons in the same valley is assumed to be elastic by the equipartition approximation. The total scattering rate is given by
| Symbol | Meaning | Value |
| mDOS | effective mass for density of states | – |
| ml | effective mass in longitudinal direction | 0.98mo |
| mt | effective mass in transverse direction | 0.19mo |
| m0 | mass of an electron | 9.11 × 10-31kg |
| ρD | material (silicon) density | 2338.0kg ⋅ m-3 |
| u | average sound (acoustic phonon) velocity | – |
| ul | sound velocity in transverse direction | 5.410 × 107m ⋅ s-1 |
| ut | sound velocity in longitudinal direction | 9.033 × 107m ⋅ s-1 |
| Ξ | scalar representing average of potential deformation tensor | 7.2eV |
Intravalley scattering by optical phonons is inelastic; energy is lost (gained) through the emission (absorption) of an optical phonon.
The total scattering rate as a function of energy is given by
![[ ]
(DtK--)2mDOS-- Nop ∘ ---------
Pe-,op(E ) = √2-πℏ3ρ ω Nop + 1 E ± ℏωop, (A.4)
D op](html_diss_c378x.png)
The value Nop denotes the mean occupancy number for optical phonons under equilibrium conditions and is given by a Bose-Einstein distribution:
Intravalley scattering with optical phonons is forbidden in the X- and Γ-valleys of silicon, due to symmetry considerations; only the L-valley electrons can undergo intravalley scattering in silicon [164].
| Symbol | Meaning | Value |
| DtK | optical coupling constant | 2.2 × 1010eV ⋅ m-1 |
| ωop | radial frequency of optical phonon | – |
| ℏωop | optical phonon energy | 0.0612eV |