Subsections

### 2.5.2.4 Intervalley Phonon Scattering

An electron can be scattered from one valley to another one both by acoustical and optical phonons. Intervalley scattering can be treated as a deformation-potential interaction [30] in the same way as intravalley scattering by optical phonons.

#### 2.5.2.4.1 Equivalent X-X Intervalley Scattering

This scattering process is subdivided into f-type and g-type processes. A process is referred to as f-type, if the initial and final orientations are different, otherwise as g-type process. The transition probability of this mechanism is given by:

 (2.115)

where is:

 (2.116)

is the equilibrium phonon number of the involved phonon type:

 (2.117)

is the number of possible equivalent final valleys of the same type. For f-type scattering and for g-type scattering . is the coupling constant, is the corresponding phonon energy.

The numerical values of the coupling constants and phonon energies [18,20] are shown in Table 2.4.

Table 2.4: Numerical values for the intervalley X-X scattering rate.
 Silicon Germanium eV/cm eV/cm eV eV eV/cm eV/cm eV eV eV/cm eV/cm eV eV eV/cm eV/cm eV eV eV/cm eV/cm eV eV eV/cm eV/cm eV eV

#### 2.5.2.4.2 Equivalent L-L Intervalley Scattering

For this type of scattering there is no separation into f- and g-type processes. The scattering rate is given as:

 (2.118)

where is

 (2.119)

is the equilibrium phonon number of the involved phonon type:

 (2.120)

for the transition between two different orientations and for scattering within the same orientation, denotes the corresponding coupling constant and is the energy of the phonon involved in the scattering process.

The numerical values of the coupling constants and phonon energies [18,20] for this type of scattering are shown in Table 2.5.

Table 2.5: Numerical values for the intervalley L-L scattering rate.
 Silicon Germanium eV/cm eV/cm eV eV

#### 2.5.2.4.3 Non-Equivalent Intervalley Scattering

This process involves transitions between all possible valleys in the conduction band. The scattering rate is given by:

 (2.121)

where is:

 (2.122)

is the equilibrium phonon number of the involved phonon type:

 (2.123)

and is given as

 (2.124)

Indices and stand for the initial and final valley, respectively, is the number of possible equivalent final valleys, is the corresponding coupling constant, is the respective phonon energy, and are the energy minima of the initial and the final valley, respectively.

The numerical values of the coupling constants and phonon energies [18,20] for this type of scattering are shown in Table 2.6.

Table 2.6: Numerical values for the non-equivalent intervalley scattering rate.
 Silicon Germanium eV/cm eV/cm eV eV eV/cm eV/cm eV eV eV/cm eV/cm eV eV

S. Smirnov: