2.4. Scattering mechanisms

2.4.1. Optical phonon scattering

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Polar electron-LO-phonon interaction

In polar materials (III-V, II-VI), the Fröhlich interaction is the dominant coupling mechanism between charge carriers and longitudinal-optical (LO) phonons. The coupling Hamiltonian reads (in SI units):

(2.4.1.1)\[H^F_{\text{e-LO}} = \sum_{q} \frac{C^F}{q} \left(a^+_q e^{iqr}+a_q e^{-iqr}\right)\]

where \(a^+_q\) and \(a_q\) are the creation and annihilation operator of a LO phonon with wavevector \(q\),

(2.4.1.2)\[C^F = e \sqrt{\frac{\hbar \omega_{\text{LO}}}{2 V \epsilon_0} \left( \frac{1}{\epsilon_r^{\infty}} - \frac{1}{\epsilon_r^{0}} \right)}\]

\(\omega_{\text{LO}}\) is the LO-phonon frequency, \(\epsilon_0\) the vacuum permittivity, \(V\) the normalization volume.

This scattering mechanism is considered by default as long as the material is polar, i.e. the high-frequency relative permittivity \(\epsilon_r^{\infty}\) differs from the static one \(\epsilon_r^{0}\).

Deformation potential electron-LO-phonon interaction

For non-polar materials (group IV), the deformation potential mechanism has to be considered. To activate this coupling, the keyword LOPhononDeformationPotential has to be used.

Tuning electron-LO-phonon interaction

In both cases, the LO-phonon scattering strength can be further controlled by the input keywords LOPhononCouplingStrength (optional).

If a constant \(\alpha\) is specified for this keyword, the tuning is done accordingly to

(2.4.1.3)\[|C^F|^2 \rightarrow \alpha |C^F|^2\]

so that the scattering rate scales proportionnaly to \(\alpha\)

2.4.2. Interface roughness scattering

Graded interfaces

(2.4.2.1)\[c(z) = c_0 + d_0 \mathrm{erf} \left[ 2\sqrt{\mathrm{ln}(2)} \frac{z - z_0}{L} \right]\]

where —.

2.4.3. Threading dislocations

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Can be controlled by the input keywords ThreadingDislocations{ }.

2.4.4. Acoustic phonon scattering

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Can be controlled by the input keywords AcousticPhononScattering and AcousticPhononScatteringEnergyMax.

2.4.5. Charged impurity scattering

Three models are available for the effective temperature of the electrons involved in electrostatic screening. The screening involved in charged impurity scattering is modeled by a homogeneous electron gas, with a temperature model specified by ScreeningTemperatureType.

Model #1

(2.4.5.1)\[T_\mathrm{eff} = T + T_\mathrm{offset} e^{-T / T_\mathrm{offset}}\]

where \(T_\mathrm{offset}\) is specified by TemperatureOffsetParameter. The screening temperature does not necessarily match the calculated average electron temperature. We found that 140 K is a reasonable, empirical value that is suited for both MIR and THz QCLs.

Model #2

The screening temperature is set to the average electron temperature, which is calculated in each NEGF iteration. This method requires several iterations of the all calculation until the effective average temperature converges below the accuracy specified by AccuracySelfConsistentElectronTemperature.

Model #3

\(T_\mathrm{eff}\) is directly specified by ElectronTemperatureForScreening. The screening temperature does not necessarily match the calculated average electron temperature.

The effective electron temperature is written to the file Effective_Temperature.dat.

The importance of the impurity scattering can be tested by changing ImpurityScatteringStrength from the default value 1.0.

2.4.6. Alloy scattering

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Can be controlled by the input keywords AlloyScattering and AlloyScatteringStrength.

2.4.7. Electron-electron scattering

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Can be controlled by the input keywords ElectronElectronScattering.

Last update: 2026/04/02