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Intervalley scattering

Intervalley scattering takes place between different valleys by both acoustic and optical phonons. The total scattering rate, as a function of energy, is given by

[ ]∘ ---------------- Pe- ,op(E) = (DtK√-)imDOSZf--- Ni E ± ℏωop - ΔEfi; (A.6) 2πℏ3ρωi Ni + 1 ( ℏωi )-1 Ni = ---- - 1 . (A.7) kBT
The equation is formally equivalent to the case of intravalley scattering by optical phonons, when setting Zf and ΔEfi equal to 1 and 0, respectively. As for the intravalley optical phonons, the top (bottom) branch of the equation yields the rate for absorption (emission).

Scattering can take place between equivalent valleys, e.g. X-X or L-L, or between non-equivalent valleys, e.g. X-L – different scattering parameters apply in each respective case. For a given transition one can distinguish between g-type phonons, which induce transitions between opposite valleys on the same axis in space, and f-type phonons, which induce transitions among orthogonal axes. The case for scattering between equivalent X-valleys is currently implemented, using the values in Table A.3.

Table A.3: Parameters for intervalley scattering (equivalent X-valleys)
SymbolMeaning Value
Zf number of equivalent final valleys (f-process) 4
Zf number of equivalent final valleys (g-process) 1
Δfi difference in energy between the minima of the initial and final valley 0.0eV
ℏωi transition energy (f-process) 0.01896eV
ℏωi transition energy (g-process) 0.01206eV

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