Electron transport in SiGe

Scattering of electrons in SiGe alloys from First Principles
Calculated n-type carrier mobility in Si1-xGex at 300 K (solid line) and experimental data from Refs. [1] (triangles), [2] and [3] (squares).
Calculated n-type carrier mobility in Si1-xGex at 300 K (solid line) and experimental data from Refs. [1] (triangles), [2] and [3] (squares).

Our purpose is to study the scattering of electrons in SiGe alloys from First Principles. The scattering can be separated into the contributions from elastic scattering by alloy sites and inelastic scattering by phonons. We calculate the elastic alloy scattering rates by finding the energy splitting of the degenerate conduction bands due to the substitution of a Ge atom by a Si atom in a supercell using a VCA alloy as background. We obtain the inelastic phonon scattering matrix elements using Linear Response Theory to calculate the dynamical matrix and the electron phonon interaction in a VCA alloy. This dynamical matrix is then used together with the mass disorder approximation to find the scattering rates with alloy disorder. The elastic and inelastic scattering rates are used in the Boltzmann Transport Equation to find the n-type carrier mobility as a function of alloy composition. We find excellent agreement with experiment for unstrained bulk alloys.

We expanded this method to include second order deformation potentials and the alloy scattering parameters as a function of strain to predict the behaviour of the mobility of SiGe under different types of strain.

References
[1] C. Herring and E. Vogt, Phys. Rev. 101, 944 (1956).
[2] M. Glicksman, Phys. Rev. 111, 125 (1958).
[3] A. Smith, Phys. Rev. 139, A 1625 (1965).

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