Berlin 2024 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 13: Poster I

HL 13.58: Poster

Monday, March 18, 2024, 15:00–18:00, Poster E

Spherical harmonics expansion method for a semi-classical matrix transport equation describing spin dynamics in semiconductors — •Felix Willert and Franz Xaver Bronold — Institut für Physik, Universität Greifswald, 17489 Greifswald, Germany

We discuss the transport of hot electrons, originating from a magnetized ferromagnet, in a semiconductor and the spin dynamics governed by the D'yakonov-Perel (DP) mechanism, which is the dominant spin relaxation process in semiconductors without inversion symmetry in the unit cell. For that we use a semi-classical model, where charge transport and scattering processes are described classically, but the spin-processes follow a quantum mechanical description. Due to the fact, that the DP mechanism changes the orientation of the spin and not directly its magnitude, it is not sufficient to describe the dynamics by two coupled equations for spin-up- and spin-down-electrons. Therefore we derive a Boltzmann equation for 2x2-density matrices in spin space with an additional term governing the DP process. To solve this equation, the H-Transformation and a spherical harmonics expansion is used.

Preliminary numerical results are presented, showing energy relaxation and partial thermal equilibration of the electron distribution as well as the spin relaxation throughout the system, which is strongly dependent on the energy, due to the DP mechanism depending on the third power of the electron momentum.

Keywords: Spin transport; D'yakonov-Perel mechanism; Spherical harmonics