Monte Carlo modeling of spin injection through a Schottky barrier and spin transport in a semiconductor quantum well

We develop a Monte Carlo model to study injection of spin-polarized electrons through a Schottky barrier from a ferromagnetic metal contact into a nonmagnetic low-dimensional semiconductor structure. Both mechanisms of thermionic emission and tunneling injection are included in the model. Due to the barrier shape, the injected electrons are nonthermalized. Spin dynamics in the semiconductor heterostructure is controlled by the Rashba and Dresselhaus spin-orbit interactions and described by a single electron spin density matrix formalism. In addition to the linear term, the third-order term in momentum for the Dresselhaus interaction is included. Effect of the Schottky potential on the spin dynamics in a two-dimensional semiconductor device channel is studied. It is found that the injected current can maintain substantial spin polarization to a length scale in the order of $1\mu \mathrm{m}$ at room temperature without external magnetic fields.