Spin-lattice relaxation times of single donors and donor clusters in silicon

Abstract

An atomistic method of calculating the spin-lattice relaxation times (T1) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence, the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of T1 with the number of donors and electrons, as well as donor locations. Without any adjustable parameters, the relaxation rates in a magnetic field for both systems are found to vary as B5, in excellent quantitative agreement with experimental measurements. The results also show that by engineering electronic wave functions in nanostructures, T1 times can be varied by orders of magnitude.