Spin relaxation of two-dimensional holes in strained asymmetric SiGe quantum wells

We analyze spin splitting of the two-dimensional hole spectrum in strained asymmetric SiGe quantum wells (QWs). Based on the Luttinger Hamiltonian, we obtain expressions for the spin-splitting parameters up to the third order in the in-plane hole wave vector. The biaxial strain of SiGe QWs is found to be a key parameter that controls spin splitting. Application to SiGe field-effect transistor structures indicates that typical spin splitting at room temperature varies from a few tenths of meV in the case of Si QW channels to several meV for the Ge counterparts, and can be modified efficiently by gate-controlled variation of the perpendicular confining electric field. The analysis also shows that for sufficiently asymmetric QWs, spin relaxation is due mainly to the spin-splitting related D'yakonov-Pere\ifmmode \acute{l}\else \'{l}\fi{} mechanism. In strained Si QWs, our estimation shows that the hole spin relaxation time can be on the order of 100 picoseconds at room temperature, suggesting that such structures are suitable for $p$-type spin transistor applications as well.