Electron-electron scattering effect on spin relaxation in multi- valley nanostructures

We develop a theory of effects of electron-electron collisions on the Dyakonov-Perel’ spin relaxation in multi-valley quantum wells. It is shown that the electron-electron scattering rate which governs the spin relaxation is different from that in a single-valley system. The theory is applied to Si/SiGe (001)-grown quantum wells where two valleys are simultaneously populated by free carriers. The dependences of the spin relaxation rate on temperature, electron concentration and valley-orbit splitting are calculated and discussed. The obtained results establish a lower bound for the spin relaxation rate in n-doped Si-based heterostructures. We demonstrate that in a wide range of temperatures the electron-electron collisions can govern spin relaxation in high-quality Si/SiGe quantum wells. Introduction. – Electron spin dynamics is among the most rapidly developing branches of the modern solid state physics due to the rise of spintronics [1, 2]. The prospects of spintronics which aims at the utilization of electron spin on equal grounds with its charge in novel semiconductor devices are related with the possibilities to create, control and manipulate the electron spins. The understanding of microscopic mechanisms of electron spin decoherence and relaxation is, hence, of high importance. The main mechanism of electron spin relaxation in bulk semiconductors and semiconductor quantum wells (QWs) is Dyakonov-Perel’ (or precession) mechanism [3, 4]. It is connected with the spin-orbit splitting of the conduction band states which acts as a wavevector (k) dependent effective magnetic field with the Larmor precession frequency Ωk. Such an effective field arises only in noncentrosymmetric systems, the most widespread examples of them being bulk III-V semiconductors and QWs on their base. Although bulk Si and Ge crystals possess an inversion center, it has been demonstrated experimentally [5, 6] that the one-side modulation-doped Si/SiGe QW structures exhibit the Rashba effect and, in these structures, the electron spin relaxation is governed by precession mechanism as well. Recently, a theoretical estimation for the electron spin-orbit splitting in Si/SiGe heterostructures have been obtained by using the empirical tight-binding model computation [7, 8]. The electron spin precession in the effective magnetic field is interrupted by the scattering events which change randomly the electron wavevector and, hence, the direction of the spin precession axis. Thus, the spin relaxation rate τ s can be estimated as 〈Ωkτ〉 where angular brackets denote the averaging over the electron ensemble and τ is the microscopic scattering time. Hence, the spin relaxation is slowed down by the scattering. It is evident that any momentum scattering process such as interaction of an electron with static impurities, interface imperfections or phonons stabilizes the spin. It is much less obvious that the electron-electron scattering can also suppress the Dyakonov-Perel’ spin relaxation contributing additively to τ [9–13] and making the time τ different from the momentum relaxation time. Indeed, it does not matter whether the electron wavevector is changed in the process of momentum scattering, due to the cyclotron motion or as a result of collision with other electrons [9]. It is established that nothing but an inclusion of the electronelectron scattering allows one to describe the temperature dependence of spin relaxation rates in high-quality GaAs QWs [12]. Here we address the electron-electron scattering effects on spin relaxation in Si/SiGe quantum wells. Their specific feature is the presence of several valleys [two in case of (001)-grown QWs] populated by electrons. The Coulomb scattering cannot transfer an electron from one valley into