Theory of the spin relaxation of conduction electrons in silicon

Using Light to Polarize and Detect Electron Spins in Silicon

Despite decades of research, demonstration of all-optical detection and control of free electron spins in silicon remains elusive. Here, we directly probe the electron spin properties in bulk silicon by measuring the polarization of luminescence following circularly polarized light excitation. The all-optical experiments performed for both direct and indirect gap excitation allow not only an experimental determination of the optical selection rules in silicon for the different phonon-assisted transitions but they also lead to the measurement of the spin relaxation of electrons in conditions that are not accessible using transport techniques. We also measure the spin properties of free excitons in bulk silicon, a very little explored field.

A study on the room-temperature magnetoplastic effect of silicon and its mechanism

Exposure to a magnetic field at room temperature was found able to promote the dislocation motion and distortion relaxation in silicon. The Kernel average misorientation maps of the silicon samples obtained by electron backscatter diffraction (EBSD) showed that a magnetic field ∼1 T can cause dislocation movement of hundreds of nanometers. And the EBSD image quality maps indicated that the magnetic field can cause the relaxation of the lattice distortion. The Δgmechanism of the magnetically stimulated changes was discussed.

Spin-phonon relaxation from a universal ab initio density-matrix approach

Designing new quantum materials with long-lived electron spin states urgently requires a general theoretical formalism and computational technique to reliably predict intrinsic spin relaxation times. We present a new, accurate and universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate spin-phonon relaxation time of solids with arbitrary spin mixing and crystal symmetry. This method describes contributions of Elliott-Yafet and D'yakonov-Perel' mechanisms to spin relaxation for systems with and without inversion symmetry on an equal footing. We show that intrinsic spin and momentum relaxation times both decrease with increasing temperature; however, for the D'yakonov-Perel' mechanism, spin relaxation time varies inversely with extrinsic scattering time. We predict large anisotropy of spin lifetime in transition metal dichalcogenides. The excellent agreement with experiments for a broad range of materials underscores the predictive capability of our method for properties critical to quantum information science.

Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO

The presence of both inversion (P) and time-reversal (T) symmetries in solids leads to a double degeneracy of the electronic bands (Kramers degeneracy). By lifting the degeneracy, spin textures manifest themselves in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is difficult to observe directly. Here, we use quantum interference measurements to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type Dirac material Sr3SnO. We find robust weak antilocalization (WAL) independent of the position of EF. The observed WAL is fitted using a single interference channel at low doping, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement.

Evidence of Pure Spin-Current Generated by Spin Pumping in Interface-Localized States in Hybrid Metal-Silicon-Metal Vertical Structures

Due to the difficulty of growing high-quality semiconductors on ferromagnetic metals, the study of spin diffusion transport in Si was limited to lateral geometry devices. In this work, by using an ultrahigh-vacuum wafer-bonding technique, we have successfully fabricated metal-semiconductor-metal CoFeB/MgO/Si/Pt vertical structures. We hereby demonstrate pure spin-current injection and transport in the perpendicular current flow geometry over a distance larger than 2 μm in n-type Si at room temperature. In those experiments, a pure propagating spin current is generated via ferromagnetic resonance spin pumping and converted into a measurable voltage by using the inverse spin Hall effect occurring in the top Pt layer. A systematic study varying both Si and MgO thicknesses reveals the important role played by the localized states at the MgO-Si interface for the spin-current generation. Proximity effects involving indirect exchange interactions between the ferromagnet and the MgO-Si interface states appears to be a prerequisite to establishing the necessary out-of-equilibrium spin population in Si under the spin-pumping action.

Strong confinement-induced engineering of the g factor and lifetime of conduction electron spins in Ge quantum wells

Control of electron spin coherence via external fields is fundamental in spintronics. Its implementation demands a host material that accommodates the desirable but contrasting requirements of spin robustness against relaxation mechanisms and sizeable coupling between spin and orbital motion of the carriers. Here, we focus on Ge, which is a prominent candidate for shuttling spin quantum bits into the mainstream Si electronics. So far, however, the intrinsic spin-dependent phenomena of free electrons in conventional Ge/Si heterojunctions have proved to be elusive because of epitaxy constraints and an unfavourable band alignment. We overcome these fundamental limitations by investigating a two-dimensional electron gas in quantum wells of pure Ge grown on Si. These epitaxial systems demonstrate exceptionally long spin lifetimes. In particular, by fine-tuning quantum confinement we demonstrate that the electron Landé g factor can be engineered in our CMOS-compatible architecture over a range previously inaccessible for Si spintronics.

Silicon-on-insulator for spintronic applications: spin lifetime and electric spin manipulation

With complementary metal-oxide semiconductor feature size rapidly approaching ultimate scaling limits, the electron spin attracts much attention as an alternative to the electron charge degree of freedom for low-power reprogrammable logic and nonvolatile memory applications. Silicon, the main element of microelectronics, appears to be the perfect material for spin-driven applications. Despite an impressive progress in understanding spin properties in metal-oxide-semiconductor field-effect transistors (MOSFETs), spin manipulation in a silicon channel by means of the electric field–dependent Rashba-like spin–orbit interaction requires channels much longer than 20 nm channel length of modern MOSFETs. Although a successful realization of the spin field-effect transistor seems to be unlikely without a new concept for an efficient way of spin manipulation in silicon by purely electrical means, it is demonstrated that shear strain dramatically reduces the spin relaxation, thus boosting the spin lifetime by an order of magnitude. Spin lifetime enhancement is achieved by lifting the degeneracy between the otherwise equivalent unprimedsubbands by [110] uniaxial stress. The spin lifetime in stressed ultra-thin body silicon-on-insulator structures can reach values close to those in bulk silicon. Therefore, stressed silicon-on-insulator structures have a potential for spin interconnects.

The Elliott-Yafet theory of spin relaxation generalized for large spin-orbit coupling

We generalize the Elliott-Yafet (EY) theory of spin relaxation in metals with inversion symmetry for the case of large spin-orbit coupling (SOC). The EY theory treats the SOC to the lowest order but this approach breaks down for metals of heavy elements (such as e.g. caesium or gold), where the SOC energy is comparable to the relevant band-band separation energies. The generalized theory is presented for a four-band model system without band dispersion, where analytic formulae are attainable for arbitrary SOC for the relation between the momentum- and spin-relaxation rates. As an extended description, we also consider an empirical pseudopotential approximation where SOC is deduced from the band potential (apart from an empirical scaling constant) and the spin-relaxation rate can be obtained numerically. Both approaches recover the usual EY theory for weak SOC and give that the spin-relaxation rate approaches the momentum-relaxation rate in the limit of strong SOC. We argue that this limit is realized in gold by analyzing spin relaxation data. A calculation of the g-factor shows that the empirical Elliott-relation, which links the g-factor and spin-relaxation rate, is retained even for strong SOC.

Hot-electron effect in spin relaxation of electrically injected electrons in intrinsic Germanium

The hot-electron effect in the spin relaxation of electrically injected electrons in intrinsic germanium is investigated by the kinetic spin Bloch equations both analytically and numerically. It is shown that in the weak-electric-field regime with E ≲ 0.5 kV cm(-1), our calculations have reasonable agreement with the recent transport experiment in the hot-electron spin-injection configuration (2013 Phys. Rev. Lett. 111 257204). We reveal that the spin relaxation is significantly enhanced at low temperature in the presence of weak electric field E ≲ 50 V cm(-1), which originates from the obvious center-of-mass drift effect due to the weak electron-phonon interaction, whereas the hot-electron effect is demonstrated to be less important. This can explain the discrepancy between the experimental observation and the previous theoretical calculation (2012 Phys. Rev. B 86 085202), which deviates from the experimental results by about two orders of magnitude at low temperature. It is further shown that in the strong-electric-field regime with 0.5 ≲ E ≲ 2 kV cm(-1), the spin relaxation is enhanced due to the hot-electron effect, whereas the drift effect is demonstrated to be marginal. Finally, we find that when 1.4 ≲ E ≲ 2 kV cm(-1) which lies in the strong-electric-field regime, a small fraction of electrons (≲5%) can be driven from the L to Γ valley, and the spin relaxation rates are the same for the Γ and L valleys in the intrinsic sample without impurity. With the negligible influence of the spin dynamics in the Γ valley to the whole system, the spin dynamics in the L valley can be measured from the Γ valley by the standard direct optical transition method.

Donor-driven spin relaxation in multivalley semiconductors

The observed dependence of spin relaxation on the identity of the donor atom in n-type silicon has remained without explanation for decades and poses a long-standing open question with important consequences for modern spintronics. Taking into account the multivalley nature of the conduction band in silicon and germanium, we show that the spin-flip amplitude is dominated by short-range scattering off the central-cell potential of impurities after which the electron is transferred to a valley on a different axis in k space. Through symmetry arguments, we show that this spin-flip process can strongly affect the spin relaxation in all multivalley materials in which time-reversal cannot connect distinct valleys. From the physical insights gained from the theory, we provide guidelines to significantly enhance the spin lifetime in semiconductor spintronics devices.

Full first-principles theory of spin relaxation in group-IV materials

We present a generally applicable parameter-free first-principles method to determine electronic spin relaxation times and apply it to the technologically important group-IV materials silicon, diamond, and graphite. We concentrate on the Elliott-Yafet mechanism, where spin relaxation is induced by momentum scattering off phonons and impurities. In silicon, we find a ~T(-3) temperature dependence of the phonon-limited spin relaxation time T(1) and a value of 4.3 ns at room temperature, in agreement with experiments. For the phonon-dominated regime in diamond and graphite, we predict a stronger ~T(-5) and ~T(-4.5) dependence that limits T(1) (300 K) to 180 and 5.8 ns, respectively. A key aspect of this Letter is that the parameter-free nature of our approach provides a method to study the effect of any type of impurity or defect on spin transport. Furthermore we find that the spin-mix amplitude in silicon does not follow the E(g)(-2) band gap dependence usually assigned to III-V semiconductors but follows a much weaker and opposite E(g)(0.67) dependence. This dependence should be taken into account when constructing silicon spin transport models.

Silicon spintronics

Worldwide efforts are underway to integrate semiconductors and magnetic materials, aiming to create a revolutionary and energy-efficient information technology in which digital data are encoded in the spin of electrons. Implementing spin functionality in silicon, the mainstream semiconductor, is vital to establish a spin-based electronics with potential to change information technology beyond imagination. Can silicon spintronics live up to the expectation? Remarkable advances in the creation and control of spin polarization in silicon suggest so. Here, I review the key developments and achievements, and describe the building blocks of silicon spintronics. Unexpected and puzzling results are discussed, and open issues and challenges identified. More surprises lie ahead as silicon spintronics comes of age.

Field-induced negative differential spin lifetime in silicon

We show that the electric-field-induced thermal asymmetry between the electron and lattice systems in pure silicon substantially impacts the identity of the dominant spin relaxation mechanism. Comparison of empirical results from long-distance spin transport devices with detailed Monte Carlo simulations confirms a strong spin depolarization beyond what is expected from the standard Elliott-Yafet theory even at low temperatures. The enhanced spin-flip mechanism is attributed to phonon emission processes during which electrons are scattered between conduction band valleys that reside on different crystal axes. This leads to anomalous behavior, where (beyond a critical field) reduction of the transit time between spin-injector and spin-detector is accompanied by a counterintuitive reduction in spin polarization and an apparent negative spin lifetime.

Observation of the inverse spin Hall effect in silicon

The spin–orbit interaction in a solid couples the spin of an electron to its momentum. This coupling gives rise to mutual conversion between spin and charge currents: the direct and inverse spin Hall effects. The spin Hall effects have been observed in metals and semiconductors. However, the spin/charge conversion has not been realized in one of the most fundamental semiconductors, silicon, where accessing the spin Hall effects has been believed to be difficult because of its very weak spin–orbit interaction. Here we report observation of the inverse spin Hall effect in silicon at room temperature. The spin/charge current conversion efficiency, the spin Hall angle, is obtained as 0.0001 for a p-type silicon film. In spite of the small spin Hall angle, we found a clear electric voltage due to the inverse spin Hall effect in the p-Si film, demonstrating that silicon can be used as a spin-current detector.

The spin Hall effect is a spin current induced by an electric current, and its occurrence in semiconductors is a promising route to controlling spins and their transport. Here, the inverse spin Hall effect, in which an electric current is induced by a spin current, is observed in silicon for the first time.

Electron theory of fast and ultrafast dissipative magnetization dynamics

For metallic magnets we review the experimental and electron-theoretical investigations of fast magnetization dynamics (on a timescale of ns to 100 ps) and of laser-pulse-induced ultrafast dynamics (few hundred fs). It is argued that for both situations the dominant contributions to the dissipative part of the dynamics arise from the excitation of electron-hole pairs and from the subsequent relaxation of these pairs by spin-dependent scattering processes, which transfer angular momentum to the lattice. By effective field theories (generalized breathing and bubbling Fermi-surface models) it is shown that the Gilbert equation of motion, which is often used to describe the fast dissipative magnetization dynamics, must be extended in several aspects. The basic assumptions of the Elliott-Yafet theory, which is often used to describe the ultrafast spin relaxation after laser-pulse irradiation, are discussed very critically. However, it is shown that for Ni this theory probably yields a value for the spin-relaxation time T(1) in good agreement with the experimental value. A relation between the quantity α characterizing the damping of the fast dynamics in simple situations and the time T(1) is derived.

Measurement of electron spin lifetime and optical orientation efficiency in germanium using electrical detection of radio frequency modulated spin polarization

We propose and demonstrate a technique for electrical detection of polarized spins in semiconductors in zero applied magnetic fields. Spin polarization is generated by optical injection using circularly polarized light which is modulated rapidly using an electro-optic cell. The modulated spin polarization generates a weak time-varying magnetic field which is detected by a sensitive radio-frequency coil. Using a calibrated pickup coil and amplification electronics, clear signals were obtained for bulk GaAs and Ge samples from which an optical spin orientation efficiency of 4.8% could be determined for Ge at 1342 nm excitation wavelength. In the presence of a small external magnetic field, the signal decayed according to the Hanle effect, from which a spin lifetime of 4.6±1.0  ns for electrons in bulk Ge at 127 K was extracted.

Introduction to spin-polarized ballistic hot electron injection and detection in silicon

Ballistic hot electron transport overcomes the well-known problems of conductivity and spin lifetime mismatch that plague spin injection attempts in semiconductors using ferromagnetic ohmic contacts. Through the spin dependence of the mean free path in ferromagnetic thin films, it also provides a means for spin detection after transport. Experimental results using these techniques (consisting of spin precession and spin-valve measurements) with silicon-based devices reveals the exceptionally long spin lifetime and high spin coherence induced by drift-dominated transport in the semiconductor. An appropriate quantitative model that accurately simulates the device characteristics for both undoped and doped spin transport channels is described; it can be used to recover the transit-time distribution from precession measurements and determine the spin current velocity, diffusion constant and spin lifetime, constituting a spin 'Haynes-Shockley' experiment without time-of-flight techniques. A perspective on the future of these methods is offered as a summary.

Spin-orbit symmetries of conduction electrons in silicon

We derive a spin-dependent Hamiltonian that captures the symmetry of the zone edge states in silicon. We present analytical expressions of the spin-dependent states and of spin relaxation due to electron-phonon interactions in the multivalley conduction band. We find excellent agreement with experimental results. Similar to the usage of the Kane Hamiltonian in direct band-gap semiconductors, the new Hamiltonian can be used to study spin properties of electrons in silicon.

Theory of spin-dependent phonon-assisted optical transitions in silicon

Silicon is an ideal material choice for spintronics devices due to its relatively long spin relaxation time and mature technology. To date, however, there are no parameter-free methods to accurately determine the degree of spin polarization of electrons in silicon. This missing link is established with a theory that provides concise relations between the degrees of spin polarization and measured circular polarization for each of the dominant phonon-assisted optical transitions. The phonon symmetries play a key role in elucidating recent spin injection experiments in silicon.

Electrical creation of spin polarization in silicon at room temperature

The control and manipulation of the electron spin in semiconductors is central to spintronics, which aims to represent digital information using spin orientation rather than electron charge. Such spin-based technologies may have a profound impact on nanoelectronics, data storage, and logic and computer architectures. Recently it has become possible to induce and detect spin polarization in otherwise non-magnetic semiconductors (gallium arsenide and silicon) using all-electrical structures, but so far only at temperatures below 150 K and in n-type materials, which limits further development. Here we demonstrate room-temperature electrical injection of spin polarization into n-type and p-type silicon from a ferromagnetic tunnel contact, spin manipulation using the Hanle effect and the electrical detection of the induced spin accumulation. A spin splitting as large as 2.9 meV is created in n-type silicon, corresponding to an electron spin polarization of 4.6%. The extracted spin lifetime is greater than 140 ps for conduction electrons in heavily doped n-type silicon at 300 K and greater than 270 ps for holes in heavily doped p-type silicon at the same temperature. The spin diffusion length is greater than 230 nm for electrons and 310 nm for holes in the corresponding materials. These results open the way to the implementation of spin functionality in complementary silicon devices and electronic circuits operating at ambient temperature, and to the exploration of their prospects and the fundamental rules that govern their behaviour.