Optical injection and detection of ballistic pure spin currents in Ge

Loren, Eric J.; Ruzicka, Brian A.; Werake, Lalani K.; Zhao, Hui; Driel, H. M. van; Smirl, Arthur L.

doi:10.1063/1.3222869

Cited by 40 publications

(41 citation statements)

References 18 publications

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“…26,27 Similar to direct band-gap semiconductors, optical orientation is an additional viable tool to investigate spin properties of electrons and holes in Ge. [28][29][30][31][32][33][34] Unlike silicon, optical orientation in Ge is efficient because of the energy proximity between the direct and indirect gaps. Spin-polarized electrons are first photoexcited to the Γ valley and then they relax via ultrafast spin conserving scattering to the conduction band edges in one of the four L valleys (located ∼140 meV below the zone center Γ-valley).…”

Section: -18mentioning

confidence: 99%

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Intrinsic spin lifetime of conduction electrons in germanium

2012

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We investigate the intrinsic spin relaxation of conduction electrons in germanium due to electronphonon scattering. We derive intravalley and intervalley spin-flip matrix elements for a general spin orientation and quantify the resulting anisotropy in spin relaxation. The form of the intravalley spinflip matrix element is derived from the eigenstates of a compact spin-dependent k·p Hamiltonian in the vicinity of the L point (where thermal electrons are populated in Ge). Spin lifetimes from analytical integrations of the intravalley and intervalley matrix elements show excellent agreement with independent results from elaborate numerical methods.

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Section: -18mentioning

confidence: 99%

“…where c j,n are constants of order unity which denote contributions from the spin-orientation dependence (n) and from the overlap of conduction basis states in different valleys: (28) implies that the ratio between spin and momentum relaxation rates due to intervalley scattering is about ∆ …”

Section: L Point Hamiltonianmentioning

confidence: 99%

Intrinsic spin lifetime of conduction electrons in germanium

2012

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“…For the state after scattering, we choose q according to the distribution inside the integration in Eq. (11). The angle between q * and k * is determined by energy conservation, in which the electron loses the energy of ω pl 1 + (q * /β) 2 , and the azimuthal angle is completely random.…”

Section: Conditionmentioning

confidence: 99%

“…2,5,8 Only very recently, however, the quasi-direct behavior of Ge has sparked interest in its photonic properties, 9,10 and stimulated the use of various optical schemes aiming at addressing its spin physics. [11][12][13][14] In Ge, the absolute minimum of the conduction band (CB) is at the L point of the Brillouin zone, but there exists a local minimum at the zone-center Γ. At low temperature the former leads to an indirect energy gap of 0.744 eV, 15 the latter to a direct-gap of 0.898 eV.…”

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confidence: 99%

Spin and energy relaxation in germanium studied by spin-polarized direct-gap photoluminescence

et al. 2013

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Spin orientation of photoexcited carriers and their energy relaxation is investigated in bulk Ge by studying spin-polarized recombination across the direct band gap. The control over parameters such as doping and lattice temperature is shown to yield high polarization degree, namely larger than 40%, as well as a fine-tuning of the angular momentum of the emitted light with a complete reversal between right-and left-handed circular polarization. By combining the measurement of the optical polarization state of band-edge luminescence and Monte Carlo simulations of carrier dynamics, we show that these very rich and complex phenomena are the result of the electron thermalization and cooling in the multi-valley conduction band of Ge. The circular polarization of the direct-gap radiative recombination is indeed affected by energy relaxation of hot electrons via the X valleys and the Coulomb interaction with extrinsic carriers. Finally, thermal activation of unpolarized L valley electrons accounts for the luminescence depolarization in the high temperature regime.

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“…1,3,10,12,[21][22][23][24][25] Also, the silicon-based microfabrication technology is well-developed and extensively used. Germanium (Ge), as a group IV element adjacent to silicon, shares the good spin-decoherent property and is fully compatible with the existing mature nanoelectronic technology in silicon (Si).…”

Section: -20mentioning

confidence: 99%

Spin-dependent intravalley and intervalley electron-phonon scatterings in germanium

et al. 2013

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We investigate the spin-dependent electron-phonon scatterings of the L and Γ valleys and the band structure near the conduction band minima in germanium. We first construct a 16 × 16 k · p Hamiltonian in the vicinity of the L point in germanium, which ensures the correctness of the band structure of the lowest three conduction bands and highest two valence bands. This Hamiltonian facilitates the analysis of the spin-related properties of the conduction electrons. We then demonstrate the phonon-induced electron scatterings of the L and Γ valleys, i.e., the intra-Γ/L valley, inter-Γ-L valley and inter-L-L valley scatterings in germanium. The selection rules and complete scattering matrices for these scatterings are calculated, where the scattering matrices for the intra-Γ valley scattering, inter-Γ-L valley scattering and the optical-phonon and the separated transverse-acoustic-and longitudinal-acoustic-phonon contributions to the intra-Γ valley scattering have not been reported in the literature. The coefficients in these scattering matrices are obtained via the pseudo-potential calculation, which also verifies our selection rules and wave-vector dependence. We further discuss the Elliott-Yafet mechanisms in these electron-phonon scatterings with the k·p eigenstates at the L and Γ valleys. Our investigation of these electron-phonon scatterings are essential for the study of the optical orientation of spin and hot-electron relaxation in germanium.

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Optical injection and detection of ballistic pure spin currents in Ge

Cited by 40 publications

References 18 publications

Intrinsic spin lifetime of conduction electrons in germanium

Intrinsic spin lifetime of conduction electrons in germanium

Spin and energy relaxation in germanium studied by spin-polarized direct-gap photoluminescence

Spin-dependent intravalley and intervalley electron-phonon scatterings in germanium

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