Spin scattering in nonmagnetic semiconductors

Transcription

1 Spin scattering in nonmagnetic semiconductors

2 Spin state Wave function: ψ Spin densit matri: ρ ψ OR, s ϕ, ϕ, ρ ρ, s ψ, s ρ ρ In general, it should be ρ, ; s, s Use Wigner s function to get ρ K, R; s, s Spin polariation vector: r P, P, P P ρ s 1 1 P P ip P ip 1P

3 Local spin polariation Number of electrons: Nn ΔV Magnetic moment: MN μ B P Z 0 ΔV 0 Y 0 X

4 Spin polariation vector P 1 P P Z t Z P Spin polariation P 1 P 3 P 4 Y P Z volution of spin polariation Z ω P Z t X Bloch equation: r dp dt P 5 r r 1 r r 1 r γp B P T T 1 P P0 X Y Spin scattering is here Toda we tal about T 1 processes

5 volution of spin polariation vector Interaction with magnetic field H μh gμ B SH μ B J/T No scattering! Pure dephasing. P T * instead of T T 1 remains the same P ϕ ωt t H t P t

6 Spin scattering T 1 processes We have to define basis for spin and. Use small magnetic field. Spin-orbit interaction lliot-yafet mechanism D aonov-perel mechanism Hperfine interaction with nuclear spins change with holes Bir-Aronov-Pius No direct interaction with phonons & non-magnetic impurities.

7 Spin flip vs. spin precession Tpe I ', ',, OR, hν Impurit Phonon Tpe II hω phonon S r r r S r Initial state Final state Impurit

8 lectron-hole echange Important in p-tpe semiconductors change Hamiltonian: H ech AJSδ r lectron Hperfine interaction Hole momentum and J can rela Hperfine Hamiltonian: H r Hf ASIδ r lectron Suppressed in strong magnetic fields Nucleus

9 Spin states:, lliott-yafet mechanism " ", mies pure spin up and down states " " r r 3/ ir," " L e u v r r 3/ ir," " L e u' v' An momentum scattering can result in a spin flip. ', ',,, hν Impurit Phonon

10 Spin-orbit interaction: H D aonov-perel mechanism SO Crstals without a center of inversion { } α Γ As Ga hω phonon S r r r S r Initial state Final state Impurit

11 D-P scattering in a device structure, eample Region is studied GaAs S Fe V n Fe GaAs n qφ α α α Γ L X B 0.7 ev 8 evα evα evα 1 μm

12 1.0 Potential Profile, Vds V Potential, V X, μm

13 Model for Monte-Carlo simulation Charge transport BT: f t q v f V h V e ε s n r N f f t d C Spin densit matri evolution: ρ t i dt e ih SO dt / SO ρ t e h ih dt / h i Spin scattering mechanism: H R η H D β < >

14 ρ ρ φ B q h h h / / / * * * m m m ± ± Injection Mechanisms q φ B fm c fs ev bias Thermionic mission: B q φ > & spin is conserved

15 Injection Mechanisms Tunneling through the Schott barrier: Tunneling probabilit: WKB approimation T tp ep h tp 0 m * [ < qφ c B ] d q φ B c tp 0 0 ± * m / h fm ρ e iφ ρ e iφ ± * m / h ev bias tp c fs

16 T T B fm B fm e e f / / ~ 1 1 lectron distribution function: qual average inetic energ in, and directions lectrons at the Ferromagnetic Contact Probabilities of spin states are based on the densities of states P P D D D P 1 and

17 Spin-orbit couplings in 3 valles of bul GaAs 1. valle 000. L valles 3. X valles { } SO H Γ α { } { } { } { } 3 / 3 / 3 / 3 / L L L L SO H α α α α X X X SO H α α α ± ± ±1 Dresselhaus Mechanism

18 T 300 K, V V Carrier Concentration concentration, m Γ valle L valle X valle X, um The etremel high electric field at the Schott barrier pumps the electrons onto up valles, especiall the X valle

19 T 300 K, V V Current Spin Polariation 1.0 Current polariation Γ valle L valle X valle X, μm Spin dephasing is much stronger in upper valles due stronger SO coupling

20 T 300 K, V 0.5 V Low bias Carrier Concentration 116 Concentratoin m Gamma L X valle X, um

21 T 300 K, V 0.5 V Current Spin Polariation 1.0 Current spin polariatoin Gamma L X X, um

22 Low temperature T 80 K, V V Carrier Concentration Γ valle L valle X valle concentration, m X Ais Title

23 Low temperature T 80 K, V V Current Spin Polariation 1.0 Current polariation Γ valle L valle X valle X, μm

24 Spin-LD h ν Spin Polariing contact n-algaas GaAs QW p-algaas CB X/ K D o ħω e 1 ħω A - h 1 AlGaAs p A 0 VB p-gaas GaAs 001 AlGaAs n GaAs M. Yasar, PhD Thesis

25 lectroluminescence 1,0,0 Spin-LD R. Mallor, et. al., Phs. Rev. B 73, Sample 1 L Intensit arb.u CB A T 6 K L Spectra X a X Bul nerg cm -1 L Intensit arb.u Sample 1 T 6 K Δ~84 cm -1 TA phonon at X L Spectra X a X Bul Polariation % Sample 1 T 6 K Feature X Feature a nerg cm Magnetic Field T

26 Spin-LD lectroluminescence 1,1,0 L Intensit arb.u Sample 3 T 6 K L Spectrum X a ' X Bul Bul feature Δ~105 cm -1 ~ phonon at K nerg cm -1

27 Questions?