Mapping spins and light in semiconductors. Vanessa Sih Physics Department

Transcription

1 Mapping spins and light in semiconductors Vanessa Sih Physics Department University of Michigan November 9, 2012

2 Topic 1: Mapping spins (spin transport and spin-orbit effects) Time and spatially resolved electron spin transport is used to measure the magnitude and direction of spin-orbit effects. Applications include electrical generation and manipulation of electron spin polarization. B M Norman C J Trowbridge J Stephens A C Gossard D D Awschalom and B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Physical Review B 82, (R) (2010) C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Optics Express 19, (2011)

3 Topic 2: Mapping light (from site-controlled quantum dots) Quantum dots typically nucleate at stochastic locations Provides a challenge for scalability of quantum dots as elements for quantum information processing 500 nm 500 nm Focused-ion-beam patterning enables the preferred nucleation of quantum dots at particular locations J. Y. Lee, M. J. Noordhoek, P. Smereka, H. McKay and J. M. Millunchick, Nanotechnology 20, (2009)

4 Topic 2: Mapping light (from templated quantum dots) Spatially-resolved micro-photoluminescence measurements of stacked layers of quantum dots grown on a templated hole array Luminescence from individual dots with 160 µev linewidth Growth method to control QD position, size(?), homogeneity(?); effects of patterning on optical and structural properties Applications: local patterning of material optical properties; for quantum information processing, scalability to many QD qubits T. W. Saucer, J.-E. Lee, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Solid State Communications 151, (2011). Jieun Lee, Timothy W. Saucer, Andrew J. Martin, Deborah Tien, Joanna M. Millunchick and Vanessa Sih, Nano Letters 11, (2011). A. J. Martin, T. W. Saucer, G. V. Rodriguez, V. Sih, and J. M. Millunchick, Nanotechnology 23, (2012).

5 A brief history of spin Spin is an intrinsic property of particles, postulated by George Uhlenbeck and Samuel Goudsmit (then graduate students) in 1925 to explain puzzling features observed in hydrogen and x-ray spectra George Uhlenbeck, Hendrik Kramers, and Samuel Goudsmit circa 1928 in Ann Arbor, Michigan (from Wikipedia) G. E. Uhlenbeck and S. Goudsmit, Naturwissenschaften 47, 953 (1925); Spinning Electrons and the Structure of Spectra, Nature 117, (1926)

6 Why study electron spins? Enabling new technologies for information processing and communication Can we use spins to encode information? Spin 1/2 in a magnetic field H B = g B B S ћω L = ΔE = gµ B B S z = +1/2 S z =-1/2 Spintronics: spin transport electronics potential to integrate logic (transistors) and magnetic storage and - potential to integrate logic (transistors) and magnetic storage and offer new device functionality, possibly with lower power dissipation

7 Progress in (Metal) Spintronics, or Magnetoelectronics In 1988, Giant Magnetoresistance (GMR) was independently discovered by groups led by Peter Grunberg and Albert Fert in Fe/Cr multilayers Ferromagnetic Metals E Spin-valve GMR E F M FM NM FM FM NM FM DOS DOS M M M M ~1 nm High R Low R Commercial GMR field sensors available in 1994, and GMR hard drive read heads were announced in 1997 and available in 2000 Fert and Grunberg were awarded the 2007 Nobel Prize in GMR or TMR now Physics used for in all the current discovery hard of drive Giant read Magnetoresistance heads, 10 9 $/yr A good review on magnetoelectronics: G. A. Prinz, Science 282, 1660 (1998)

8 Why semiconductors? More knobs to turn! Knobs = carrier density, mobility, energy, confinement, dopants, etc. -> tunable electrical and optical (and spin/magnetic) properties Image from Evident Tech. The Physics of Low-Dimensional Semiconductors: An Introduction by John H. Davies

9 Introducing spin polarization into semiconductors Apply a large magnetic field ћω L = ΔE = gµ B B = 0.03 mev/t k B T = 0.1 mev/k Inject spin-polarized carriers from a magnetic metal Make a magnetic semiconductor Use circularly polarized light

10 Optical orientation of spin polarization in semiconductors Band structure (near k = 0) E cb Selection Rules (near k = 0) E g lh sh hh 0 k Circularly polarized light allows us to prepare electron spin polarization with ~50% efficiency i Similarly, spin polarization can be detected during recombination through circularly-polarized luminescence F. Meier, B. P. Zakharchenya, eds., Optical Orientation (Elsevier, Amsterdam, 1984)

11 Establishing electron spin coherence 76 MHz Ti:Sapphire 100 fs B y z x pump S x III-V semiconductor 1) A circularly-polarized laser pulse establishes electronic spin polarization C.B. V.B. equilibrium excitation time

12 Coherent precession of electron spins B y 100 fs pump z ћω L = ΔE = gµ B B x s z = -1/2 s z = +1/2 Zeeman-split levels 2) Electron spin polarization precesses about the applied magnetic field L E recombination & precession (1 st ~100ps) precession time

13 Time-resolved Faraday rotation B F M x S x 100 fs Faraday Rotation pump probe t 3) Linearly-polarized probe pulse measures the spin polarization at time t F 2 L t Absorption Refractive Index Optically probe precession + - Energy S. A. Crooker et al., Phys. Rev. B 56, 7574 (1997)

14 Time-resolved Faraday rotation () t Aexp( t/ )cos( gbt / )

15 Spin splittings due to the spin-orbit interaction H = H B + H SO = gµ B B S + (ћ/4m 2 c 2 )( V p) S Δ S k e - Spin-orbit coupling is the interaction of the electron spin and orbital angular momentum. Spin-orbit coupling introduces a momentum-dependent spin splitting that acts like an internal magnetic field

16 Spin splittings due to the spin-orbit interaction What makes spin up different than spin down? Why would they have different energies? Space inversion symmetry: E(k, ) = E(-k, ) Time reversal symmetry: E(k, ) = E(-k, ) E(k, ) = E(k, )

17 Spin-orbit interaction in zincblende semiconductors Bulk inversion i asymmetry (BIA): G. Dresselhaus, Phys. Rev. 100, 580 (1955) Due to lack of inversion symmetry in zincblende crystal Ga As Structural inversion asymmetry (SIA) Y. YA. Bychkov and de. I. Rashba, J. Phys. C 17, 6039 (1984) Bychkov-Rashba splitting in asymmetric quantum wells, heterojunctions Spin-splitting depends on asymmetry of the structure and is voltage tunable

18 Strain-induced spin-orbit splitting strain Strain can distort the crystal lattice and introduce asymmetry. side view V top view z 100 m 2m n-gaas 2m AlGaAs stressor SI-GaAs substrate contact z GaAs channel AlGaAs window substrate E contact

19 Strain in lattice-mismatched heterostructures Different atoms have different sizes, and different materials have different lattice constants. Indium arsenide (InAs) has a larger Indium arsenide (InAs) has a larger lattice constant than gallium arsenide (GaAs)

20 Lattice-mismatched heterostructures Growing InAs on a GaAs substrate will introduce biaxial compressive strain and tensile strain along the growth direction If the lattice mismatch is too large, dislocations will be energetically favored, and the InAs film will strain relax. Coherently strained/pseudomorphic Strain relaxed

21 Spatially-resolved Faraday rotation: time-resolved Dragging an optically-generated spin packet in gallium arsenide using electric fields reveals an effective internal magnetic field, or spin splitting Y. Kato,R.C.Myers,A.C.Gossard and S. A. Crooker and D. L. Smith, D. D. Awschalom, Nature 427, 50 (2004) Phys. Rev. Lett. 94, (2005)

22 Measuring the effective magnetic field F A exp t T * 2 cos g B tb ћ tot Fa araday rota ation (a.u. ) t=13.1ns resonant spin amplification B ext z PRL 80, 4313 (1998) (summation of consecutive pulses, E=0 i.e., t = 13.1 ns, 26.2 ns, 39.3 ns, ) B ext //B int z E B int z B ext // E B B tot tot B ext B B 2 ext int B 2 int B ext (mt) Y. Kato et al., Nature 427, 50 (2004)

23 Previous measurements on (partially) strain-relaxed samples Measurements on a series of lattice-mismatched InGaAs (7% In, 93% Ga) heterostructures with channels along [110] and [110] BIA SIA β BIA = (β[110] β[110])/2 β SIA = (β[110] + β[110])/2 Measured strain and spin splittings do not have a straightforward dependence. Y. Kato et al., Nature 427, 50 (2004)

24 Spin-orbit interaction in strained bulk semiconductors Strain breaks inversion i symmetry and introduces two k-linear spin splitting terms: one depends on biaxial strain, and the other depends on shear strain H1 D( zz xx )( xkx yky) Thought to be small (higher order term) C3 2 ( ) 2 3 xy H x ky y kx B. A. Bernevig and S.-C. Zhang, Physical Review B 72, (2005)

25 Measurements on coherently-strained InGaAs We can minimize the inhomogeneous effects of strain relaxation by studying coherently strained, or pseudomorphic, films InGaAs epilayers with 4% In and 96% Ga on GaAs We can separate ate the BIA and SIA-type terms by measuring channels oriented along [100] and [010], where these fields are perpendicular

26 Measurements on coherently-strained InGaAs Measurements of Faraday rotation for the [010] channel at T = 30 K Black: 0.0 V Red: 1.0 V Green: 2.0V Both a parallel and perpendicular internal field is observed! B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Physical Review B 82, (R) (2010)

27 Measurements on coherently-strained InGaAs B int perpendicular to k B int parallel to k

28 Summary of measurements on strained InGaAs BIA SIA Consistent with sum and difference of [110] and [110] measurements, but not great quantitative agreement with [100] and [010] measurements B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Physical Review B 82, (R) (2010)

29 Summary of measurements on strained InGaAs H1 D( zz xx )( xkx yky) C H k k 2 3 xy 2 ( x y y x) From measurements on [010] and [100] channels: ~34-40 nev ns µm -1 ~ nev ns µm -1 Not small! B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Physical Review B 82, (R) (2010)

30 Introducing spin polarization into semiconductors Apply a large magnetic field ћω L = ΔE = gµ B B = 0.03 mev/t k B T = 0.1 mev/k Inject spin-polarized carriers from a magnetic metal Make a magnetic semiconductor Use circularly polarized light Apply an electric field

31 Experimental measurements of spin polarization Measure spin polarization using Faraday rotation due to electric field. No optical pumping!

32 Current-induced spin polarization Detect spins using static Faraday rotation under DC bias (no optical pumping) B int V=V 0 laser spot S 0 B E 200m V=0 60m strained In 0.07 Ga 0.93 As epilayer FR (a.u.) E=5 mv m -1 0 E=10 mv m E=15 mv m-1 0 E=20 mv m -1 [001] [110] [110] B (mt) Y. Kato et al., Phys. Rev. Lett. 93, (2004)

33 Current-induced spin polarization Assuming constant spin orientation rate, signal is expected to be dt 0 γ exp ω el τ L 2 τ 1 ω L t / sin ω t L 0 S 0 0 Bint FR (a.u.) 0 E=5 mv m -1 E=10 mv m -1 E=15 mv m-1 laser B 0 E=20 mv m -1 sample This model assumes that spins are always polarized along effective magnetic field (not equilibrium polarization picture) B (mt) Y. Kato et al., Phys. Rev. Lett. 93, (2004)

34 Current-induced spin polarization From Faraday rotation amplitude, determine the electrically-generated spin density as a function of electric field. 0 E=5 mv m -1 From the spin density and lifetime as a function of electric field, determine the electrical spin generation efficiency: η (μm -2 V -1 ns -1 ) FR (a.u.) 0 0 E=10 mv m -1 E=15 mv m-1 However, the mechanism is still an open question, and we still need to determine how this effect depends on the spin-orbit splitting and other parameters. 0 E=20 mv m B (mt) Y. Kato et al., Phys. Rev. Lett. 93, (2004)

35 Results from Kato et al. Previous measurements on a series of lattice- mismatched InGaAs (7% In, 93% Ga) heterostructures with channels along [110] and [110] Y. K. Kato et al., Phys. Rev. Lett. 93, (2004)

36 Results from previous measurements ncy on efficien -1 ) generatio m -2 V -1 ns - ical spin g η (μm Electri Measured spin splitting coefficient β (nev ns μm -1 ) Kato [110] Kato [1-10] 10] Y. K. Kato et al., Phys. Rev. Lett. 93, (2004)

37 Comparison with previous measurements ncy on efficien -1 ) generatio m -2 V -1 ns - ical spin g η (μm Electri Measured spin splitting coefficient β (nev ns μm -1 ) Kato [110] Kato [1-10] 10] Norman (100) Norman (110) linear fit to Norman (100) Measurements on [100] and [010] channels appear to show that spin generation efficiency increases with spin splitting But [110] and [1-10]???

38 Topic 2: Mapping light (from templated quantum dots) Spatially-resolved micro-photoluminescence measurements of eleven stacked layers of quantum dots grown on a templated hole array Luminescence from individual dots with 160 µev linewidth Growth method to control QD position, size(?), homogeneity(?); effects of patterning on optical and structural properties Applications: local patterning of material optical properties; for quantum information processing, scalability to many QD qubits T. W. Saucer, J.-E. Lee, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Solid State Communications 151, (2011). Jieun Lee, Timothy W. Saucer, Andrew J. Martin, Deborah Tien, Joanna M. Millunchick and Vanessa Sih, Nano Letters 11, (2011). A. J. Martin, T. W. Saucer, G. V. Rodriguez, V. Sih, and J. M. Millunchick, Nanotechnology 23, (2012).

39 Quantum dots Size-dependent optical properties Example: chemically-synthesized quantum dots in solution Atomic force microscope image of self-assembled InAs quantum dots grown on GaAs Image from Evident Tech. T. Yoshie et al., Nature 432, 200 (2004)

40 Growth of self-assembled quantum dots Morphology depends on microscopic processes: deposition, surface diffusion, nucleation, evaporation

41 Quantum dots as atoms Discrete energy levels Atom Quantum Dot E atom (~ ev) E QD (~ mev) ~ 1 Å ~ Å Ground and excited state excitons Image from Evident Tech. E g E 1 E 2 D. Dalacu, et al., Phys. Rev. B 82, (2010)

42 Quantum dots for quantum information processing Quantum dots are promising i solid-state qubits Requirements for quantum computing: Scalable physical system with well characterized qubits Ability to initialize the state of the qubit Long relevant decoherence times, much longer than gate operation A universal set of quantum gates A qubit-specific measurement capability D.P. DiVincenzo, Fort. der Phys. 48, 771 (2000).

43 Controlled coupling of QDs using an optical cavity Proposed by Imamoglu et al. Each QD can be selectively addressed, but all couple to a cavity mode. Challenge: self-assembled QDs form at random positions, but coupling strength depends on position! A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Physical Review Letters 83, 4204 (1999)

44 Integration of QDs into photonic crystal cavities free cavity 3Q( / n) 2 4 V eff E( r ) c ( e c ) c Emax ( ( ) d E r ( ) d E r 2 Purcell factor detuning position orientation Planar photonic crystal enables design of cavities and waveguides, with the potential for building a quantum network

45 Templated quantum dots for quantum information processing Pre-pattern substrate with holes using an in vacuo focused-ion beam 500 nm 500 nm Deposit InAs. Quantum dot nucleation occurs at the hole sites and is below the critical thickness outside of the patterned region J. Y. Lee, M. J. Noordhoek, P. Smereka, H. McKay and J. M. Millunchick, Nanotechnology 20, (2009)

46 Imaging of FIB-templated individual quantum dots PL inte ensity PL peak (nm) nm T (K) Scanning micro-photoluminescence spectroscopy of multilayer sample -Standard S confocal collection ~1 µm lateral and axial and 0.05 nm spectral resolution Wavelength (nm) -0.1 nm (160 µev) QD linewidth PL peak intensity -Can determine peak position with greater accuracy than spatial resolution Horizontal position (um) J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, (2011).

47 Optical mapping of FIB-templated quantum dots Scanning micro-photoluminescence spectroscopy -Standard S confocal collection ~1 µm lateral and axial and 0.05 nm spectral resolution Two dots with similar wavelength and desired spacing at nm! J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, (2011).

48 Optical mapping of FIB-templated quantum dots Collect statistics over a 10 x 10 micron area containing 26 optically-active QDs ( nm) At least 65% of sites contain an optically active quantum dot J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, (2011).

49 Emission dynamics of dots in a cavity For all-optical switching, quantum dots offer a system with a highly non-linear optical response Investigate the emission dynamics of dots by varying the time delay between two pulses. The signal depends on the non-linearity of the emission. delay line Pulsed laser sample cryostat objective lens beamsplitter signal Spectrometer/CCD The dynamics reveal the Purcell effect of the cavity on the exciton lifetime. J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick and V. Sih, in review (2012)

50 Summary Spin-orbit splittings in semiconductors can be used to electrically manipulate spin polarization. Separately measure isotropic splitting due to uniaxial strain and anisotropic splitting due to biaxial strain. B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Physical Review B 82, (R) (2010). C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Optics Express 19, (2011). FIB-patterning results in at least 65% of sites with an optically-active QD Promising technique to control QD position, size, homogeneity for building a scalable quantum network T. W. Saucer, J.-E. Lee, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Solid State Communications 151, (2011). J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, (2011).