Mapping spins and light in semiconductors

Vanessa SihPhysics Department

University of MichiganUniversity of Michigan

November 9, 2012

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 andB. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Physical Review B 82, 081304(R) (2010)C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Optics Express 19, 14845 (2011)

Topic 2: Mapping light (from site-controlled quantum dots)

Provides a challenge for scalability of quantum dots as elements for quantum information processing

Quantum dots typically nucleate at stochastic locations

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, 285305 (2009)

Topic 2: Mapping light (from templated quantum dots)

Luminescence from individual

Spatially-resolved micro-photoluminescence measurements of stacked layers of quantum dots grown on a templated hole array

Growth method to control QD

Luminescence from individual dots with 160 µeV linewidth

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, 269-271 (2011).

Jieun Lee, Timothy W. Saucer, Andrew J. Martin, Deborah Tien, Joanna M.

A. J. Martin, T. W. Saucer, G. V. Rodriguez, V. Sih, and J. M. Millunchick, Nanotechnology 23, 135401 (2012).

yMillunchick and Vanessa Sih, Nano Letters 11, 1040-1043 (2011).

Spin is an intrinsic property of particles postulated by George

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 Goudsmitcirca 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, 264-265 (1926)

circa 1928 in Ann Arbor, Michigan (from Wikipedia)

Why study electron spins?

Can we use spins to encode information?

Enabling new technologies for information processing and communication

p

Spin 1/2 in a magnetic fieldSz = +1/2

Sz = -1/2HB = g B B · S ћωL = ΔE = gµBB

Sz 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

Progress in (Metal) Spintronics, or Magnetoelectronics

In 1988 Giant Magnetoresistance (GMR) was independently discovered by

Ferromagnetic Metals

In 1988, Giant Magnetoresistance (GMR) was independently discovered by groups led by Peter Grunberg and Albert Fert in Fe/Cr multilayers

E

EF M FM NM FMFM NM FMSpin-valve GMR

DOS DOS M MM M

~1 nm Low RHigh R

Commercial GMR field sensors available in 1994, and GMR hard drive read heads were announced in 1997 and available in 2000

9 $

Fert and Grunberg were awarded the 2007 Nobel Prize in Physics “for the discovery of Giant Magnetoresistance”GMR or TMR now used in all current hard drive read heads, 109 $/yr

A good review on magnetoelectronics: G. A. Prinz, Science 282, 1660 (1998)

Physics for the discovery of Giant Magnetoresistance

Why semiconductors?

M k b t t !More knobs to turn!

Knobs = carrier density, mobility, energy, confinement dopants etcconfinement, dopants, etc.

-> tunable electrical and optical (and spin/magnetic) propertiesspin/magnetic) properties

“The Physics of Low-Dimensional Semiconductors: An Introduction” by John H. Davies

Image from Evident Tech.

Introducing spin polarization into semiconductors

Appl a large magnetic fieldApply a large magnetic field

ћωL = ΔE = gµBB = 0.03 meV/T kBT = 0.1 meV/K

Inject spin-polarized carriers from a magnetic metal

Make a magnetic semiconductorMake a magnetic semiconductor

Use circularly polarized light

Optical orientation of spin polarization in semiconductors

Selection Rules (near k = 0)

cbEBand structure (near k = 0)

Eg

hhlhsh

k

0 k

Circularly polarized light allows us to prepare electron spin polarization ith 50% ffi i

Similarly, spin polarization can be detected during recombination through circularly-polarized luminescence

with ~50% efficiency

circularly polarized luminescence

F. Meier, B. P. Zakharchenya, eds., Optical Orientation (Elsevier, Amsterdam, 1984)

Establishing electron spin coherence

B zB

100 fs76 MHzTi:Sapphire

yx

pumpSx

III V semiconductor1) A circularly-polarized laser pulse establishes electronic spin polarization

III-V semiconductor

C.B.

V.B.

equilibrium excitation

time

Coherent precession of electron spins

B zB

100 fs

zy

xsz = -1/2

ћωL = ΔE = gµBB

pump

Zeeman split levels

sz = +1/2E

L

2) Electron spin polarization precesses about the applied magnetic field

Zeeman-split levels

time

recombination & precession (1st ~100ps) precession

Time-resolved Faraday rotationF Mx SxB

100 fs Faraday Rotation

pump

probet

F L2

3) Linearly-polarized probe pulse measures the spin polarization at time ∆t

t

t) y p p p p p

Absorption Refractive Index

Optically probe precession + -

EnergyS. A. Crooker et al., Phys. Rev. B 56, 7574 (1997)

Time-resolved Faraday rotation

( ) exp( / ) cos( / )t A t g Bt

Spin splittings due to the spin-orbit interaction

H = HB + HSO = gµBB · S + (ћ/4m2c2)( V × p) · SΔ

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

Spin splittings due to the spin-orbit interaction

What makes spin “up” different than spin “down”?

Why would they have different energies?y y g

Space inversion symmetry: E(k, ↑) = E(-k, ↑)

Time reversal symmetry: E(k, ↑) = E(-k, ↓)

E(k ↑) E(k ↓) E(k, ↑) = E(k, ↓)

Spin-orbit interaction in zincblende semiconductors

B lk i i t (BIA)Bulk inversion asymmetry (BIA):

Due to lack of inversion symmetry in zincblende crystal

G. Dresselhaus, Phys. Rev. 100, 580 (1955)

Due to lack of inversion symmetry in zincblende crystal

Ga As

Structural inversion asymmetry (SIA)Y A B hk d E I R hb J Ph C 1 6039 (1984)

Bychkov-Rashba splitting in asymmetric quantum wells, heterojunctions

Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984)

Spin-splitting depends on asymmetry of the structure and is voltage tunable

Strain-induced spin-orbit splitting

strain

id i t i

Strain can distort the crystal lattice and introduce asymmetry.

side view

z

top viewV

100 m

2m AlGaAs stressor2m n-GaAs

AlGaAsGaAs channel

SI-GaAs substrate

substrate

contact contactwindow

Ez

Strain in lattice-mismatched heterostructures

Different atoms have different sizes, and different materials have different lattice constants.

Indium arsenide (InAs) has a largerIndium arsenide (InAs) has a larger lattice constant than gallium arsenide (GaAs)

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

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,Y. Kato, R. C. Myers, A. C. Gossard and D. D. Awschalom, Nature 427, 50 (2004)

S. A. Crooker and D. L. Smith, Phys. Rev. Lett. 94, 236601 (2005)

Measuring the effective magnetic field

totB

*2

FtBgcos

TtexpA

ћ

resonant spin amplificationPRL 80, 4313 (1998)(summation of consecutive pulses, )

t=13.1ns

E 0

zBext

( p ,i.e., t = 13.1 ns, 26.2 ns, 39.3 ns, …)

atio

n (a

.u.

0

z

Bext //Bint

E=0

intexttot BBB

arad

ay ro

ta

0z

E

2int

2exttot BBB

Fa

0Bext // E

z

Bint

Bext (mT)0 25-25

Y. Kato et al., Nature 427, 50 (2004)

Measurements on a series of lattice-mismatched InGaAs

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

βSIA = (β[110] + β[110])/2βBIA = (β[110] – β[110])/2

Y. Kato et al., Nature 427, 50 (2004)

Measured strain and spin splittings do not have a straightforward dependence.

St i b k i i t d i t d t k li i litti

Spin-orbit interaction in strained bulk semiconductors

Strain breaks inversion symmetry and introduces two k-linear spin splitting terms: one depends on biaxial strain, and the other depends on shear strain

1 ( )( )zz xx x x y yH D k k

Thought to be small (higher order term)

3 ( )xyCH k k

32 ( )

2xy

x y y xH k k

B. A. Bernevig and S.-C. Zhang, Physical Review B 72, 115204 (2005)

Measurements on coherently-strained InGaAs

We can minimize the inhomogeneous effects of strain relaxation byWe 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 the BIA and SIA-type terms by

y

e ca sepa ate t e a d S type te s bymeasuring channels oriented along [100] and [010], where these fields are perpendicular

Measurements on coherently-strained InGaAs

Measurements of Faraday rotation for the [010] channel at T = 30 KMeasurements of Faraday rotation for the [010] channel at T 30 K

Black: 0.0 VRed: 1.0 VRed: 1.0 VGreen: 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, 081304(R) (2010)

Measurements on coherently-strained InGaAs

Bint parallel to kBint perpendicular to k Bint parallel to kBint perpendicular to k

Summary of measurements on strained InGaAs

SIABIA

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, 081304(R) (2010)

great quantitative agreement with [100] and [010] measurements

Summary of measurements on strained InGaAs

1 ( )( )zz xx x x y yH D k k 32 ( )

2xy

x y y x

CH k k

2From measurements on [010] and [100] channels:

~83-111 neV ns µm-1~34-40 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, 081304(R) (2010)

Not small!

Introducing spin polarization into semiconductors

Appl a large magnetic fieldApply a large magnetic field

ћωL = ΔE = gµBB = 0.03 meV/T kBT = 0.1 meV/K

Inject spin-polarized carriers from a magnetic metal

Make a magnetic semiconductorMake a magnetic semiconductor

Use circularly polarized light

Apply an electric field

Experimental measurements of spin polarization

Measure spin polarization using p gFaraday rotation due to electric field.

No optical pumping!

Current-induced spin polarization

Detect spins using static Faraday rotationunder DC bias (no optical pumping)

B 0E=5 mV m-1

BS0Bint

0

0

E=10 mV m-1

V=V0

60m

V=0Elaser spot

FR (a

.u.)

0 E=15 mV m-1

200mstrained In0.07Ga0.93As epilayer

F0 E=20 mV m-1

[001][110] 0 25 50-25-50

[110]B (mT)

Y. Kato et al., Phys. Rev. Lett. 93, 176601 (2004)

Current-induced spin polarization

i/d

Assuming constant spin orientation rate, signal is expected to be

0E=5 mV m-1

sin/exp

el

0

τω

tωtγdt

L

L

S0 0

0

E=10 mV m-1

12

τωL Bint

FR (a

.u.)

0 E=15 mV m-1

BlaserF

0 E=20 mV m-1

laser

sample

This model assumes that spins are 0 25 50-25-50

Y. Kato et al., Phys. Rev. Lett. 93, 176601 (2004)

always polarized along effective magnetic field (not equilibrium polarization picture)

B (mT)

Current-induced spin polarization

0E=5 mV m-1

From Faraday rotation amplitude, determine the electrically-generated spin density as a function of electric

0

0

E=10 mV m-1

field.

From the spin density and lifetime as

FR (a

.u.)

0 E=15 mV m-1

η (μm-2 V-1 ns-1)

a function of electric field, determine the electrical spin generation efficiency:

F0 E=20 mV m-1

However, the mechanism is still an

η (μm V ns )

0 25 50-25-50

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

Y. Kato et al., Phys. Rev. Lett. 93, 176601 (2004)

B (mT)p p g

parameters.

Results from Kato et al.

P iPrevious measurements on a series of lattice-mismatched InGaAsmismatched InGaAs(7% In, 93% Ga) heterostructureswith channels alongwith channels along [110] and [110]

Y. K. Kato et al., Phys. Rev. Lett. 93, 176601 (2004)(2004)

Results from previous measurements

0 6

0.7

Kato [110]Kato [1-10]nc

y

0.5

0.6 Kato [1 10]

on e

ffici

en-1

)

0.3

0.4

gene

ratio

m-2

V-1

ns-

0.1

0.2

ical

spi

n g

η(μ

m

-30 0 30 60 90 120-0.1

0.0

Ele

ctri

-30 0 30 60 90 120 Measured spin splitting coefficient

β (neV ns μm-1)Y. K. Kato et al., Phys. Rev. Lett. 93, 176601 (2004)

Comparison with previous measurements

0 6

0.7

Kato [110]Kato [1-10]nc

y

0.5

0.6 Kato [1 10] Norman (100) Norman (110) linear fit to Norman (100)

on e

ffici

en-1

)

0.3

0.4

gene

ratio

m-2

V-1

ns-

Measurements on [100] and [010] channels appear to show that spin

0.1

0.2

ical

spi

n g

η(μ

m appear to show that spin generation efficiency increases with spin splitting…

-30 0 30 60 90 120-0.1

0.0

Ele

ctri splitting…

But [110] and [1-10]???

-30 0 30 60 90 120 Measured spin splitting coefficient

β (neV ns μm-1)

Topic 2: Mapping light (from templated quantum dots)

Luminescence from individual

Spatially-resolved micro-photoluminescence measurements of eleven stacked layers of quantum dots grown on a templated hole array

Growth method to control QD

Luminescence from individual dots with 160 µeV linewidth

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, 269-271 (2011).

Jieun Lee, Timothy W. Saucer, Andrew J. Martin, Deborah Tien, Joanna M.

A. J. Martin, T. W. Saucer, G. V. Rodriguez, V. Sih, and J. M. Millunchick, Nanotechnology 23, 135401 (2012).

yMillunchick and Vanessa Sih, Nano Letters 11, 1040-1043 (2011).

Quantum dots

Size-dependent optical properties

Example: chemically-synthesized

Atomic force microscope image of self-assembled InAs quantum dots grown on GaAsExample: chemically synthesized

quantum dots in solutiongrown on GaAs

Image from Evident Tech.

T. Yoshie et al., Nature 432, 200 (2004)

Growth of self-assembled quantum dots

Morphology depends on microscopic processes: deposition, surface diffusion, nucleation, evaporationp

http://pil.phys.uniroma1.it/twiki/bin/view/Pil/IrregularSurfaces

Quantum dots as “atoms”

Discrete energy levelsDiscrete energy levels

Atom Quantum Dot

∆ Eatom (~ eV)∆ EQD (~ meV)

~ 1 Å ~ 20 ‒ 500 Å

Ground and excited state excitons

Image from Evident Tech.Eg E1 E2

D. Dalacu, et al., Phys. Rev. B 82, 033301 (2010)

Quantum dots for quantum information processing

Q d i i lid biQuantum dots are promising 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 operationLong 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).

Controlled coupling of QDs using an optical cavity

Proposed by Imamoglu et alProposed 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)

strength depends on position!

Integration of QDs into photonic crystal cavities

2223 )( E

2

max

22

2

2

3

)()()(

)(44)/(3

rEdrEd

E

rEVnQ

cce

c

effcavity

free

Purcell factor

detuning “position” orientation

Planar photonic crystal enables design of cavities and waveguides, with the potential for building a quantum network

Templated quantum dots for quantum information processing

Pre-pattern substrate with holes using an in vacuo focused-ion beam

500 nm 500 nm500 nm 500 nm

Deposit InAs Quantum dot nucleation occurs at the hole sites and is belowDeposit 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, 285305 (2009)

Imaging of FIB-templated individual quantum dotsen

sity

0.1 nm 891

892

PL p

eak

(nm

)

Scanning micro-photoluminescence spectroscopy of multilayer sample

S f

PL in

te

10 20 30 40 50 P

T (K)-Standard confocal collection

~1 µm lateral and axial and 0.05 nm spectral resolution

888 890 892 894 896 898 900Wavelength (nm)

y-0.1 nm (160 µeV) QD linewidth

-Can determine peak position with greater accuracy than spatial resolution

peak

inte

nsity

-2 -1 0 1 2

PL p

Horizontal position (um)

J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, 1040-1043 (2011).

Optical mapping of FIB-templated quantum dots

Scanning micro-photoluminescence spectroscopy

S f-Standard confocal collection~1 µm lateral and axial and 0.05 nm spectral resolution

Two dots with similar wavelength and desired spacing at 898.8 nm!

J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, 1040-1043 (2011).

and desired spacing at 898.8 nm!

Optical mapping of FIB-templated quantum dots

Collect statistics over a 10 x 10 micron area containing 26 optically-activeCollect statistics over a 10 x 10 micron area containing 26 optically-active QDs (870-950 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, 1040-1043 (2011).

Emission dynamics of dots in a cavity

For all optical switching quantum dots offer a system with a highly non linear

Investigate the emission dynamics of dots by varying the time delay between

For all-optical switching, quantum dots offer a system with a highly non-linear optical response

g y y y g ytwo pulses. The signal depends on the non-linearity of the emission.

delay

Pulsed laser

yline

sample

Spectrometer/CCDsignal

objective lenscryostat

beam-splitter

signal

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick and V. Sih, in review (2012)

The dynamics reveal the Purcell effect of the cavity on the exciton lifetime.

SummarySpin-orbit splittings in semiconductors can be used to electrically manipulate spin polarization

Separately measure isotropic splitting due to uniaxialstrain and anisotropic splitting due to biaxial strain

to electrically manipulate spin polarization.

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 081304(R) (2010)

FIB patterning results in at least 65%

Physical Review B 82, 081304(R) (2010).C. J. Trowbridge, B. M. Norman, J. Stephens, A. C. Gossard, D. D. Awschalom and V. Sih, Optics Express 19, 14845-14851 (2011).

FIB-patterning results in at least 65% of sites with an optically-active QD

Promising technique to control QD

T. W. Saucer, J.-E. Lee, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih,

position, size, homogeneity for building a scalable quantum network

Solid State Communications 151, 269-271 (2011).

J. Lee, T. W. Saucer, A. J. Martin, D. Tien, J. M. Millunchick and V. Sih, Nano Letters 11, 1040-1043 (2011).