Picosecond carrier spin relaxation in III-V compound semiconductors

Atsushi Tackeuchi Waseda University, Tokyo, Japan

Outline *Observation of spin relaxation *Spin relaxation mechanism *Spin relaxation time vs Band-gap energy *Applications Picoseconds all optical gate switch Influence on Vertical Cavity Surface Emitting Laser

Observation of spin relaxation

Spatial relation in transition from heavy hole to electron states

Generation of spin polarization using spin-orbit interaction

MQW Parallel spin

e

e

e Left circularly polarized light

Electron

Heavy hole

-1/2

-3/2

+1/2

+3/2

m j = e

GaAs QW

e

MQW Right circularly polarized light Anti-parallel spin

e

e

e

𝜎𝜎+ 𝜎𝜎−

Δ𝑚𝑚𝑗𝑗 = +1 𝜎𝜎+ 𝜎𝜎− Δ𝑚𝑚𝑗𝑗 = −1

Light hole -1/2 +1/2

𝜏𝜏𝑠𝑠 EC

EV

Population change of down- or up-spin carriers

MQW

After excitation of 100% down-spin carriers

Time

Car

rier p

opul

atio

n

0

N0/2

0

N0 Down-spin 100%

Up-spin 0%

50%

: spin relaxation time : recombination lifetime

Spin relaxation

Equilibrium condition

50 % up 50 % down

e e e e

100 % down Initial condition

e e e e

0 % up

𝜎𝜎+

𝜏𝜏𝑠𝑠 𝜏𝜏𝑟𝑟

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= −𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝜏𝜏𝑠𝑠

+ 𝑑𝑑𝑢𝑢𝑢𝑢𝜏𝜏𝑠𝑠

- 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝜏𝜏𝑟𝑟

Rate equation

𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 =𝑁𝑁02 1 + 𝑒𝑒−

𝑑𝑑𝜏𝜏𝑠𝑠/2

𝑁𝑁𝑢𝑢𝑢𝑢 =𝑁𝑁02 1 − 𝑒𝑒−

𝑑𝑑𝜏𝜏𝑠𝑠/2

𝜏𝜏𝑠𝑠

Solutions of rate eq.

The first time-resolved measurement of spin relaxation in III-V semiconductors

R. J. Seymour and R. R. Alfano, APL. 37 (1980) 231.

Spin relaxation time:

60 ps

Bulk-GaAs at 77 K 88 ± 34 ps

In 1990s, picoseconds carrier spin relaxation became observable.

Pump & Probe : A. Tackeuchi et al., APL. 56, 2213 (1990). Photoluminescence: T. C. Damen et al., APL. 58, 1902 (1991). Photoluminescence: M. Kohl et al., PR. B. 44, 5923 (1991).

R. J. Seymour and R. R. Alfano, APL. 37 (1980) 231.

Pump and probe measurements to investigate carrier dynamics

W. Lin, R. W. Schoenlein, J. G. Fujimoto, E. P. Ippen, IEEE JQE, 24, 267 (1988).

W. H. Knox et al., PRL 54, 1306 (1985).

In 1980s, time resolved measurements were dramatically improved.

The first time-resolved measurement of spin relaxation in III-V semiconductors

GaAs MQW

Pump pulse

Probe pulse

Time resolution is determined only by the convolution of optical pulses: ~ 1.5∆t.

Spin dependent pump and probe measurement

Pump pulse generates spin polarized electrons

Probe pulse detects population change of spin polarized electrons

𝜎𝜎+ 𝜎𝜎+

∆𝑡𝑡

∆𝜏𝜏

Ti :

Sapp

hire

lase

r

Photo- diode

Spin dependent pump and probe measurement Experimental setup

Sample

Beam splitter

Light chopper

100 fs

pump

Lock-in Amp.

Quarter Wave plate

probe

or

c: Speed of light

Time resolution～100 fs

∆𝑡𝑡 =2∆𝑥𝑥𝑐𝑐

∆𝑥𝑥 𝜎𝜎+

𝜎𝜎+

𝜎𝜎−

Observation of spin relaxation process for GaAs multiple quantum wells using spin-dependent pump and probe absorption measurement

A. Tackeuchi, S. Muto, T. Inata, and T. Fujii, APL. 56, 2213 (1990)

RT

-10 0 10 20 30 40 Time (ps)

Tran

smis

sion

(arb

.uni

ts)

Population change of down-spin carriers

Population change of up-spin carriers

Experiment

From exponential decay,

= 32 ps

Time

Car

rier p

opul

atio

n

0

N0/2

0

N0

Solutions of rate eq.

Symmetrical behavior of down-spin carrier decay and up-spin carrier accumulation is clearly observed.

Co- circularly polarized signal

Anti-circularly polarized signal

𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 =𝑁𝑁02 1 + 𝑒𝑒−

𝑑𝑑𝜏𝜏𝑠𝑠/2

𝑁𝑁𝑢𝑢𝑢𝑢 =𝑁𝑁02 1 − 𝑒𝑒−

𝑑𝑑𝜏𝜏𝑠𝑠/2

(𝜎𝜎+𝑢𝑢𝑢𝑢𝑝𝑝𝑢𝑢,𝜎𝜎+𝑢𝑢𝑟𝑟𝑑𝑑𝑝𝑝𝑝𝑝)

(𝜎𝜎+𝑢𝑢𝑢𝑢𝑝𝑝𝑢𝑢,𝜎𝜎−𝑢𝑢𝑟𝑟𝑑𝑑𝑝𝑝𝑝𝑝)

Spin relaxation mechanism

Spin relaxation mechanism

Elliott-Yafet process

D’yakonov-Perel’ process

Bir-Aronov-Pikus process

Spin flip by exchange interaction between electron and hole dominant at low temperature

dominant at room temperature

Spin flip by scattering related to band-mixing

Spin flip by effective magnetic field originating from spin-orbit splitting

M. I. D'yakonov and V. I. Perel’ : Sov. Phys. Solid State 13 (1972) 3023. M. I. D'yakonov and V. Yu. Kachorovskii : Sov. Phys. Semicond. 20 (1986) 110.

R. J. Elliott: Phys. Rev. 96, (1954) 266. Y. Yafet: Solid State Phys. 14 (1963) 1.

G. L. Bir, A. G. Aronov and G. E. Pikus: Sov. Phys. JETP 42 (1976) 705.

Temperature dependent

Temperature dependent

Temperature independent Carrier density dependent

Mechanism of Spin Relaxation

D'yakonov-Perel' process

k

E

Spin-flip by spin-orbit splitting

∆ E

Spin-orbit splitting

k 3 γ <110> =

Energy bands split dependent on spin by spin-orbit interaction. The energy difference works as an effective magnetic field. Spin relaxation depends on kinetic energy. It also depends on temperature.

M. I. D'yakonov and V. I. Perel’ : Sov. Phys. Solid State 13 (1972) 3023. M. I. D'yakonov and V.Yu. Kachorovskii : Sov. Phys. Semicond. 20 (1986) 110.

Elliott-Yafet process

Wave function of conduction band

k

E

S

,R - R + ,Z

k＝0

Spin flip probability by perturbing potential U(r)

Ψ Ψ k ' - U ( r ) k + 2

= {aU (r )S} 2

2

+ - e (

k z k R

+ - k k

Z 2

) ↓ = ( aS - b k k R + c Ψ +

k k

- R +d

k z k Z ) ↑

Ψ+ = aS

k≠0

However, at k not 0, since the wave functions of the conduction band are nonpure spin states due to the band mixing, the scattering probability have a finite value. The spin flips by the elastic scattering on impurities or phonons.

EY process is a spin-flip process caused by scattering. At k=0, the scattering probability becomes 0, due to the orthogonality of up and down spin functions.

Ψ− = aS ↓ ↑

↓ = 0

+ + -

≠ 0 Ψ Ψ k ' - U ( r ) k + 2

Since the band mixing becomes larger for narrower band-gap material, spin-flip rate by EY process becomes greater for InGaAs QW than GaAs QW.

R. J. Elliott: Phys. Rev. 96, (1954) 266. Y. Yafet: Solid State Phys. 14 (1963) 1.

Bir-Aronov-Pikus process

Spin flip by the exchange interaction between electron and hole.

dominant at low temperature

Spin relaxation time depends on carrier density.

Spin relaxation time does not depend on temperature.

G. L. Bir, A. G. Aronov and G. E. Pikus: Sov. Phys. JETP 42 (1976) 705.

2

4

6 8

10

30

50

10 100 Temperature (K)

τ s ∝ T -1.1

300

Spin

rela

xatio

n tim

e (p

s)

Example : Exciton spin relaxation in InGaAs/InP quantum wells

Bir-Aronov-Pikus process No temperature dependence

S. Akasaka, S. Miyata, T. Kuroda, and A. Tackeuchi, Appl. Phys. Lett. 85, 2083 (2004).

Typical temperature dependence of spin relaxation time

In0.53Ga0.47As

InP

9.7 7.0 nm

1.55 µm Optical communication

0 4 Time (ps)

(σ , σ ) − + + (σ , σ ) + -

(σ , σ ) + + pump probe

RT

8 -2 In

tens

ity (a

rb. u

nits

)

2 6

(σ , σ ) + - pump probe

0.1

1

10

100

1000

0 0.5 1 1.5 2 2.5 3 3.5 4

Cubic GaN

15K GaAs bulk 10K

InAs Q.Dot 10K

10K

13K RT

GaInNAs QW Free exciton

InGaAs/ InP QW

InGaAs /InP QW

GaAs QW

RT

Wurtzite GaN

ABE

FEA

25K

150K

400 600 800 1550 1000

InGaAs Bulk/Ge 77K

InAs Columnar Q.Dot 10K

InGaAs/AlAs/ AlAsSb QW RT

Spin relaxation time vs Bandgap energy Band gap energy (nm)

Spin

rela

xatio

n tim

e (p

s)

Band gap energy (eV)

APL 84 (2004) 3576 InAs Q.Dot & GaAs bulk

APL 56, 2213 (1990) GaAs/AlGaAs QW

APL 68, 797 (1996)

FEA: APL 85, 3116 (2004) Wurtzite GaN

ABE: APL 89, 182110 (2006)

APL 70, 1131 (1997) APL 85, 2083 (2004)

InGaAs/AlAsSb QW

GaInNAs/GaAs QW APL 92, (2008) 051908

Cubic GaN APL 88, 162114 (2006)

In the zinc-blend structure spin relaxation time becomes shorter for narrower band-gap semiconductors. The spin-orbit interaction which is the origin of D’yakonov-Perel process becomes larger for the narrower band gap semiconductors.

10000

InGaAs/InP QW

APL 100, 092401 (2012)

InGaAs bulk/Ge substrate APL 100, 252414 (2012)

= 0.47 ps

Fastest spin relaxation : Bulk GaN

0

0.5

1

1.5

2

2.5

3

-0.5 0 0.5 1 1.5 2

150K

Ref

lect

ion

inte

nsity

(arb

. uni

ts)

Time (ps)

I +

I -

T. Kuroda, T. Yabushita, T. Kosuge, A. Tackeuchi, K. Taniguchi, T. Chinone, and N. Horio, APL. 85 (2004) 3116.

Co-circularly polarized signal I+ :

I- : Anti-circularly polarized signal

1

10

100

-0.5 0 0.5 1 1.5 2

Spi

n po

lariz

atio

n (%

)

Time (ps)

I+- I- I++I-

Spin polarization = At least one order of magnitude shorter than InGaAs QW or GaAs QW.

𝜏𝜏𝑠𝑠

Applications

Application : Ultra-fast All-optical Gate Switch using Spin Relaxation

Analyzer (Perpendicular to polarizer)

Lens

GaAs/AlGaAs MQW etalon

Polarizer

Probe

Pump (Circularly polarized light to generate spin polarized electrons)

T. Kawazoe, T. Mishina and Y. Masumoto, JJAP 32, L1756 (1993).

Y. Nishikawa et al. IEEE J. Selected Topics in QE, 2 (1996) 661.

Before pump

Probe beam Polarization

Analyzer

During spin relaxation

Amplitude difference

Phase difference

During spin relaxation, optical gate opens.

Optical gate opens during spin relaxation

AlAs/Al0.25Ga0.75As DBR 9.5 periods

GaAs (2.8 nm)/

MQW 156 periods

DBR 14 periods

Al0.51Ga0.49As (4.2 nm)

Y. Nishikawa, A. Tackeuchi and S. Muto, APL. 66 (1995) 839.

All-optical Gate Switching of GaAs MQW etalon

Recovery time

Gate width

τR = τs/4

0

5

10

15

20

Out

put i

nten

sity

(arb

. uni

ts)

Time delay (ps) 0 40 80

RT

-40

50 fJ/µm2

7 ps

4 ps

τG = (ln0.5)τs/4 = 0.17 τs

760 nm

• 5 - 20 ps switching at 1.5 µm by InGaAsP MQW J. T. Hyland, A.Miller et al. IEEE Photo. Tec. Lett. 10, 1419 (1998).

• 300 fs switching at 1.5 µm by InGaAs MQW R. Takahashi et al. Optical and Quantum electronics, 33, 999 (2001).

• Sub-ps switching using CdSe/ZnS QDs Kwangseuk Kyhm and Jihoon Kim, QMN-O-01, ISPSA2008.

• Large throughputs (>40%) High contrast (>40 dB) switching W. J. Johnston et al., APL 87, 101113 (2005).

Spin flip model

21

21

−

23

−23Heavy hole

Electron J. Martin-Regalado et al. IEEE J. QE 33, 765 (1997).

A. Dyson and M. J. Adams J. Opt. B 5, 222 (2003).

Y. Matsui et al. IEEE J. QE 39, 1037 (2003).

τs > 12 ps Elliptical polaraization

Influence on Vertical Cavity Surface Emitting Lasers

This has never been observed based on test results from over 1000 chips. It is suggested that the inhibition for chaos or elliptical polarization state for our VCSELs is a result of the fast spin relaxation time for InP-based material systems as opposed to GaAs-based VCSELs.

H. Ando, T. Sogawa and H. Gotoh, APL 73, 566 (1998) .

While our (InP-based) VCSEL showed stable operation in the polarization state, GaAs VCSELs often exhibit an elliptical polarization state at higher injection conditions in spite of the gain and loss anisotropy created by various techniques. In our simulations, an elliptical polarization state appeared when the spin relaxation time exceeded 12 ps at an operating wavelength of around 1560 nm.

Application using spin-polarization or relaxation Spin Function Interesting features • Fast decay as short as picoseconds

• Spin-relaxation time can be controlled by changing the parameters, such as the confinement energy and the momentum relaxation time.

• We can easily generate or detect spin polarization using circularly polarized light with the help of excitonic optical nonlinearity.

• GaAs and InGaAs are popular semiconductors used for present devices. This implies that the same fabrication and integration technologies can be applied.

Application region • Fast optical switching device using fast spin relaxation

• Electronic transport device such as transistor by extending spin-relaxation time

• Quantum computing by extending spin-relaxation time