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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