කㄇ㉫䜱䝧䝮䜦䛮䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷䛴㉰㧏㏷䝄䜨䝎䝣䜳䜽୯ᮟୌ㝧᮶ாᕝᴏኬᏕᚺ⏕䜿䝭䝣䝇䜳䜽◂✪ᡜ

ERL@KEK(2007/7/10)

Outline•••䜨䝷䝌䝱䝄䜳䜻䝫䝷䟺䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷䟻
䝕䝯䜽X⥲Ⓠ⏍᫤㛣ฦよX⥲ᅂᢙῼᏽ– 䝘䜷⛂᫤㛣䜽䜵䞀䝯䠌GaAs㡚㡢䝙䜭䝒䝷䝕䝯䜽ఎᦑ– 䝙䜫䝤䝌⛂᫤㛣䜽䜵䞀䝯䠌CdTeකᏕ䝙䜭䝒䝷ᣲິ•䜄䛮䜇2䝙䜭䝒䝷䟺䠄ཋᏄ├⥲᰹Ꮔ䟻

l-1

ll+1

d 2U lM 2 = f (ul + ul +1 " 2U l )dt
d 2 ulm 2 = f (U l + U l +1 " 2ul )
dt

m

M
a

1/ 2 30 *$'f(M+m)4Mm
qa
21± +1#" ±2 =
sin 2 & ). 52% 2 (/ 54Mm 21 , (M + m)!

"i#ti) ω−䛴䝦䞀䝍䛵q->0䛭ω−>0䛮䛰䜐䚮 ul = u0e!
ωකᏕ䝦䞀䝍ධ䛬䛴ཋᏄ䛵ྜྷన┞䛑䛪ྜྷᣲᖕ䛭ᣲິ䛟䜑䛙䛮䛱䛈䜑䠌㡚㡢Ⓩᣲິ!
ii) ω+䛴䝦䞀䝍䛵q->0䛭䚮

" +2 =2 f (M + m)
Mm㝼䜐ྙ䛩䛥␏⛸ཋᏄ䛒䛣䛴㈻㔖䛱ཬẒౚ䛝䛬䚮
!
㏣న┞䛭䟺ཬᑊ᪁ྡྷ䛱䟻ᣲິ䛝䛬䛊䜑䠌කᏕ䝦䞀䝍q㡚㡢䝦䞀䝍-π/a0π/a3⇍ᣲິ䛮䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷⇍ᣲິ䠌྘ཋᏄ䛴ᣲິ䛴న┞䛒䝔䝭䝔䝭䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷䠌྘ཋᏄ䛴ᣲິ䛴న┞䛒ᥖ䛩䛥≟ឺ᰹Ꮔᣲິ䛴ᣲິ࿔᭿䜎䜐䜈༎ฦ▯䛊䝕䝯䜽ທ㉫䛭Ⓠ⏍䛟䜑䛙䛮䛒䛭䛓䜑

4䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷Ⓠ⏍䝥䜯䝏䜾䝤• Ⓠ⏍䝥䜯䝏䜾䝤• DECP(displacive excitation of coherent phonon)– කྺ཭䛱䜎䜑ທ㉫≟ឺ䛭䛴ᣲິ䠌Ⓠ⏍䜱䝧䝮䜦㔖䛱Ẓౚ䛝䛥ንన– ↋ᴗᛮ䛰༖㔘ᒌ䜊↋ᶭ∸㈻• ISRS (Impulsive stimulated Raman scattering)– කທ㉫䛱䜎䜑ᇱᗇ≟ឺ䛭䛴ᣲິ䠌ທ㉫කᙁᗐ䛴䠄஋䚮䝭䝢䝷Ὡᛮ䛰䝦䞀䝍– ྺ཭䛒↋䛊∸㈻• USSC(ultrafast screening of space-charge field)– කྺ཭䛱䜎䜐Ⓠ⏍䛝䛥䜱䝧䝮䜦䛱䜎䜑⾪㟻㞹Ⲭᒒ䛴䜽䜳䝮䞀䝏䝷䜴䟺䝔䝷䝍䝝䝷䜴䜧䝷䜴䛴΅ᑛ䟻– ᴗᛮ䛴䛈䜑༖ᑙమୌ⯙Ⓩゝῼ᪁Ἢ䠌䝙䜫䝤䝌⛂䝰䞀䜺䞀䛴㐛ῳཬᑏ⋙䝿㐛ῳ㏩㐛⋙ῼᏽ5䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷䜷䝷䝌䝱䞀䝯䟺Bi䟻

StopEnhance

Hase et al. Appl. Phys. Lett., 69 (1996) 2474
6••කᏕῼᏽ䜘⏕䛊䛥䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷䛴ゝῼ䛭䝙䜭䝒䝷䛴ᑋ࿤䚮㞹Ꮔ䝙䜭䝒䝷┞பష⏕䛒◂✪䛛䜒䛬䛊䜑䚯䝕䝯䜽ἴᙟᩒᙟ䛱䜎䜐䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷䜘โᚒ䛝䚮ක䛱䜎䜑ᵋ㏸โᚒ䜘┘ᣞ䛝䛥◂✪⾔䜕䜒䛬䛊䜑䚯කᏕῼᏽ䛭䛵䚮ཋᏄንన㔖䜊ᵋ㏸䛒䜎䛕ฦ䛑䜏䛰䛊㉰㧏㏷᫤㛣ฦよX⥲ᅂᢙ䜘⏕䛊䛥䜷䝖䞀䝰䝷䝌䝙䜭䝒䝷◂✪7

Time-resolved measurement of coherent phonon• Coherent phonon has been studied extensively using
several optical measurement techniques: timedomain spectroscopy– reflection or transmission, SHG, THz radiation• T.K. Cheng, APL 59 (1991) 1923
• M. Hase et al. PRL 88 (2002) 067401.

• Lattice displacement has been directly studied with Xray diffraction by several groups– Acoustic phonon propagation• A. Rousse et al. Nature 410 (2001) 65– Coherent optical phonon• K. Sokolowski-Tinten et al. Nature 420 (2003) 287.

8

Motivation: Materials Dynamics
Elucidate dynamics of phase transition of condensed matter and control•Transition time (Δt)?
䟼• Pathway of structural changes (A1-A2) ?
• Transition structure (*) ?

A䟼A䠃

A䠄

BΔt
Rate constantLaserΔt

X-raysDiffraction

How
Structural change is directly monitored byusing ultrafast X-ray diffraction with pumpand probe technique
Ultrashort pulsed X-rays are required!

Picture of atomic motion

9Quantum emissions
High-energy short-pulsed beams of electrons, ions and photons (X-rays)
generated from femtosecond intense laser field (>1016W/cm2).

Hard X-ray pulse
Ponderomotiveforce

Intense femtosecond
laser pulse(>1016W/cm2)

High-energy electron pulse

Target materials (Z)10Quantum emission

High-energy short-pulsed beams of electrons, ions and photons (X-rays)
generated from femtosecond intense laser field (>1016W/cm2).
protonselectrons
X raysLasere,pCu-foil at I=2x1018W/cm2

11Femtosecond laser induced Hard X-ray pulse (I = 1017 W/cm2)

Energy spectra

Pulse width of CuKa
6.5x1010photons/4πsr/pulse

Characteristic X-rays obtained by X-ray CCD
camera at power density of 3×1016 W/cm2.

The temporal profiles obtained by the X-ray streak
camera. The energy extends from 1 to 10 keV areaccumulated. I ~㻃㻔㻓㻔㻚㻃㻺㻒㼆㼐㻕

M. Yoshida et al. APL 73 (1998) 2393; Y. Fujimoto et al. JJAP 38 (1999) 6754

12

Picosecond time-resolved X-ray diffraction fromfemtosecond laser-excited GaAs(111):
Acoustic phonon propagation

Ref: C. Rose-Petruck et al., Nature 398 (1999) 310
H. Kishimura et al., JCP 117 (2002)10239

13

Schematic of experimental setup

Pump Laser Pulse

X-ray
CCD
Probe X-raypulse

TW laser system (Ocs. Reg. Amp)
300ps, 800 mJ/max

300ps

Sample crystal

Time-step: 10ps
Pulse compressor

60fs
Optical delay line

70mJ/cm250fs
Pulse compressorvacuum

X-ray generationchamberCuKa

X-ray CCDGaAs(111)14

CCD image and rocking curve of X-ray diffraction from laser irradiated GaAs(111)

Under laser irradiatedInitial state
2d sinθ = λDiffraction Angle
CCD camera image

A low angle shift䊲㻨xpansion
A high angle shifts䊲㻦ompression)(300shot integrated15

Picosecond time-resolved X-ray diffraction from 60-fs laser irradiated GaAs(111)16

Electronic system

Lattice system

Carrierabsorption

Lattice expansion
Phononexcitation

Interband
absorptionAugerrecombination

Acoustic phonon
propagation
Temperature
increases

Rate equations: N(x,t), T(x,t)

Diffusion equations: T(x,t)
Hydro-dynamic equations: u(x,t)
17Model of laser heating and phonon generation

Laser irradiation# (1 ! R) 2"N N
" 2 N $ (1 ! R)+=D+I ( x, t ) +I ( x, t ) 22"t % R"xE2EInter-band absorption%I ( x, t ) = $[" + #N + !I ( x, t )]I ( x, t )%tRate eq., diffusion eq.

Electron-hole plasma
Carrier absorption
Carrier diffusion"R =Auger recombination

Optical phonon
Temperature increase
Thermal diffusion

1!N 22#/T/ 2 T E g N - E ' E g * &- 1 (1 ' R)
* 0 (1 ' R)+(= DT+++.
N+I
(x,t)
+($! I ( x, t )/t/x 2 C v2 R +, C v () %,E2E)"Acoustic phonon pulse
Hydro-dynamics

Lattice deformation
2!E g !N! 2u!T2 ! u# 2 = #v
+B+
3B"!t!z 2!P !z!z18

Strain generated by impulsive laser excitationz#vtvt+ #z%.
# (#11$$$" = "0 -e ''1# e ** # esgn(z # vt)0-, & 20/) 2!

η: strain
V: sound velocity
ξ: absorption length

C.Thomsen, et al., Phys. Rev. B 34, 4129 (1986)
19

Simulation of strain profile inside the GaAs(111) crystal

Maximum strain㻃䚭㻃㻃㻃㻃0.30%
Absorption length㻃䚭255nm
20Obtained effective absorption length in this study: ξ= 255 nm
c.f. linear absorption length of GaAs at 800nm: ξ= 900 nm

I䠌Intensityα䠌 An absorption coefficient
α0䠌 A linear absorption coefficientβ䠌 A two-photon absorption coefficient

Intensity䚭I = 1.17 GW/cm2
䊲㻃A two-photon absorption coefficient㻃䚭β= 27±11 cm/GW
c.f. β= 26±8 cm/GW (using ps laser pulse)(T.F.Boggess, et al., IEEE J. Quantum Electron. 21, 5 (1985))
21

Femtosecond time-resolved X-ray diffraction fromfemtosecond laser-excited CdTe:Coherent optical phonon

Ref: K. Sokolowski-Tinten et al., Nature 422 (2003) 287 and (2006): Bi-film
Y. Hironka et al., Ultrafast Phenomena (2006)22

Effect of coherent optical phonons in ultrafast time-resolved X-ray diffraction• No change in diffraction angle• Diffraction intensity changes as a change of structural factor: F2F = FF * = I " f l f l' exp(l2#i2#i(S % S0 )(Rl % Rl' ))exp((S % S0 )(&l % &l' ))$$2' F0 + " iQexp(i(t + ) l )(Thermal: Debye-Waller factor)l!

Rlδl23

Experimental geometry and diffraction image

Pump Laser Pulse

X-ray CCD

Position at the sample

CCD image of X-ray diffraction

Probe X-raypulseSample crystal
Diffraction angle

Symmetric Bragg diffraction geometry
2dsinθ=λ

Reflecting Plane : CdTe(111)θB=11.88384 deg. θB=11.9138 deg
24

fs-TRXD from 50-fs laser irradiated CdTe(111)Intensity ratio

1.00

0.98

0.96
11.811.9 12.0Angle (degree)
0.94
-30

-20-100

102030Relative delay time (ps)Temporal profile of diffracted X-ray
intensity

Diffraction angle

No shift of the diffraction peak but
modulation of diffracted X-ray intensity
25

Coherent optical phonons in CdTe(111):fs-TRXRD60108Intensity (arb. unit)

8650

4640

4

20
3.0

2

4.0

5.0

6.0

14

16300

20-2

10-4-60.0

0
0.5

1.0

1.5

Relative delay time (ps)Modulation in X-ray diffraction intensity

02

4

68

10

12Frequency (THz)
Fourier power spectrum of modulation in X-ray
diffraction intensities and normal Raman
spectrum of CdTe (inset).
26

Phonon dispersion of CdTe

Phonon frequency (THz)

Phonon dispersion curve of CdTe

Γ (k=0)7[001][111]LO phonon

5031X

ΛΓ

ALWave vector (k-space)
From J.M. Rowe et al. PRB10(1974)27

Experimental setup for fs time-resolved optical reflection @NIMS

http://www.nims.go.jp/ldynamics/Femto/SU.html

28

Fs-time resolved optical reflection from CdTe(111)
K. Ishioka et al., Jpn. J. Appl. Phys.45 (2006) 9111

6-6542
Intensity

Intensity change !"/"

4x100

32-2
1-40

0.0

0.5

1.0

1.5

Delay time (ps)modulation in phonons (5mW):

2.02345678

Frequency (THz)

Fourier spectrum

LO(CdTe): 4.97 THz, τ =2.39 ps
A(Te): 3.82 THz, τ =1.49 ps
29

Summary• Transient lattice deformation due to propagation of acoustic••phonon and shock wave inside semiconductor crystals has beenobserved by picosecond TR-XRD
Coherent optical phonons of CdTe (5THz) has been observed byfemtoseconf TR-XRD
Time-resolution of 200fs in TR-XRD has been achieved30

Acknowledgement• TRXRD– TokyoTech: Prof. K. Kondo, Dr. Y. Hironaka, Dr. H. Kishimura, Dr. Y. Okano• CP by optical reflection– NIMS: Prof. M. Kitajima, Prof. K. Ishioka, Dr. M. Hase

• Coherent control in condensed matter– Ohmori group, Matsumoto group (IMS), Kitajima group (NIMS)– Funds: MEXT, IMS

31