*Materials and Structures Laboratory, Tokyo Institute of Technology,
4259 Nagatsuta, Midori, Yokohama 226-8503, Japan
Abstract. Direct observation of lattice dynamics of a 300 ps laser irradiated silicon crystal is performed by means of picosecond time-resolved X-ray diffraction. Change in X-ray diffraction profiles corresponds to propagation of a strain pulse inside the sample with sound velocity. The strain profiles are simulated by considering carrier dynamics and thermo-elastic treatment.
X-ray diffraction is the most popular technique for determining crystal structure, because X-ray can interact with inner-shell electrons and are sensitive to atomic position. Ultrafast X-rays, generated by laser plasma with an intense femtosecond pulse, enable detection of structural changes as they undergo a phase transition, surface melting or recrystallization on picosecond time scale [1-6]. Real time observation using Xray diffraction is needed to determine a transient crystal structure and transformation mechanisms under shock wave propagation. However, because of various experimental limitations, it is difficult to obtain quantitative X-ray diffraction in shocked solids [7-
9]. Pump-probe technique with picosecond pulsed X-ray can apply to detect structural change under laser-induced shock compression, because the generated X-rays are completely synchronized with the driving laser. It is possible to understand transformation mechanism under shock compression in detail. In order to keep high-pressure state for a relatively long duration, long-pulse laser is required.
In this work, we studied the lattice dynamics of Si(lll) under 300 ps pulsed laser irradiation by picosecond time-resolved X-ray diffraction. The picosecond pulsed Xrays are generated using laser plasma induced by femtosecond laser irradiation on metal target. Transient changes in lattice are directly observed.
The laser system used was a table-top terawatt laser system (B.M. Industries,alOus).
The laser pulses centered at 780 nm (E ~ 1.6 eV) are generated at 76 MHz by a
Ti:sapphire laser oscillator (25 fs). The output is pulse stretched to 300 ps with energy of
400 mJ/pulse. This 300 ps pulsed beam is divided into two beams by a beam splitter (10
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247

%). One beam (10 %) is used for irradiation to Si through an optical delay line as a pump beam, and the other (90 %) is compressed to about 50 fs and used for X-ray generation.
Pulsed X-rays (10 ps pulse width) are generated by focusing the 50 fs pulse on a Fe target in a vacuum chamber at laser power density of about 10
17
W/cm
2
[10]. X-ray diffraction was performed with a characteristic Ka line of Fe in a symmetrical Bragg diffraction geometry. The diffracted X-rays were recorded with an X-ray charge-coupled devices area image sensor. A 300 ps pump laser was irradiated to the surface of sample at a spot size of 1 x4 mm
2
. The sample used was a nondoped Si(l 11) wafer of 860 jiim thickness. The sample was mounted on a motorized XY stage and moved for each lasershot. In the experiment, two types of irradiation conditions were performed (Single shot and Multiple shots). In single shot experiment, the pump fluence was 1.0 mJ/cm
2
and
XY stage moved without overlapping of the pump spot. On the other hand, in multiple shot experiment, the pump fluence was 1.2 mJ/cm
2
and laser irradiated 200 shots at approximately same spot. The diffracted signal was obtained by the accumulation of
600 data values. Details of the experimental setup are described elsewhere [5, 6].
Figure l(a) shows a typical example of the CCD image of diffracted X-rays from laser-irradiated Si(lll) at a pump-probe delay time of 350 ps. The two lines are the diffracted Kai (1.9360 A) and Ka
2
(1.9399 A) X-rays, whose diffraction angles (0) are 17.98 and 18.02 degrees, respectively. The diffraction patterns broaden at the laserirradiated area. Figure l(b) shows the rocking curves from the laser-irradiated area
(solid line) and the unirradiated area (dotted line). In symmetric Bragg diffraction configuration, the lattice strain can be estimated using the equation: Ad/d = — A0cot0#, where d is the lattice spacing, A0 the shift, and OB the Bragg angle. The rocking curve of the laser-irradiated Si(lll) shows a lower-angle shifted component, which indicates the lattice expansion. The total intensity of diffraction from the irradiated area is twice the original value. This is explained by a transition from dynamical diffraction to kinematical diffraction due to an increase of strained layers.
In Fig. 2, the measured time-resolved diffraction profiles are shown as a function of the diffraction angle (rocking curves) and the time delay between X-ray and the pump pulses. Time delay t = 0 is defined as the time when lower-angle shifted component first appears. Time-resolved measurements were performed from —100 ps to 1000 ps at intervals of 50 ps. In the early delay time, both of the original Ka lines broaden, while new lines appear. The new lines are broader and weaker than the original lines and deviate by approximately —0.08 degrees relative to the original Bragg angle. As the delay time increases, these new lines decrease in width, increase in intensity and merge with shifted main lines. The diffraction profile looks like a single peak at around
600 ps, and separates at longer delay time (> 800 ps). Finally the main lines deviate by approximately —0.02 degrees relative to the original Bragg angle at 1 ns.
The evolution of diffracted profiles directly depends on acoustic strain distribution.
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The acoustic strain pulse is excited under laser irradiation and can be monitored by Xray diffraction. In order to confirm a generation of strain pulse, model calculation which is described by rate and diffusion equation for carrier density TV and lattice temperature
T and a fluid equation was performed. Assuming that the problem is one dimensional, depth distribution ofN(x,t) and T(x,f) depends on distance x from the surface and time
t. Rocking curves were calculated using dynamical diffraction theory. The equations for
N and T can be expressed as follows [1 1-14]:
, , , t ) , ( 3 ) where the Auger recombination life time ?R is represented by
Here, D and DT are the ambipolar and thermal diffusion coefficients, a the linear absorption coefficient, /3 the two-photon absorption coefficient, 0 the free-carrier absorption cross-section, R the reflectivity, I(x,t) the space and time dependent intensity of the laser pulse, C v
the specific heat per unit volume and 7 the Auger coefficient [15-18]. In these equation, the absorption coefficient and the specific heat are treated as a function of T and approximated by the fifth-order polynomial, fitted to the experimental data [16-18].
The equation of motion for elasticity is expressed by electronic volume effect,
3
2 u d
2 u where u is the displacement, p the density, v the sound velocity, B the bulk modulus,
/ the linear thermal expansion coefficient, which depends on lattice temperature, and dE g
/dP the electrical contribution for Si(lll) [19, 20]. The strain can be obtained by the solution of Eq. (5) for u.
These equations were solved numerically. The laser intensity profile /(;c,f) is treated as Gaussian (FWHM 300 ps) centered at t=Q. In the calculation, the following values were used[14, 21, 22]: D = 18 cm
2
/s, /3 = 2 cm/GW, y = 4 x 10~
31
cm
6
/s, dE g
/dP =
-2.4 x 10~
24
cm
3
, p = 2.3 g cm~
3
, v = 9.4 x 10
3
m/s. The reflectivity R is set to be
0.35 for an initial value, 0.72 for T > T m
, where T m
is the melting temperature (1685
K) [23]. The reflectivity of e — h plasma is described with the help of the Drude model.
Numerically calculations were done at time between —450 ps to 1150 ps with a time step of 20 fs.
Figure 3 shows the strain profiles as a function of depth at various delay times on a gray-scale map. Significant lattice expansion is observed near the surface and small
249

(a)
(b)
•f 2000
1500
1000
17.8 17.9 18.0 18.1
Diffraction angle 6 (deg)
18.2
FIGURE 1. A typical example of the CCD image of diffracted X-rays from 300 ps laser irradiated
Si(l 11) at a pump-probe delay time of 350 ps (a) and the rocking curves of X-ray diffraction (b). The solid curve is from the laser-irradiated area and the dashed curve is from unirradiated area.
compression is observed ahead of the expansion. The propagating strain pulse (acoustic
:10
3 ms which is the sound velocity of Si(l 11).
The calculated rocking curves are shown as a function of diffraction angle and time in
Fig. 4. The new lines appear and deviate by approximately —0.08 degrees relative to the original Bragg angle at 400 ps. As the delay time is increased, these new lines decrease in width and shifts to higher angle. Finally the main lines deviate by approximately
—0.01 degrees relative to the original Bragg angle. The computational results agree approximately with the experimental data. In the calculation, gradually changes at lowerangle component can be explained.
The results of X-ray diffraction from Si(lll) under multiple laser irradiation displayed in Fig. 5. Time-resolved measurements were performed from 0 ps to 950 ps at intervals of 50 ps. At early times, the intensities of rocking curves decreased and a new diffraction component at higher angles was observed. At later times, shifted component gradually decreased in width. The observed shift indicates lattice compression in contrast with the result of single shot experiment, although power density of both ex-
250

1C80
I mi 1»: lilt. IIJ ill
Diffraction angle 0 (deg)
FIGURE 2. Rocking curves for 300 ps laser irradiated Si(lll) for various delay time. Dashed lines indicate Bragg diffraction angle for Fe Ka\ and Fe K<XI lines from the pristine Si(l 11).
0.8
0.6
0.4
0.2
0.0
-0.2
0
- -150 ps
----- 50 ps
- - - 150 ps
--- 550ps
- 950 ps
10
Depth (jim)
15
FIGURE 3. Calculated strain profiles at several delay time. Positive and negative values correspond to lattice expansion and compression, respectively.
periment were almost same. The maximum change of lattice spacing was obtained to be
-0.9%. Because the lattice compression is -2.6% at approximately 5.4 GPa [24], the maximum pressure is estimated to be 1.9 GPa. We suggest that the present phenomena are shock compression due to reaction of laser ablation. It is considered that surface of irradiated area is damaged and optical properties are changed during multiple laser shot.
We believe that the laser ablation occurs under multiple laser shot and the momentum transfer due to the laser ablation causes lattice compression. The time evolution of the rocking curves observes the shock wave propagation directly.
251

1000H
17.80 17 J! Hit llli
:
***
; fi ii
'-
+iH
***
*N
S3:
I; '2»H
0-
IIJ 17JI 1100 1110
FIGURE 4. Time-resolved X-ray rocking curves for 300 ps laser irradiated Si(lll) as a function of diffracted angle and of pump-prove time delay: (a) experimentally measured (b) calculated by thermoelastic treatment.
i
17J ifS ill III
Diffraction angle 0 (deg)
11.2
FIGURE 5. Rocking curves for Si( 111) under multiple laser irradiations for various delay time. Dashed lines indicate Bragg diffraction angle for Fe Ka\ and Fe Kai lines from the pristine Si(l 11).
252

We have directly observed structural dynamics on picosecond time scale in 300 ps laser excited Si(lll) crystal. The evolution of lattice motion is observed by ultrafast X-ray diffraction at a time step of 50 ps. In single shot experiment, lattice expansion was observed. Numerical simulation on carrier density and lattice temperature is performed using rate and diffusion equation under laser irradiation. Calculated rocking curves using the strain profiles represented the experimental data. On the other hand, transient lattice compression under multiple laser irradiations was observed and maximum pressure of inside silicon was 1.9 GPa. Shock-compressed state was achieved by 300 ps laser irradiation. Structuralchange in elastic-plastic transition and structural phase transition can be studied by using intense laser irradiation.
The authors thank M. Hasegawa for his help in constructing the experimental setup.
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