Journal of Luminescence 83}84 (1999) 33}36

Ultrafast electron transport phenomena
in highly excited gold "lms
Akihide Hibara, Tomohiro Morishita, Isao Tsuyumoto, Takehiko Kitamori,Tsuguo Sawada*
Department of Applied Chemistry, School of Engineering, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Abstract
Non-equilibrium dynamics of hot electrons in highly excited gold "lms has been investigated by using the femtosecond
transient re#ecting grating method. Transport processes which compete with electron}phonon coupling processes wereinvestigated by observing thermal surface displacements. The results were compared with calculations by a simple
thermoelastic equation and the two-temperature model with two di!erent conditions for the thermal conductivity. The
results suggested that non-thermal states of the hot electrons still contribute transport processes on time scales of several
picoseconds. ( 1999 Elsevier Science B.V. All rights reserved.
Keywords: Gold "lm; Hot electrons; Transport phenomena; Thermal surface displacement

1. Introduction
Ultrafast non-radiative processes in metals, including hot electrons dynamics, play importantroles in physical and chemical phenomena occurring on the surface [1]. Direct measurements of thehot electrons in metals have been performed byusing a two-photon photoemission method [2] anda transient re#ectivity method [3]. For highly excited metal targets, the processes have been investigated in order to understand the initial stage oflaser-induced plasma and X-ray generation [4].
According to recent reports, the hot electrons pro-* Corresponding author. Tel.: #81-3-5841-7236; fax: #813-5841-6037.
E-mail address: tsawada@hongo.ecc.u-tokyo.ac.jp(T. Sawada)

duced in metals by fs-laser irradiation a!ects
surface chemical reactions such as laser-induced
desorption [5] and surface redox reactions [6].
However, detailed analysis of these chemical reactions have been di$cult because the reaction processes compete with hot electrons' energy
dissipation processes such as electron}phonon(e}p) coupling and transport processes. In order toinvestigate the hot electrons e!ects on the chemical
reactions, it is necessary to quantify the energy
dissipation processes.
We reported that the transient re#ecting grating(TRG) method is a powerful tool to investigate theenergy dissipation processes of the hot electrons[7]. In that report, the processes were analyzed by
the two-temperature model (TTM) and by the theory of the transient grating method. It was foundthat the e}p coupling and thermal di!usion processes could be investigated independently. We also0022-2313/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 0 7 0 - 8

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A. Hibara et al. / Journal of Luminescence 83}84 (1999) 33}36

reported that the TRG method can measure fastsurface displacements due to longitudinal acoustic
pulse echoes and surface acoustic waves [8]. The
surface displacements induced by fs-laser irradiation were analyzed by the TTM coupled with athermoelastic model. It was found that transportphenomena of the hot electrons can be investigated by the surface displacements analysis. In
these reports, temperature dependence of the thermal conductivity i has been investigated and foundto be iJ¹~1 or iJ¹0. The dependence has also%%
been investigated theoretically in a recent report[9].
In this report, we measured surface displacement
dynamics of highly excited gold "lm by the TRG
method. The pump laser power dependence of thedynamics was measured and compared along withpredictions by the TTM and thermoelastic equation with two di!erent models for the thermal conductivity i.

Fig. 1. A schematic "gure of the experimental setup for the TRG
method. BS, beam splitter; HM, half mirror; ODL, optical delayline; PD, photodiode.

3. Results and discussions
2. Experimental
A schematic "gure of an experimental setup for
the TRG method is shown in Fig. 1. TRG responses
are measured by a pump}probe technique. A regeneratively ampli"ed Ti : sapphire laser system, which
has an autocorrelaton of 200 fs, a wavelength of
800 nm and a repetition rate of 1 kHz, is used as thelaser system. Fluence of the pump pulse varies from
0.8 to 3.0 mJ/cm2. Two pump pulses of the same
wavelength (j"400 nm) cross on a sample
16.1
surface with crossing angle of 2h and form an optical interference pattern with the fringe spacing
K"j/(2 sin h). The fringe spacing is set to16.1
2.7 lm in this report. The temporally generated
interference fringes act as a transient di!ractiongrating. A probe pulse (j"800 nm) is incident
130"%
normal to the grating, after passing through an
optical delay line, and is di!racted by the grating.
Intensities of the di!racted light are recorded as
TRG signals.
A 300 nm-thick polycrystalline gold "lm deposited on a glass plate was used for the measurements.
The penetration depth of the pump pulse was calculated as 16 nm. All the experiments were performed in air at 296 K.

TRG responses of a 300 nm-thick gold "lm areshown in Fig. 2. The lines (a) and (b) in Fig. 2 represent the responses obtained by pump #uences of
3.0 and 0.8 mJ/cm2, respectively. In both cases, theexcitation fringe spacing K is set to 2.7 lm. The
sharp peaks around 0 ps correspond to dielectric
constant changes due to generation and relaxationof the hot electrons. Since analysis of these faster
responses have been reported in our previous paper[7], we do not discuss these responses any furtherin this paper. The TRG response, except the sharp
peak represents surface displacement dynamics resulting from temperature rise due to laser irradiation. The response denotes the following processes.
At "rst, the hot electrons energy generated by fslaser irradiation is deposited to lattice system andthermal expansion begins. This thermal expansion
brings about surface displacement and the generation of longitudinal acoustic (LA) pulse. The LA
pulse re#ects at both "lm/substrate and "lm/airinterfaces. When the LA pulse arrives at themeasuring plane ("lm/air interface) it negates thesurface displacement due to thermal expansion.
Therefore, periodic decrease of the signal in Fig. 2(b)corresponds to the arrival of the LA pulse echoes.

A. Hibara et al. / Journal of Luminescence 83}84 (1999) 33}36

35

In order to analyze the transport phenomena of
the hot electrons, the two-temperature model(TTM) was introduced. The TTM assumes that theelectron and the lattice systems are in local equilibrium and have characteristic temperatures, which isthe electron temperature ¹ and the lattice temper%
ature ¹ . The electron system is not in equilibriumwith the lattice system within several picoseconds
and ¹ is coupled with ¹ by the electron}phonon%
coupling. The temporal evolution of the systems
can be written by a set of coupled di!erential equations [12]. Namely,
L¹%"+(i+ ¹ )!G(¹ !¹ )#Q,
c¹% Lt%%L¹l"G(¹ !¹ ),C- Lt%-Fig. 2. Experimental and theoretical TRG responses. (a) Experimental pumped with 3.0 mJ/cm2. (b) Experimental pumped with
0.8 mJ/cm2. (c) Theoretical pumped with 3.0 mJ/cm2. (d) Theoretical pumped with 0.8 mJ/cm2.

Very slow gradual increase of signal is due to thesurface acoustic wave (SAW), where wavelengthof SAW agrees with the fringe spacing K [10,11].
These surface displacement dynamics were con"rmed and reported in our earlier paper [8].
In Fig. 2(a) and (b), the "rst surface expansion
peaks around 100 ps are normalized to unit intensity in order to compare the dynamics. The two
responses agree with each other almost completely.
This result means that the surface expansion andLA pulse generation processes are not a!ected bychanging the pump #uence. When temperaturedependent thermal conductivity is assumed [7], thepulse width of the LA wave becomes broader withhigher pump #uence. Therefore, our results shownin Fig. 2(a) and (b) suggest that the temperaturedependence of thermal conductivity presented inRef. [7] is not su$cient to describe the hot electrons dynamics. In this paper, we demonstrate
one possible case to explain our results shown inFig. 2(a) and (b).

(1)

where c¹ and C are the electronic and lattice heat%
capacity, G is the electron}phonon coupling factor
and Q is the energy source term. In Eq. (1), di!usionand energy source terms for the lattice systems are
neglected because these contributions are small. To
calculate the surface displacement u, the simplest
form of the thermoelastic equation was introduced
and coupled with ¹ . Namely,
Lu 1 L2u 3bB L¹-,"!
(2)
Lt l2 Lz2o Lz
Lwhere z is the axis perpendicular to the surface
plane (to thickness direction), l is the longitudinalL
acoustic velocity, b is the linear thermal expansion
coe$cient, B is the bulk modulus and o is thedensity. Eq. (2) is coupled with the boundary condition at the free surface. In our analysis, Eqs. (1) and(2) are numerically solved. For the source term Q,
a sech2 function is used for the time-evolution of
the pump pulse.
In our analysis, i is regarded as a constant. Since
our previous reports [8] clari"ed the value for i inequilibrium state ("317 W/(m K)) is not su$cient,
we use the value 950 W/(m K) for i, which is suggested in Ref. [7]. The theoretical curves calculatedwith di!erent pump #uences, 3.0 and 0.8 mJ/cm2,
are shown in Fig. 2(c) and (d). The two theoreticalresponses agree well. Therefore, constant thermal
conductivity is strongly suggested for the transport
process of the hot electrons. In the relaxation time36

A. Hibara et al. / Journal of Luminescence 83}84 (1999) 33}36

approximation (RTA) theory, the thermal conductivity is expressed as i"(1/3)l2qC , where l is the%electronic velocity, q is the relaxation time andC ("c¹ ) is the electronic heat capacity. As long%%as the RTA theory is assumed, l2q should be proportional to ¹~1. As electron}electron scattering%
time is considered to be dominant in the relaxation
time in high ¹ region, q may be regarded as elec%tron}electron scattering time. When i is independent of ¹ , the relaxation time should be expressed%
as qJ¹~1. This temperature dependence does%
not agree with the well-known relation ship,is the electron}electron
q J¹~2, where q%%~%%~%scattering time. This inconsistency may be attributed
to nonthermal properties of the hot electrons.
4. Conclusions
The surface displacement dynamics has been measured on a highly excited gold "lm. The dynamics
has been analyzed by TTM and the thermoelastic
equation. In conclusion, temperature independent
thermal conductivity is suggested for the transport
process of the hot electrons. This non-thermal property of the hot electrons may a!ect the ultrafast
surface chemical reactions. A continual investigation
will be made on the relation between the surface
redox reactions and the non-thermal properties of
the hot electrons, which have been observed atPt/Cl~ [6] and TiO /SCN~ [13] interfaces.
2Acknowledgements
Part of this work was supported by `Precursory
Research for Embryonic Science and Technology

21a of Japan Science and Technology Corporation
and Grant-in-Aid for Scienti"c Research in Priority
Areas of Electrochemistry of Ordered Interfaces(No. 11118219) from the Ministry of Education,
Science, Sports and Culture of Japan.

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