ANALYTICAL SCIENCES APRIL 2000, VOL. 16
2000 © The Japan Society for Analytical Chemistry403

Femtosecond Transient Reflecting Grating Methods and Analysisof the Ultrafast Carrier Dynamics on Si(111) Surfaces
Tomohiro MORISHITA,* Akihide HIBARA,* Tsuguo SAWADA,* Isao TSUYUMOTO,**and Akira HARATA****Department of Applied Chemistry, School of Engineering, The University of Tokyo,

Hongo, Bunkyo, Tokyo 113–8656, Japan**Department of Environmental Systems Engineering, Kanazawa Institute of Technology,Ohgigaoka, Nonoichi, Ishikawa 921–8501, Japan***Department of Molecular Science and Technology, Graduate School of Engineering Science,

Kyushu University, Kasugakoen, Kasuga, Fukuoka 816–8580, JapanThe femtosecond transient reflecting grating (TRG) method was developed and applied to monitor the ultrafast dynamics
of photo-excited carriers on Si(111) surfaces. TRG responses were measured as a function of the pump beam intensityand fringe spacing, and two relaxation components were observed. An analysis of the results has suggested that the slow
component corresponds to carrier diffusion and that the fast component corresponds to a combined process between
ballistic transport and carrier-carrier scattering of non-equilibrium carriers.
(Received October 6, 1999; Accepted January 31, 2000)

The ultrafast carrier dynamics of semiconductor surfaces on a
sub-picosecond time scale has become a significant area forstudy from the viewpoints of basic science and technologicalinnovations1,2 because of the explosive development of thelarge-scale integration of semiconductor circuits. Among surface
materials, Si is one of the most important for electronic devices,and many studies on its surface ultrafast carrier dynamics havebeen performed using such methods as the two-photon photoemission method3,4 and the transient-reflectivity (TR) method.5,6
The time-resolved two-photon photo-emission method has
provided useful information about the carrier thermalization
process via carrier-carrier scattering, and the TR method has
elucidated the multi-body effect of photo-excited carriers.
However, ultrafast carrier dynamics has not yet been clarified.
For instance, the time evolutions of a distribution of photoexcited
carriers and of the Coulomb interaction should be taken into
account under a strong excitation condition on a femtosecond timescale; the validity of the random-phase approximation has alreadybeen investigated under such a condition.7 Experimental
difficulties are derived from the fact that most of the ultrafast
phenomena are non-radiative processes, and thus band-to-bandrelaxation cannot be directly observed. For such a case,photothermal spectroscopy, which measures any heat orrefractive-index change due to photo-excitation, would be a
powerful tool. As a photothermal method, we have developed atransient reflecting grating (TRG) method with a time resolutionof 80 ps, and have applied it to semiconductor surfaces.8,9 The
TRG method has many advantages, such as surface selectivity,
high sensitivity, background-free detection, and providing
directional information. We can expect to observe carrier
thermalization and carrier transport dynamics by raising the time
resolution to the femtosecond time region of the TRG method.
In this study, we developed a femtosecond time-resolved TRG(fs-TRG) method and applied it to measure Si(111) surfaces.

We want to use it to clarify the behavior of photo-excitedcarriers at these surfaces. We present results suggesting theballistic transport of non-equilibrium carriers, and the Auger
recombination and carrier diffusion of equilibrium carriers.

Experimental
Since the experimental setup for the TRG method was the sameas that described in our previous report,10 only an outline ispresented here based on Fig. 1. Two pump pulses of the same
wavelength, λ pump, were crossed on a sample surface to form an
optical interference pattern with a fringe spacing (Λ) of Λ =λ pump/2sinθ, where θ is the pump beam incident angle normal tothe surface. This interference pattern induced a periodic
refractive-index change, which acted as a transient diffraction
grating. The probe pulse was incident normal to the grating,and diffracted light was observed. The intensity of the diffracted
light was monitored as a function of the delay time of the probebeam. The TRG signal reflected dynamic information about thesurfaces, such as a refractive-index change by carrier excitationand heat generation.
The light source was a regeneratively amplified Ti:sapphirelaser system which had an auto-correlation of 150 fs, awavelength of 800 nm and a repetition rate of 1 kHz. Theoutput beam (800 nm wavelength) was partly reflected by a half
mirror to generate the probe beam, which passed through a
computer-controlled optical delay line. The residual beam wasfrequency-doubled by a BBO crystal to generate a 400 nm
beam, which was split into two parts. Each pump pulse had aspot size of 600 µm and p-polarization. The polarizations of thepump and probe beams were perpendicular to each other. The
diffracted light was detected by a PIN photodiode. The outputof the photodiode was fed into a fast-gated-integrator, and its

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ANALYTICAL SCIENCES APRIL 2000, VOL. 16

Fig. 2 Typical TRG responses with a constant fringe spacing of 1.2µm. The symbols
andcorrespond to pump beam powers of
0.75 (mJ/cm2) and 3.74 (mJ/cm2), respectively. The solid lines are
best fits of the bi-exponential function.

Fig. 1 Schematic of the experimental apparatus of the femtosecond
TRG method.

average signal was recorded as a TRG response.
In order to examine multi-body effects of photo-excited carriers,the photo-excited carrier density was controlled by changing thepump beam intensity. Furthermore, in order to differentiate
information parallel to the surface and perpendicular to it, thedependence of the TRG responses on the fringe spacing wasmeasured by changing the incident angle of the pump beam.
A single crystal of Si(111) was used for the measurements.
The oxidized layer on the Si surface was 100 nm thick. All
experiments were performed in air at 296 K.

Results and Discussion
Analysis of the TRG signals
Typical TRG responses are shown in Fig. 2. We first discuss
how to analyze them. The TRG responses reflect the change inthe refractive index (∆n) on the Si surface, as induced by thepump beam. ∆n is evaluated as ∆n = ∆nN + ∆n∆T, where ∆nNand ∆n∆T are the carrier and temperature contributions to ∆n,respectively. For small N and ∆T, ∆nN and ∆n∆T are given by∆nN = (∂n/∂N)N, ∆n∆T = (∂n/∂T)∆T with ∂n/∂N and ∂n/∂Tbeing constant, where N is the density of the photo-excited
carriers and ∆T is the temperature rise on the Si surface.
To discuss ∆nN due to the carrier effect, we need to calculate
the proportional constant, ∂n/∂N, by applying the Drude modelfor the optical properties of quasi-free carriers to the photoexcited electron-hole pairs.11 The change in the refractive index(∆n) is given by∂nNe2∆nN = —— N = – —————— ≤ 0,∂N
2n0m*ehε 0ω p2(1)

where N is the photo-excited carrier density, e the fundamental
electron charge (1.60 × 10–19 C), n0 the absolute refractive indexof Si at 800 nm (3.6912), ε 0 the dielectric constant (8.85 × 10–12 Fm–1), meh* the effective reduced mass of the electron-hole pair(1.17 × 10–31 kg13) and ω p the radial frequency of the probe light(2.36 × 1015 s–1). From Eq. (1), the change due to the carrier

effect (∆nN) becomes negative. In this experiment, thecalculated value of ∂n/∂N is –6.0 × 10–22 cm3.
We next discuss ∆n∆T due to a temperature rise on the Si
surface through a variety of effects, including electron-phonon
coupling or Fermi smearing. The change in the refractive index
induced by the temperature rise (∆n∆T) is given by∂n∂k∆n∆T = —— ∆T + —— ∆T,∂T∂T
where n and k are the real and imaginary parts of the refractiveindex, respectively. Based on a previous report,14 the temperaturedependence of ∂n/∂T and ∂k/∂T can be neglected. At a probe
wavelength of 800 nm, we estimate the temperature coefficientsas ∂n/∂T = 5.1 × 10–4 K–1 and ∂k/∂T = 5.2 × 10–5 K–1 fromliterature values.15,16 Because the effect of ∂n/∂T on ∆n isminor,6 ∆n induced by the temperature rise is approximated as∆n∆T ≈ ∂n/∂T∆T ≥ 0. The temperature rise (∆T) at equilibrium
is estimated to be 144 K.17
∆nN is given by∂n∆nN = —— N = (–6.02 × 10–22) × (7.25 × 1020) = –0.437∂Nand ∆n∆T is given by∂n∆n∆T = —— ∆T = 5.1 × 10–4 × 144 = 7.34 × 10–2.
∂TThus, the contributory ratio, χ = ∆nN/∆n∆T, is calculated as χ =–5.95. Because the intensity of the TRG responses is proportionalto (∆n)2, the dominant component in the TRG responses is thecarrier effect. This result is supported by our previous report, inwhich we measured the negative change in the refractive index
from the transient reflectivity responses on a Si surface on apicosecond time scale.6 We can thus regard the change in therefractive index as being mainly due to the carrier effect.
The decay curve (R(t)) is fitted with a summation of some
exponential functions. A bi-exponential model provides thebest fitting with the TRG responses. The decay curve (R(t)) isformalized astt
R(t) = Cexp (– —) + (1 – C)exp (– —) ,τfτs
where τf and τs are the relaxation-time constants of the fastdecay component and of the slow one, respectively, and C is apre-exponential factor. We discuss ultrafast carrier dynamics
by analyzing these two relaxation processes below.

ANALYTICAL SCIENCES APRIL 2000, VOL. 16405

Fig. 3 Dependence of the relaxation rate of the fast component(τf–1) on the carrier density (N). The solid line is an eye-guide; thedotted line has a slope of 2.

Dependence on the photo-excited carrier density
As shown in Fig. 2, the TRG responses were drastically
influenced by the photo-excited carrier density (N), which wascalculated from the light-absorption volume, reflectivity18 andintensity of the pump beam. For a detailed analysis, the carrier
density (N) vs. the relaxation rate is plotted in Fig. 3. The
relaxation rate of the fast component increased with increasing
photo-excited carrier density, whereas that of the slow one wasindependent of the carrier density (N).
Here, we focus on the fast-relaxation component. The decayof the photo-excited carrier density with time is given by19∂ 2N∂N—— = –γ 1N – γ 2N2 – γ 3N3 + D —— + I (t = 0),∂x2∂twhere N is the photo-excited carrier density; γ 1, γ 2 and γ 3 are thecarrier-recombination rates of linear, two-body and three-bodyprocesses, respectively. D is the carrier-diffusion coefficient andI is the intensity of the pump beam at time zero. Considering
the experimental condition of the high carrier density (≈ 1020cm–3) and a previous report,5 the Auger-recombination process
is expected to be the dominant process for the fast component.
In this case, the above equation is approximated as ∂N/∂t ≈–γ 3N3 and the relaxation time (τf) is given by τf = I/γ 3N2; theslope in Fig. 3 would thus be 2 cm3/ps. However, theexperimental slope was clearly smaller than 2. This result
suggests that the fast-decay component includes anotherultrafast multi-body process as well as the Auger-recombination
process. The one- and two-body recombination processes are106-times slower than this result. We thus consider that anotherultrafast multi-body effect, the energy-dissipation process via
carrier-carrier scattering, called the carrier-thermalization process,occurs. It is known that the carrier-thermalization process
occurs on a sub-picosecond time scale following the generationof hot carriers, which don’t equilibrate with the phonon system.
Actually, the calculation for the effective mass14 indicates thatthe contribution of the non-equilibrium state to the TRG
response is 36-times stronger than that of the equilibrium state.
This also supports our result. This result suggests that the fastdecay component contains the thermalization process via
carrier-carrier scattering, and that the TRG responses arestrongly affected by the carrier-thermalization process.
Dependence on the fringe spacing ΛThe dependence of the relaxation rates of the fast and slow
components on the fringe spacing (Λ) was measured with apump beam power of 3.4 mJ/cm2. The fringe spacing (Λ) waschanged by controlling the incident angle (θ) of the pump beam.
The dependence of the relaxation rates of the fast and slow
components on the fringe spacing (Λ) is shown in Fig. 4. Boththe fast and slow relaxation rates increased with decreasing theFig. 4 Dependence of τf–1 and τs–1 on the fringe spacing (Λ). The
symbols and correspond to τf–1 and τs–1, respectively.

fringe spacing. If the phenomenon corresponding to thecomponents occurred perpendicular to the surface, nodependency on the fringe spacing should be observed. The
dependency of both components on the fringe spacing indicatesthat both decay components can be regarded as a phenomenon
parallel to the surface. We estimated the diffusion coefficientsof photo-excited carriers from this result using the transient
grating theory,20 and found that the values of the slow and fastcomponents are 20 cm2 s–1 and 60 cm2 s–1, respectively.
First, we discuss the slow component. Since the slow
component is over 10 ps, this is probably due to diffusion of thecarriers after equilibrium with phonons. We estimated thecarrier mobility from Einstein’s relation, D/µ = kBT/e, by
substituting the experimental diffusion coefficient of the slow
component and the estimated temperature (T = 440 K) on the Si
surface, which was calculated assuming that all surplus energy
given to carriers is used for the temperature rise of theequilibrium carrier and phonon systems. The obtained value is
530 cm2 s–1 V–1, which agrees with the previously reported valueof 572 cm2 s–1 V–1.21 Therefore, we conclude that the slowdecay component corresponds to diffusion of the photo-excited
carriers after equilibrium with phonons.
We next discuss the fast-decay component. For the fastcomponent, the transport of non-equilibrium carriers andequilibrium carriers is probable. However, from an earlier
discussion, the fast component cannot be explained by diffusion ofthe equilibrium carriers. This suggests that the fast component
is mainly due to diffusion of the non-equilibrium carriers, i.e.,there is little carrier scattering with phonons during fast decay.
We thus propose the ballistic transport of non-equilibrium
carriers occurring before the carrier-thermalization process via
carrier-carrier scattering, in which there is no scattering processduring several hundred femtoseconds.
Details can be added by an analysis of the non-equilibrium
carrier condition. By approximating the photo-excited carrierson the Si surface as quasi-free carriers in a metal, we obtain thetheoretical Fermi velocity, νF = 2.8 × 107 (cm/s). On the otherhand, the velocity of the photo-excited carriers is estimated byusing the following equation from this experiment:∂N∂N—— = V —— ,∂t∂xwhere N is the carrier density and V is the transport velocity.
We obtain an experimental value of 1.2 × 107 cm/s for VF. Thisvalue agrees with the theoretical one in terms of the time scale.
We believe that this result suggests the ballistic transport ofnon-equilibrium carriers. Considering the results for the406
dependence on the photo-excited carrier density, we conclude
that the fast-relaxation component corresponds to a process ofballistic transport and carrier-carrier scattering of nonequilibrium carriers.
In conclusion, we have developed a femtosecond time-resolved
transient-reflecting grating (fs-TRG) method, and havesuccessfully measured the ultrafast carrier dynamics on Si
surfaces. An analysis of the TRG responses as a function of thepump beam intensity and fringe spacing suggests that the slow
component corresponded to the carrier diffusion, and that thefast component corresponded to a combined process of ballistictransport and carrier-carrier scattering of non-equilibriumcarriers. We believe that the fs-TRG method will provide
significant information about the relation between the electric
property and the photo-excited carriers, especially nonequilibrium carriers in the ultrafast time region, and that it will
be a powerful tool for evaluating defects on semiconductor
surfaces.

Acknowledgements
This work was supported by Grand-in-Aids for Specially
Promoted Research (No. 07102004) and for Scientific Researchon Priority Areas of Electrochemistry of Ordered Interfaces(No. 09237219) from the Ministry of Education, Science andCulture of Japan.

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