Micro-Raman spectroscopy of Si nanowires: Influence of diameter and temperature

Article abstract of DOI:10.1063/1.3284647

Raman spectroscopy provides nondestructive information about nanoscaled semiconductors by modeling the phonon confinement effect. However, the Raman spectrum is also sensitive to the temperature, which can mix with the size effects borrowing the interpret

Full text of DOI:10.1063/1.3284647

Micro-Raman spectroscopy of Si nanowires: Influence of diameter and
temperature
A. Torres, A. Martín-Martín, O. Martínez, A. C. Prieto, V. Hortelano et al.
Citation: Appl. Phys. Lett. 96, 011904 (2010); doi: 10.1063/1.3284647
View online: http://dx.doi.org/10.1063/1.3284647
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APPLIED PHYSICS LETTERS 96, 011904 ͑2010͒
Micro-Raman spectroscopy of Si nanowires: Influence of diameter
and temperature
A. Torres,1 A. Martín-Martín,1 O. Martínez,1 A. C. Prieto,1 V. Hortelano,1 J. Jiménez,1,a͒
A. Rodríguez,2 J. Sangrador,2 and T. Rodríguez2
1GdS Optronlab, Ed IϩD, UVa, P. de Belén, 1, 47011 Valladolid, Spain
2Tecnología Electrónica, ETSIT, UPM, 28040 Madrid, Spain
͑Received 28 October 2009; accepted 5 December 2009; published online 5 January 2010͒
Raman spectroscopy provides nondestructive information about nanoscaled semiconductors by
modeling the phonon confinement effect. However, the Raman spectrum is also sensitive to the
temperature, which can mix with the size effects borrowing the interpretation of the Raman
spectrum. We present an analysis of the Raman spectra of Si nanowires ͑NWs͒. The influence of the
excitation conditions and the temperature increase in the NWs are discussed. The interpretation of
the data is supported by the calculation of the temperature inside the NWs with different
diameters. © 2010 American Institute of Physics. ͓doi:10.1063/1.3284647͔
Nanoscaled semiconductors attract a great attention be-
cause of their unique optical and electrical properties, which
make them suitable for advanced device applications.1
Therefore, a great deal of characterization effort has been
devoted to the study of the nanowires ͑NWs͒ properties,
which depend on its diameter. Experimental techniques al-
lowing the assessment of that kind of information are highly
interesting for the understanding of the relation between the
dimension and the NWs properties. Raman spectroscopy is a
powerful nondestructive tool suitable to such study, because
of the spectral changes related to the phonon confinement in
reduced diameter NWs;2–5 also because it provides informa-
tion about phonons, which are very relevant to the transport
phenomena, both electronic and thermal. As a consequence
of the breakdown of the translational symmetry in structures
of reduced dimensions, the phonon correlation length be-
comes finite, and the momentum selection rule is relaxed
allowing scattering by phonons out of the zone center.6,7 The
result is the downshift and asymmetric broadening of the
one-phonon Raman bands. The analysis of the Raman spec-
tra is based on the phenomenological confinement model in-
troduced by Ley and coworkers,6 later refined by Campbell
et al.7 for NW geometry. The one phonon Raman spectrum
of Si NWs has reached a great deal of controversy, because
of the discrepancies between the expected and measured line
shapes; failing in the accurate estimation of the NW
diameter.2–5 Different reasons have been argued as possible
causes for the inconsistency of the Raman parameters mea-
sured in Si NWs. The one phonon Raman line shape can be
modified by NW diameter distribution,2 Fano scattering from
photogenerated carriers,3 and laser induced NW heating.4
The Raman microprobe works with a relative high laser
power density; the energy absorbed by the sample needs to
be dissipated; if the heat evacuation is not efficiently
achieved the scattering volume can reach temperatures above
the ambient, which deform the Raman bands. Therefore, the
thermal conductivity of the probed system has to be consid-
ered if one looks for a straightforward interpretation of the
Raman data. Usually, nanostructures are embedded in an en-
vironment medium, which can have poor thermal conductiv-
ity, as is the case of NWs in air. The poor thermal conduc-
tivity of the air, and the very small base of the NW in contact
with the substrate where they were grown make difficult the
heat dissipation from the NW; therefore, one can expect a
non-negligible temperature enhancement in the NWs under
the laser exposure during the Raman measurement.
The Si NWs used in this study were fabricated by the
vapor-liquid-solid method using colloidal Au as catalytic
metal and a low pressure chemical vapor deposition reactor.
The NW growth was carried out at 500 °C using Si2H6 as a
precursor gas with a flow of 10 SCCM ͑SCCM denotes cubic
centimeter per minute at STP͒, N2 as carrier gas with a flow
of 90 SCCM and a total pressure of 400 mTorr. Typical NWs
had diameters ranging from 10 to 120 nm, and several mi-
crometers in length. The Raman spectra were acquired with a
Labram UV-HR 800 Raman spectrometer from Jobin Yvon.
The excitation was done with an Ar+ laser ͑514.5 nm͒ using
a 0.95 numerical aperture 100ϫ objective; excitation power
densities on the sample surface up to 100 kW/cm2 were
used. The NWs appear as seen in the scanning electron mi-
croscopy ͑SEM͒ image, Fig. 1, forming tangles of wires. The
circle in Fig. 1 represents the laser beam on the focus, which
means that only a reduced number of wires are probed in a
Raman measurement.
The Raman spectra for different laser power densities
are shown in Fig. 2͑a͒. The one phonon band downshifts and
FIG. 1. SEM image of Si NWs. The circle represents the laser beam at the
focus. The zoom shows that only a few NWs ͑4 in this case͒ with different
diameters are excited by the laser beam.
a͒
Electronic mail: jimenez@fmc.uva.es.
0003-6951/2010/96͑1͒/011904/3/$30.00
96, 011904-1
© 2010 American Institute of Physics
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011904-2
Torres et al.
Appl. Phys. Lett. 96, 011904 ͑2010͒
FIG. 3. Calculated Raman spectra taking account of temperature ͑8 nm
diameter͒.
obtained the dependence of the Raman parameters with
temperature on the bulk Si control sample. The variation in
␻
and ⌫o with temperature was approached to a linear
o
function ͓␻ ͑cm−1͒=521.9−0.0242 T͑°C͒; ⌫o͑cm−1͒=2.8
o
+0.0102 T͑°C͔͒. The temperature dependence of the A and
B parameters for phonons with qꢀ0 is not available; there-
fore, the full phonon branch was taken rigid, and assumed to
follow the same temperature dependence for each q. This is
an approximation, since one can expect variations in the an-
harmonic constants of NWs respect to the bulk values.10
The Raman line shape was insensitive to the laser power
when the measurements were carried out with the sample
immersed in water. Nevertheless, the bandwidth was larger
than the bandwidth of the bulk Si control sample, which
should be due to phonon confinement effects. The effect of
the temperature in the Raman spectrum of NWs was calcu-
lated with Eq. ͑1͒, Fig. 3; the Raman peak shifts to the low
frequency with increasing temperature, while the band
broadens, becoming more symmetric with respect to the pure
phonon confinement profile. The experimental spectra mea-
sured in standard conditions, with the NWs in air, cannot be
fitted using a single NW diameter and the temperature effect.
In fact, the spectra obtained at high laser power, Fig. 2͑a͒, do
not look symmetric as expected for NWs at high tempera-
ture. The line shape of the experimental spectra can only be
accounted for on the basis of an inhomogeneous temperature
distribution inside the scattering volume. Adu et al.5 modeled
the Raman spectra taking account of a temperature gradient
inside the laser excited region of the NWs; they assumed a
NW diameter and needed a very large axial temperature
variation ͑⌬TϾ100 K͒. In order to study the temperature
distribution inside the NWs, we carried out finite element
analysis of the heat dissipation in the NWs under the expo-
sure to a laser beam ͑514.5 nm͒ with a Gaussian power pro-
file. The calculation took account of the dependence of the
thermal conductivity with the NWs diameter.11 A detailed
description of the procedure will be given elsewhere. The
results for a laser beam power density of 100 kW/cm2 are
summarized in Fig. 4. The temperature inside the region of
the NWs exposed to the laser beam presents a strong depen-
dence with the NW diameter, significant temperature differ-
ences can be reached in between NWs of different diameter
under the laser beam excitation. On the other hand, the axial
temperature variation inside the laser beam in a single NW
does not exceed 20 °C, see the inset of Fig. 4, where the
axial temperature profile in a 20 nm diameter NW is repre-
sented; the asymmetry of the profile reflects the asymmetry
FIG. 2. Raman spectra measured in air ͑a͒, and water ͑b͒. The laser power
densities are 10 ͓only in ͑a͔͒, 25, 50, and 100 kW cm−2. The spectrum of the
control sample is also shown in ͑b͒.
asymmetrically broadens with increasing laser power excita-
tion; this suggests NW heating induced by the laser beam.
NW heating with increasing laser power density excitation
was confirmed by the measurement of the Stokes/anti-Stokes
intensity ratio;8 which estimates average temperatures of a
few hundred degree Celsius ͑300–400 °C͒ under the laser
exposure. The Raman spectra were also measured with the
NWs immersed in deionized water, Fig. 2͑b͒; the spectrum of
a bulk Si control sample is also plotted. The two series of
spectra, in air, and in water, show that the deformation of the
phonon bands strongly depends on the thermal conductivity
of the surrounding media,4 ͑0.58 W/mK for water versus
0.024 W/mK for air͒.
In order to interpret the Raman spectra, one should ana-
lyze the temperature dependence of the one phonon Raman
band of Si NWs. In the frame of a Gaussian localization
factor,6,7 the Raman intensity of particles of diameter L can
be expressed as follows:
q2L2
d3q
I͑␻,L͒ ϰ exp −
,
͑1͒
ͩ ͪ
͵
2
16␲
⌫
0
͓␻ − ␻͑q͔͒2 +
ͩ ͪ
2
where ␻͑q͒ is the phonon dispersion function, and ⌫o the full
width at half maximum ͑FWHM͒ of the bulk material; the
linewidth includes the instrument broadening contribution,
which in our experimental conditions gives a FWHM for a
high quality Si bulk crystal of 2.8 cm−1 at room temperature.
The phonon wave vector modulus, q, is expressed in units of
2␲/a, where a is the lattice parameter of crystalline Si. In
the case of the NWs, the symmetry is cylindrical with in-
plane phonon confinement, therefore, d3q=2␲q dq. The pho-
non dispersion relation for pure Si can be approximated by
1/2 1/2
␻͑q͒ = ͑A + ͕A2 − B͓1 − cos͑␲q͔͖͒
͒
,
͑2͒
where, A and B are determined from the phonon dispersion
curve.9 If one takes account of the temperature, one should
replace in Eq. ͑1͒ ␻͑q͒ by ␻͑q,T͒, and ⌫o by ⌫o͑T͒. We
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011904-3
Torres et al.
Appl. Phys. Lett. 96, 011904 ͑2010͒
FIG. 5. Experimental ͑dots͒ Raman spectrum of NWs in air ͑laser power
density ϳ100 kW/cm2͒, and calculated ͑line͒ spectrum considering wires
with different diameters and their corresponding laser beam induced
temperatures.
FIG. 4. Calculated maximum temperature induced by the laser beam in the
region of the NWs under the laser excitation as a function of the NWs
diameter for an incident laser power density of 100 kW/cm2 ͑Gaussian
distribution͒. The inset shows the axial temperature distribution inside the
area excited by the laser beam in a 20 nm diameter wire.
the thermal conductivity with the NWs diameter is respon-
sible for a strong temperature inhomogeneity inside the scat-
tering volume, which is mainly due to the different tempera-
tures reached by the probed NWs depending on their
diameter.
of the laser beam position respect to the ends of the NW and
the different dissipation of each other; note that this gradient
is even lower for NWs with larger diameter; these gradients
cannot account by themselves for the anomalous broadening
of the experimental Raman bands. However, these data pro-
vide the information necessary to interpret the Raman spec-
tra of discrete sets of NWs with dispersed diameters. Under
this approach, one can fit the experimental Raman bands
considering a reduced number of NWs of different diam-
eters, and therefore, different temperatures induced by the
laser beam excitation. Figure 5 shows the fit of the experi-
mental Raman spectrum considering the contribution of
wires with diameters, Ϸ20, 30, 40, and 100 nm, which ac-
cording to the data of Fig. 4, estimated for a laser power
density of 100 kW/cm2, equivalent to our experimental con-
ditions, reach temperatures around 400, 325, 250, and
150 °C. The contribution of each NW was weighted accord-
ing to its corresponding contribution to the scattering volume
in order to get the best fit.
This work was funded by the Spanish Government
͑Grant No. MAT-2007-66181͒ and by Junta de Castilla y
León ͑Grant No. VA051A06 -GR202͒.
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In conclusion, the micro-Raman spectrum of Si NWs is
strongly dependent on the excitation laser power density,
which induces NW heating, because of the reduced thermal
conductivity of the surrounding media. The dependence of
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