Simultaneous topographic and thermal imaging of
silicon nanowires using a new SThM probe
Etienne Puyoo1,2, Stéphane Grauby1, Jean-Michel Rampnoux1, Wilfrid Claeys1, Emmanuelle
Rouvière1, Stefan Dilhaire1
1
CPMOH,Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex, France,
2
CEA - DRT/LITEN/DTNM, LCH, 17 Rue des Martyrs, 38 054 Grenoble cedex
stephane.grauby@u-bordeaux1.fr, tel :33 (0)5 4000 2786, fax : 33 (0)5 4000 6970
Preference for an oral presentation
Hinz[16] determined the thermal conductivity of a 3nm thick
HfO2 film with a spatial resolution around 25nm. However,
the probe plays a crucial role to achieve nanothermal
analysis with SThM and these low spatial resolutions are not
obtained with commercial probes but with home-made
probes, which represents a technological difficulty. With
commercial probes, such as the classical well-known
Wollaston one, which is the most commonly used probe, the
resolution is of the order of 1µm and hardly lower[17].
But recently, a new commercial SThM probe has become
available and seems very promising in terms of spatial
resolution but also of time response, enabling a fast
acquisition speed. In this paper, we hence first present the
geometry and electrical characteristics of this new probe.
Then, in section III, we present topographic and thermal
images of silicon nanowires to appreciate the spatial
resolution and acquisition speed. Nevertheless, this probe is
new and there is no thermal model available in order to
calibrate it if we plan to extract thermal properties, such as
thermal conductivities, from the thermal images.
Consequently, section IV presents a thermal model of this
probe when out of contact and section V resumes the probe
parameters extracted from the model.
Abstract- In Scanning Thermal Microscopy (SThM)
techniques, the probe, and more particularly the tip, plays a
major role in the spatial resolution limitation and in the
acquisition speed. We present a new commercial resistive SThM
probe constituted of a Palladium (Pd) film on a SiO2 substrate.
We first describe its geometry and electrical properties. Then,
we present topographic and thermal images of silicon nanowires,
which show the very good spatial resolution (<100nm) and the
high acquisition speed obtained with this probe. To extract
thermal parameters from a thermal image, a calibration of the
probe is necessary. Hence, we propose a model for the probe and
we finally use it to identify its geometric, electrical and thermal
parameters.
I.
INTRODUCTION
With the increasing integration density of microelectronic
circuits and the development of nanotechnology, there is a
need for experimental methods able to measure local thermal
properties at nanometric scales with short acquisition time.
As a consequence, temperature measurement methods such
as infrared imaging [1-3], liquid crystals measurements or
temperature measurements using micrometric thermocouples
deposited on the surface of the device[4] are not adapted to
this kind of samples as they offer a bad spatial resolution
(hardly lower than 5µm) regarding the device dimensions.
Visible optical methods such as thermoreflectance[5-7] or
interferometry[7,8], which are diffraction limited, cannot
reach such a resolution neither.
Since its invention in 1986, the Scanning Thermal
Microscopy (SThM)[9] is presented as the most efficient
technique to study thermal transport in nano-objects and
nanomaterials. It is based on an Atomic Force Microscope
equipped with a thermal probe to carry out thermal images
while simultaneously obtaining contact mode topography
images[9-11].
The SThM has two different working configurations: the
active and the passive modes. In the passive mode, the
sample is locally heated and the passive probe, used as a
thermometer, generates a temperature map. In 2000,
Shi[12,13] thus measured the temperature distribution in
current-carrying carbon nanotubes with a spatial resolution
around 50nm. On the contrary, in the active mode, the tip
also serves as a heater. By measuring the tip temperature, we
can evaluate the tip-to-sample heat flux exchange, which
depends, among other things, on the sample thermal
properties. Then, the SThM in active mode can measure
local thermal properties[14,15]. In 2008, using this mode,
II. GEOMETRIC AND ELECTRICAL PROPERTIES OF THE
PROBE
Let us first present this new probe and determine its
electrical characteristics, which will enable to choose the
appropriate experimental conditions, such as the working
frequency or the acquisition speed.
Fig.1. SEM pictures of the Pd/SiO2 probe.
1
The probe is a new commercial Pd/SiO2 probe (from
Anasys Instruments). Fig. 1 shows SEM pictures of this
probe. It is a specially designed SiO2 silica contact mode
probe that incorporates a thin Palladium (Pd) film near the
apex of the tip. Two Nickel Chromium current limiters are
placed upstream from the tip. Here, the thin Pd film acts as
the thermo-resistive element. Its temperature coefficient has
been measured: α=1.210-3K-1. The probe total electrical
resistance is R0=368. It is the constituted of 3 resistors in
series: a Pd one corresponding to the tip itself RTip, the
limiters one RNiCr and a second Pd one corresponding to the
rest of the Pd probe RPd. As the Pd layer is very thin on the tip
(about ten nanometers) and much thicker on the rest of the
probe (≈250nm), and considering the other probe dimensions,
RPd is negligible. We have measured RTip=187 and RNiCr+
RPd=181.
The probe will be used in the active SThM working
configuration performed in the ac-regime using the 3ωmethod[18], whose principle will be recalled in detail in the
following section. To sum it up, the probe is supplied by a ω
pulsation current and warms up due to Joule effect. Then, the
3ω probe voltage depends on the probe temperature
variations.
As a consequence, it is useful to determine the probe cutoff frequency in order to choose the appropriate ω electrical
pulsation of the function generator. Indeed, the probe behaves
as a low-pass filter[19]. So, if we do not want to attenuate the
thermal signal, we must choose a working frequency within
the probe bandwidth. But, in addition, the probe thermal cutoff frequency 2f or its thermal time response rules the
maximum scan speed achievable to carry out thermal
imaging. Indeed, the time spent on each measurement point
must be several times higher than the lock-in time constant,
which in turn must be several times higher than the thermal
excitation period of the signal. Consequently, the cut-off
frequency limits the acquisition speed. Practically, choosing
the time spent on each point at least ten times higher than the
thermal period is a good compromise to keep a fast
acquisition speed without affecting the 3ω signal.
Therefore, we measured the Bode response of the probe
(Fig. 2), collecting the V3ω amplitude, hence the temperature
variation T2ω, as a function of the thermal pulsation 2ω. The
2f thermal cut-off frequency of the Pd/SiO2 probe is
measured equal to 2750Hz. It is 11.5 times higher than the
classical Wollaston probe which is one of the most used
commercial SThM probes. The acquisition time is then
reduced by the same factor.
In the experiments described in section III we will then
choose a f=1kHz electrical excitation frequency for the
Pd/SiO2 probe. Hence, the thermal excitation frequency is
2kHz. Then the measurement time spent on each point is
5ms. Typically, for a 256256 point image, it reduces the
image acquisition time from about 1h with a Wollaston
probe to less than 6 minutes with a Pd/SiO2 probe.
III. TOPOGRAPHIC AND THERMAL IMAGES OF SILICON
NANOWIRES
The 3ω-method[18,20] is particularly well adapted for
SThM active measurements when using a thermoresistive
probe like the Pd/SiO2 one. Indeed, a ω pulsation sinusoidal
current passes through the thermoresistive probe which
warms up itself due to Joule effect. The dissipated heat flux
PJoule in the probe is given by:
PJoule  R(T )
I02
(1  cos(2t )) (1)
2
where R(T) is the temperature dependant electrical resistance
of the probe, and I0 the alternative current amplitude.
Consequently, the probe temperature variations ΔT can be
related to the static temperature amplitude T DC and the second
harmonic one T2ω, respectively:
T  TDC  T2 cos(2t   )
(2)
where Φ is the phase shift between the thermal and electrical
signals. The 3ω probe voltage V3ω is then expressed as
follows:
V3 
RI 0T2
cos(3t   )
2
(3)
where R is the probe resistance at room temperature and α is
the probe temperature coefficient expressed in K-1.
Then, measuring the 3ω probe voltage during a scan in
contact, we can make a T2ω probe temperature variations map.
When the probe comes into contact with a material, a heat
flow goes from the tip to the sample and this flow depends on
the sample thermal conductance. Consequently, the T2ω probe
temperature variations depend on an equivalent thermal
conductance Geq which is the connection of the tip-to-sample
contact thermal conductance GC and of the sample thermal
conductance GS. The more conductive the sample, the lower
the 2ω thermal variations.
Fig. 2. Normalized modulus of the 2ω temperature variations as a function
of thermal pulsation (Bode response).
2
To measure the 3ω probe voltage V3ω, the probe is
included in a Wheatstone bridge connected to an
amplification isolation system (Fig. 3). The variable resistor
Rpot is adjusted so that its electrical resistance should be equal
to the probe electrical resistance. A lock-in measurement of
the 3ω probe voltage V3ω is made during each scan.
The sample is an assembly of Si nanowires
embedded in a silica SiO2 die. Their diameter vary from 30 to
80nm with a 50nm mean value. Many nanowires jut out
above the silica die of a few tens of nanometers. The Si
nanowires have been grown via Au catalyzed Vapor Liquid
Solid reaction in an epitaxial chamber[21]. The nanowires are
first oxide etched with an HF solution and the Au catalyser
residues are suppressed with a IK:I2 solution. The nanowires
array is then encapsulated by spin-coating a solution of SOG
(spin-on glass) material on the substrate. The sample top
surface is then submitted to a CMP (Chemical Mechanical
Polishing) process in order to reduce surface roughness and
hence, to facilitate the SThM scanning. A final etch is
realized with an HF solution during a few seconds to ensure a
good digging out of the nanowires.
We carry out simultaneously a topographic image and a
thermal image of the sample top surface. The two images
presented in Fig. 4 are 3µm2µm sized pictures, with a
resolution of 256 pixels256 pixels. On the topographic
image, we can observe many NWs extremities jutting out
above the SiO2 dye. The digging out height is appreciatively
20 nm. We recall that the image acquisition time is less than
6 minutes. On the thermal image, we observe that the sample
impedance increases when the heat flux is applied directly in
closed proximity of each NW. In fact, a high voltage
observed in the thermal image implies large thermal
impedance. The measured mean diameter of the nanowires,
estimated by the full width at half maximum on several
nanowires, is 91nm. This shows that we can thermally probe
individual Si NWs with a spatial resolution below 100 nm.
Fig. 4. SThM imaging of silicon nanowires embedded in a silica matrix: (a)
topographic image and (b) thermal image obtained with a Pd/SiO2 probe.
Obviously, this commercial probe turns out to be
performing, in terms of scan speed and spatial resolution. By
comparison with the well-known Wollaston wire SThM
probe, the reached spatial resolution is appreciatively 1 µm
in atmospheric conditions, and the frequency cut-off is
around 200Hz[18] which corresponds to an 1h acquisition
time to acquire an 256pixels256pixels thermal image.
Nevertheless, the main drawback of this new probe is the
fact that there is no model available for it unlike the
Wollaston probe which has been widely studied.
Consequently, we have developed a model for the calibration
of this probe based on the model developed in [18] for the
Wollaston one.
IV. PROBE CALIBRATION
The model developed here corresponds to a thermal
description of the probe behaviour out of contact. By
comparing the theoretical V3ω modulus and phase signals with
experimental data, it allows us to quantify the geometric,
thermal and electrical properties of the probe. Indeed, this
part of the model corresponds to a calibration of the probe.
The theoretical V3ω curves are also compared with
measurements performed in vacuum (10 -5 Torr) to identify the
convective losses parameter hair in the air.
As illustrated in Fig. 1, the tip is made of SiO2 with a thin
layer of Palladium deposited on the back surface. The probe
has a symmetry plan and hence, the system is simplified
considering just one side of this plan. A schematic
representation of the semi-probe is described in Fig. 5. The
heat equation is applied on the primitive volume dV of the
simplified studied system. Moreover, the system is supposed
to be isothermal in the y and z directions.
Fig. 3. 3ω-scanning thermal microscopy principle.
Fig. 5. Schematic representation of the Pd/SiO2 probe.
3
First, we introduce a Joule dissipation source term ФJ:
j 
 elec1 dxI 0 ²
S1
where Kampli is the amplification isolation system gain.
Besides, this parameter is set as a constant in the V 3ω
calculation. The Kampli modulus and phase Bodes have
previously been measured and the 3ω amplification system
output voltage are corrected in consequence to deduce the 3ω
probe voltage V3ω.
The first experimental results revealed that current
limiters, placed upstream from the tip on the probe (Fig. 1),
generate 3ω signal because of their high electrical resistance.
The limiters are ribbons made of Nickel Chromium alloy. It is
necessary to include these limiters in the model to get
acceptable fitting curves. We can simply model their thermal
behaviour as a first order low pass filter expression:
(4)
where the index 1 refers to the Pd thin film, ρelec1 is the Pd
electrical resistivity, S1 the Pd layer section. A diffusive term
is then added on the two sections at positions x and x+dx:
T
x 
x
T
x  dx
 2 S 2
x
 x  2 S 2
 x  dx
(5)
V3  Lim iters 
where the index 2 refers to the SiO2 layer, 2 is the SiO2
thermal conductivity and S2 the SiO2 layer section. The heat
diffusion in the Pd film is voluntary neglected since it is very
thin, about ten nanometers, and represents a barrier to heat
diffusion compared to the 1 µm thick SiO2 layer. Finally, the
convective heat losses in the air are expressed as:
 h  hair p 2 dxT
(6)


I ²
T2   elec1 0
22 S1 S 2

V3  Distortion  V D exp( i D )
(7)

(13)
Fig. 6 present the theoretical modulus and phase curves
of the 3ω voltage. The three curves represents: the (V3ω)Tip Pd
tip 3ω voltage alone, the sum (V3ω)Tip+(V3ω)Distortion of both Pd
tip and generator distortion 3ω voltages and the sum of the
three contributions V3ω. These curves show that the distortion
of the generator mainly influences the phase at frequencies
higher than 2kHz whereas the limiters influence both phase
and modulus for frequencies lower than 2kHz.
T2
( x  L)  0 (8)
x
1 L
T2 ( x,  )dx
L 0
(12)
V3  V3 Tip  V3  Limiters  V3  Distortion
We assume the ends of the Pd ribbon are at room
temperature since the larger and thicker Pd connectors are
considered to constitute a thermal sink. As a consequence, the
heat flux at the middle of the Pd ribbon is set to zero. The
temperature profile is then averaged on the tip length L
because the voltage measurement corresponds to the spatial
average of the probe resistance:
T2 ( ) 
(11)
where VD and ФD are the modulus and phase of the third
harmonic distortion term. The total 3ω bridge voltage is
expressed as:
where a2 is the SiO2 thermal diffusivity. The boundary
conditions can be written:
T2 ( x  0)  0 and

1 i
c
where G is the DC limiters 3ω voltage and ωc the cut-off
pulsation. Finally, we take into account the generator third
harmonic distortion. The correspondent term added in the V 3ω
expression can be written:
where hair is the convective losses parameter and p2 the SiO2
layer perimeter. The alternative regime part of the heat
equation is then solved in Fourier space:
d ²T2  2i hair p 2
 

dx²
2 S 2
 a2
G
(9)
Consequently, the 3ω tip voltage can be expressed as:
V3 Tip  K am pli
Fig. 6. Theoretical modulus and phase curves presenting the various
contributions in V3ω.
RTipI 0
T2 ( )
2
 I L
 K am pli 0 elec1 T2 ( )
S1
(10)
4
V. PARAMETERS IDENTIFICATION
All the parameters entered in the model are referenced in
Table 1. The geometry of the probe has previously been
evaluated with SEM pictures. However, it remains an
uncertainty on Pd width l and length L. These two parameters
are then adjusted in the model. The SiO2 thermal properties
and Pd electrical properties have been extracted from
literature[22]. The four parameters left concerning the limiters
and distortion properties are also adjusted in the model.
The measured parameters used are: e=1µm measured on SEM
images, I0=308µA, RTip=187 and α=1.210-3K-1. For the
SiO2, we have taken 2 =1,3 W.m-1.K-1 and a2 =8,6.10-7 m2.s-1.
A first calibration is made under vacuum (P=10 -5 Torr),
which means that hair=0. The sensitivity curves concerning the
6 remaining free parameters in the model are exposed in Fig.
7.
The sensitivities on each parameter are not correlated one
with another which enables us to fit easily theoretical curves
on experimental data. The parameters L, VD and ФD are
identified using the phase signal, L in the 10 3-105 rad.s-1
pulsation region and both distortion parameters above the 10 5
rad.s-1 pulsation. Then, the three other parameters are obtained
from the modulus signal, l above 5103 rad.s-1 pulsation, G
for low pulsations below 5102 rad.s-1 and ωc in the 102-104
rad.s-1 pulsation region.
Then, another calibration is made under normal pressure
conditions (atmospheric conditions) to identify hair. Among
the other parameters, only G and ωc depend on the pressure
conditions. Fitting curves on V3ω modulus and phase signals
are presented in Fig. 8 under vacuum and under atmospheric
conditions.
Fig. 7. Modulus and phase sensitivity curves of 6 free parameters.
We observe an excellent agreement between the
experimental and theoretical V3ω modulus and phase profiles,
whether it be for the curves under vacuum or for the curves
under atmospheric conditions. All the values identified are
summed up in table 2. The distortion amplitude parameter V D
corresponds to the total harmonic distortion value indicated in
the Agilent 33210A function generator specifications
(THD<10-4). The Pd length L and width l are evaluated to be
8.8 µm and 1.72µm respectively, which are coherent with
values measured in SEM images.
TABLE I
PARAMETERS USED FOR THE MODEL
ID: IDENTIFIED, MEAS: MEASURED, LIT: FROM LITERATURE
geometry
Pd
tip
Thermal
properties
Electrical
properties
Current limiters
Generator
distortion
L
l
e
2
a2
hair
I0
RTip
α
G
ωc
VD
ФD
Tip length(m)
Tip width(m)
Tip thickness(m)
SiO2 conductivity (W.m-1.K-1)
SiO2 diffusivity (m².s-1)
Convection loss coefficient
(W.m-2.K-1)
Current amplitude (A)
Pd resistance ()
Temperature coefficient (K-1)
Gain (V)
Cut-off pulsation(rad.s-1)
Distortion modulus (V)
Distortion phase (rad)
id
id
meas
lit
lit
id
meas
meas
meas
id
id
id
id
Fig. 8. V3ω modulus and phase experimental curves and fits under vacuum
(P=10-5 Torr) and under atmospheric conditions: circles are used for
experimental data and continuous lines for the fits.
5
[14]
TABLE 2
hair(W.m-2.K-1)
G(V)
ωc(rad.s-1)
L(µm)
L(µm)
VD(V)
ФD(rad)
IDENTIFIED PARAMETERS
0 (vacuum)
0.0232
700
8.8
1.72
0.045
-0.4
6100 (atm)
0.0135
1000
[15]
[16]
[17]
We have hence characterized a new SThM probe. It seems
very promising as offering a very good spatial resolution
(<100nm) and a relatively high thermal cut-off frequency,
which means a reduced acquisition time. We have presented a
model that enables to calibrate this probe and hence to
identify its geometrical, electrical and thermal characteristics.
Next step will consist in adapting this model to develop a
model of the probe in contact with a sample under test in
order to extract thermal parameters, such as the sample
thermal conductance or conductivity, from thermal images.
[18]
[19]
[20]
[21]
ACKNOWLEDGMENT
This work has been supported by the ANR PNANO.
[22]
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Keywords: Scanning Thermal Microscopy probe, thermal model, nanowire imaging.
Biography: Stéphane Grauby obtained a Ph.D. at the Université Pierre et Marie Curie (Paris 6) in 2000. He
is currently an assistant professor at the Université Bordeaux 1 where he is part of a team engaged in the
thermomechanical characterization of materials and electronic devices.
7