Thickness microscopy based on photothermal radiometry for the measurement of thin films

Article abstract of DOI:10.1016/j.saa.2008.10.009

The photothermal detection technique is an innovative and non-contact method to investigate the properties of films on workpieces. This paper describes a novel experimental set-up for thickness microscopy based on photothermal radiometry. The correlation

Full text of DOI:10.1016/j.saa.2008.10.009

Spectrochimica Acta Part A 72 (2009) 361–365
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and
Biomolecular Spectroscopy
journal homepage: www.elsevier.com/locate/saa
Thickness microscopy based on photothermal radiometry for the measurement
of thin films
Liping Wanga,∗, Helmut Prekelb, Hengbiao Liua, Yanzhuo Denga, Jiming Hua, Gert Gochb
a College of Chemistry and Molecular Science, Wuhan University, Wuhan, Hubei Province 430072, PR China
b Bremen Institute for Metrology, Automation and Quality Science (BIMAQ), Linzer Str. 13, 28359 Bremen, Germany
a r t i c l e i n f o
a b s t r a c t
Article history:
The photothermal detection technique is an innovative and non-contact method to investigate the prop-
erties of films on workpieces. This paper describes a novel experimental set-up for thickness microscopy
based on photothermal radiometry. The correlation between the thermal wave signal and the film thick-
ness is deduced and evaluated to determine the film thickness with a lateral resolution of less than 1 mm.
Results indicate that the thickness microscopy is a useful method to characterize thin films and has the
potential to be applied in-process.
Received 1 November 2007
Received in revised form 20 August 2008
Accepted 9 October 2008
Keywords:
Film thickness
Microscopy
© 2008 Elsevier B.V. All rights reserved.
Photothermal radiometry
1. Introduction
optically transparent films, eddy current and resistivity can be
used for metallic films, beta backscatter and X-ray fluorescence are
Generally, thin films are deposited on workpieces to improve
properties like wear resistance, hardness, optical transmission
and many more. Numerous methods exist to deposit thin films,
for instance plasma spray, physical (PVD) and chemical vapor
deposition (CVD), and the sol–gel method. The latter is a pop-
ular technique with many advantages: No vacuum is required,
objects of almost unrestricted size and shape can be coated and,
in many cases, sintering at moderate temperatures (T ≤ 300 ◦C) is
sufficient. Zirconia oxide (ZrO2) layers, which can be deposited
by the sol–gel technique, are often used to protect metals
against heat, wear and corrosion [1]. As an active research field,
the preparation and characterization of ZrO2 films is still of
great interest and therefore a matter of current investigation
[2].
As it is well known, coating properties, like thickness,
microstructure, stress, adhesion to the substrate, hardness and
others, determine the quality of the product and require precise
measuring methods. The layer thickness, for instance, can be deter-
mined by direct methods, which often implies a contacting and
destructive procedure [3]. Several non-contact and non-destructive
methods exist, usually applicable only to certain types of coatings
[4–6]: Optical interferometry and optical ellipsometry measure
convenient for certain metallic and other optically opaque films.
Unfortunately, there is still no effective and simple non-destructive
method to measure thickness of coated films.
Photothermal radiometry, based on temperature phase mea-
surements, can be used for the detection of film thickness. In
this method, heat is generated by the absorption of an intensity-
modulated laser beam by the film. It can be applied for both
optically opaque and transparent layers [7], if the thermal prop-
erties of the layer are different from those of the substrate. Two of
the methods applicable for the analysis of thermal waves are the
infrared detection and the beam deflection. So far, the photother-
mal radiometry for the thickness detection of zirconia oxide film
has not been reported.
In this paper, ZrO2 films were prepared using the sol–gel
method. A thickness microscopy based on photothermal radiom-
etry was built and applied for the experiments described herein.
Furthermore, this set-up was used to measure ZrO2 films thickness
and deduced the correlation between the thermal wave signal and
the film thickness.
2. Experiments
2.1. Preparation of ZrO2 film
∗
Polished aluminum disks were used as substrate (thick-
Corresponding author. Tel.: +86 27 68754410; fax: +86 27 68756037.
E-mail address: liping wang 2002@yahoo.com.cn (L. Wang).
ness = 9 mm,
diameter = 50 mm).
The
main
components
1386-1425/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.saa.2008.10.009

362
L. Wang et al. / Spectrochimica Acta Part A 72 (2009) 361–365
Fig. 1. Sketch of the experimental set-up.
of the sol were tetraethoxysilan (TEOS 99.999%, Aldrich),
methacryloxypropyl-trimethoxysilance (MATMS. 98%, Aldrich),
zirconium (IV) tetrapropoxide (ZPT), 1-propanol, methacylic acid
and water with some drops of HCl. The sol was deposited by
spin coating. Varying the rotational speed from 1000 to 2500 rpm
formed colorless and smooth coatings with different thicknesses.
Then, the wet coatings were dried at 100 ◦C for 24 h. Reference
values of the film thicknesses were measured destructively using
the ball cratering method (ENV 1071-2) in order to calibrate
photothermal measurements.
thermal wave causes the emission of modulated infrared radi-
ation, which is detected by an infrared sensor. The detector
signals imply information about the coating properties, such as
microstructure, thickness, thermal material parameters, and coat-
ing defects.
The solutions of the thermal diffusion equation (TDE) Eq. (1)
describe the heat diffusion process, i.e. the temperature distribu-
tion T (x, t) with its spatial and time dependency, due to a thermal
load Q (x, t) (from the exciting laser beam)
ꢀ
ꢁ
d
dx
d
dx
d
dt
ꢀ(x) T(x, t) − ꢁ(x)c(x) T(x, t) = Q(x, t)
(1)
2.2. Experimental set-up
For a periodic excitation with a certain modulation frequency,
thermal waves propagate within the sample. Their penetration
depth is given by the thermal diffusion length ꢂ, which, according
to Eq. (2), depends on the thermal parameters of the sample and is
inversely proportional to the square root of the exciting frequency
f
Fig. 1 illustrates the set-up for the thickness microscopy, based
on photothermal radiometry. A CO2 laser (output power = 10 W cw,
wavelength = 10.6 ␮m, made by Synrad, Inc.) was used as excitation
source. An acousto-optical modulator (AOM, type AA.MG40/A6,
made by Opto-Electronique, France) modulated the intensity of
the laser beam. The laser beam of about 3 mm diameter gen-
erated an average heating power of about 800 mW on the
sample surface. An InSb infrared detector (type J10D-M204-
R100U-20, from Judson Technologies, LLC, USA), combined with
an IR optical system consisting of CaF2 lenses and a germa-
nium cut-on filter, detected the thermal waves. This arrangement
was capable to detect thermal waves with a lateral resolu-
tion of about 150 ␮m. A DSP lock-in amplifier (SR850, Stanford
Research Systems, Inc.) was used to filter the weak signal and
to analyze its phase lag relative to the modulated heating laser
beam.
ꢂ
ꢂ
ꢂ
ꢃ
2˛
ω
2˛
ω0
ω0
ω
f0
f
ꢂ =
=
= ꢂ0
(2)
with the thermal diffusivity ˛ = ꢀ/ꢁc and ω = 2ꢃf (thermal conduc-
tivity ꢀ, specific heat c and mass density ꢁ). ꢂ0 is the thermal
diffusion length at f0 = 1 Hz.
In physical terms, ꢂ is that propagation distance of the ther-
mal wave, after which its amplitude is damped by a factor of
1/e.
If the excitation laser beam covers a large area compared to the
thermal diffusion length ꢂ, the TDE is reduced to a one-dimensional
equation. It requires an opaque sample, which means that the opti-
cal penetration depth must be much smaller than the thermal
diffusion length ꢂ. For this constellation, the amplitude of the tem-
perature oscillation directly at the surface of a layered material is
given by [8]
3. Results and discussion
In photothermal radiometry, heat is generated by the inter-
action between an intensity-modulated light beam and an
extended, three-dimensional sample. Absorption and subsequent
deexcitation–relaxation produce heat energy, which propagates
into the sample, forming a strongly damped thermal wave. The
I0 1 + R exp(−2ꢄd)
T =
(3)
2ꢀꢄ 1 − R exp(−2ꢄd)

L. Wang et al. / Spectrochimica Acta Part A 72 (2009) 361–365
363
Fig. 2. Phase contrast for different values of the thermal reflection coefficient R.
where I0 denotes the laser intensity, d the layer thickness, ꢀ the
thermal conductivity and ꢄ = ꢂ/(1 + i).
R is called the thermal reflection coefficient, which is a real
number within the interval [−1, 1] and can be calculated from
Fig. 4. Phase contrast of the radiometric signal as a function of the modulation
frequency.
1 − (es/e)
R =
(4)
In this equation, q is the layer thickness, normalized to the ther-
mal diffusion length: q = d/ꢂ.
1 + (es/e)
es, el are the thermal effusivities of the substrate (s) and the layer
(l) with
Fig. 2 shows the function ϕ (q) for different values of R. The thick-
ness interval between the maximum and minimum of the curve is
nearly linear and can be used conveniently for layer thickness mea-
surements. Theoretically, a measured phase might be attributed to
two different values of the layer thickness. In practise, this problem
can be avoided by either evaluating additionally the photothermal
amplitude S or by a second phase measurement using a different
modulation frequency.
Elaborating a calibration curve by Eq. (3) requires the precise
knowledge of the thermal properties for the involved materials. If
layer and substrate are not opaque, then the photothermal model
must be extended considerably. For instance, in layers which do
not absorb the excitation energy directly at the surface, the thermal
wave will be generated within the whole layer, maybe additionally
within the substrate. Depending on the reflectivity of the interfaces
(layer–gas, layer–substrate), optical interference effects must be
taken into account. As the infrared signal will be generated not only
from the layer surface, contributions from the whole layer volume
must be summed up. The chance to find all the required input data
for such an extended photothermal model is low, hence, it will be
the easiest and most reliable way to elaborate a calibration curve
by measurements.
ꢄ
ej =
ꢀjꢁjcj
(5)
The thermal conductivity ꢀ, the density ꢁ and the specific heat
capacity c are assumed to be constant within layer and substrate
and change abruptly at the interface.
Considering that Eq. (3) is complex valued, the photothermal
phase signal is given by
ꢀ
ꢁ
Im(T)
Re(T)
ϕ = arc tan
,
(6)
where Im (T) and Re (T) are the imaginary and the real part of Eq.
(3).
Some basic calculation yield
ꢅ
ꢆ
−1 + R2 exp(−4q) − 2R exp(−2q) sin(2q)
1 − R2 exp(−4q) − 2R exp(−2q) sin(2q)
ϕ = arc tan
(7)
Fig. 3. ZrO2 coated on the aluminum substrate.
Fig. 5. Phase contrast as a function of the film thickness at 1 kHz.

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L. Wang et al. / Spectrochimica Acta Part A 72 (2009) 361–365
Fig. 6. Phase shift measured at f = 1 kHz while scanning the sample surface from 0 mm to 50 mm.
For a non-homogeneous sample like the ZrO2 coated samples
in this research, the resulting temperature distribution and the
measured surface temperature (amplitude S and phase ϕ) depend
on the two combined materials, the ZrO2 coated film thickness
and any possible thermal contact resistance in between. For a
photothermal characterization of unknown objects, the sample
properties have to be extracted and calculated from the measured
data.
In order to eliminate the influence from the electronic devices,
the two photothermal signals (amplitude S and phase ϕ) are usu-
ally normalized to values measured at a sufficiently thick surface
layer, where, due to the damping of the thermal waves, no ther-
mal interference effect occurs. This yields the so-called “contrast
curves”. The amplitude and phase signals, which correlate with
material properties, are derived from the temperature signal T (t)
by the lock-in technique. While the amplitude signal is influenced
by variations of the laser power and the working distance, the
phase signal is essentially independent of these parameters. There-
fore, only the phase contrast curves are presented in the following
graphs.
Three ZrO2 coated samples with thicknesses of 6.4 ␮m, 8.0 ␮m
and 13.3 ␮m were studied. Fig. 3 shows one of the ZrO2 coated sam-
ples. As shown in the figure, the surfaces of the ZrO2 coated samples
were smooth visually. The phase contrast ϕ = ϕref (f) − ϕsample
(f) was calculated by subtracting the phase of the examined
sample from the measured phase of a reference sample. Fig. 4
shows the measured phase contrast as a function of the mod-
ulating frequency. As it is difficult to produce sufficiently thick
ZrO2 layers by the sol–gel method, the phase values measured
at the thickest layer (thickness d = 13.3 ␮m) were taken as ref-
erence. The noise of the phase contrast was about 2◦. The
results indicate that the photothermal phase signal measured
for ZrO2 coatings is highly sensitive, yielding contrast values of
almost 30◦ at f = 1 kHz and a signal/noise ratio of more than
10.
A calibration curve was derived from the phase contrast curves
at 1 kHz (Fig. 5). Obviously, the phase contrast linearly depends on
the layer thickness d within the examined range of thickness.
Fig. 6 shows the results of phase measurements at different
positions and at a constant modulating frequency of 1 kHz, Fig. 7
reflects the corresponding layer thicknesses, calculated using the
mentioned calibration function (Fig. 5). The surface scanning was
carried out from one sample edge to the opposite edge. Obviously,
the sample with ZrO2 thickness of 8.0 ␮m was coated homoge-
neously, whereas the sample with a coating thickness of 13.3 ␮m
shows a variation. It is assumed that this was induced by handling
the sample shortly after the spin coating procedure. The surface
scan of the sample with a coating thickness of 6.4 ␮m shows a sharp
peak (Figs. 6 and 7). In this case there was a defect on the coating,
Fig. 7. Thickness microscopy on the sample surface from 0 mm to 50 mm.
probably caused by dust or impurities of the sol. The estimated
defect size was less than 7.0 mm.
At a modulation frequency of f = 1 Hz, the thermal diffusion
length of metals and semiconductors will be in a range of 2–4 mm,
whereas for most dielectric materials, ꢂ (f = 1 Hz) will be about
200 ␮m. Considering the frequency dependence of Eq. (2), the ther-
mal diffusion length of the layer will be about 6 ␮m at the chosen
frequency of f = 1000 Hz. This means that the lateral resolution will
be limited essentially by the size of the infrared sensor element and
not by the thermal diffusion length.
4. Conclusion
According to the results shown above, the photothermal set-up
can be used to measure the thickness of ZrO2 layers. Scanning the
surface revealed the size and position of a coating defect. This is
helpful to study the quality of thin films and to improve the pro-
cedure of preparation. In contrast to other methods of thickness
measurement, the photothermal techniques offer a near-process
or an in-process inspection in industrial environments.
Acknowledgements
The authors gratefully acknowledge the financial supports by
the National Natural Science Foundation of China (No. 20375029),
the International Office of the German Federal Ministry of Edu-
cation and Research (BMBF) and the Sonderforschungsbereich
SFB-TR4 of the German Science Foundation (DFG). Furthermore, the
authors thank Dr. A. Mehner, Institute for Material Science (IWT),
Bremen, Germany for the preparation of the samples.

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