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Insight into the kinetics of oxidization of metallic and semi-conductor
surfaces and monitoring of oxidization processes are of great interest for the
industry. In the last years, X-ray reflectance [1], Atomic-Force-Microscopy
[2], Reflection High-Energy Electron Diffraction (RHEED) [3] or Spectroscopic
Ellipsometry [4] have been applied to determine the growth laws of oxide layers
on metals or semi-conductors.
The experimental arrangement used in this study resembles a
photo-thermal set-up commonly used for lateral and depth dependent
characterization of materials with respect thermal [5] and electronic
properties [6] or for the measurement of transient high temperatures [7,8]. In
this latter case, the dependence of the optical parameters on the temperature
is used to interpret the measurements, whereas in the present experiment, irreversible
changes of the optical properties are induced by temperature changes. To
measure the changes of the optical properties, the modulated optical
reflectance technique is applied in this work, which is based on the excitation
of additional small thermal waves and on the detection of the modulated optical
reflectance of the surface by means of a probe beam. This technique had already
been applied successfully to monitor deposition of multi-layers [9] and to
analyse the effects of laser-induced oxidization [10]. Here, we investigate the
thickness of an oxide layer on a sample heated by a step flux.
In Section 2, the measurement device is presented and subsequently in
Sect. 3 a brief description of the theoretical analysis is given. In Sect. 4,
we show experimental results obtained on silicon with an oxide layer of
constant thickness and results obtained on copper, where increasing oxidization
under the effect of constant heating is observed. Finally, possible
improvements and the application potential of the method are discussed.
The measurement system, which is similar to the device used earlier to
measure transient high temperatures [7,8], is schematically shown in Figure 1:
The rear surface of the sample of 1 or 2 mm thickness is heated by the focused
beam of a Xenon lamp. Heat pulses with the duration of a few minutes are
applied to obtain transient high sample temperatures of several hundred degrees
above ambient temperature. The detection of the resulting changes of the
optical reflectance takes place at the sample’s front surface. To this
finality, the beam of a He-Ne laser (633 nm) is split into three
intensity-modulated beams by using an acousto-optic-deflector (AOD). The first
modulated beam, which is used as probe beam, is directed to the reflecting
sample surface in nearly vertical incidence, and the reflected beam is then
focused on Photodiode 1.The second modulated beam is directed to the sample
under an incidence of 20° and is then detected by Photodiode 2 (not shown in Figure
1). The third modulated beam is directly sensed by Photodiode 3 and used as
reference. The modulated signal of Photodiode 1 is received by a Lock-in
amplifier which generates a TTL signal used to synchronise the acousto-optic
deflector. The amplitude output of the Lock-in amplifier is then acquired by a
numerical oscilloscope, the external trigger of which is activated by the onset
of the heating pulse. The measured data are transferred via an IEEE interface
to a micro-computer. In order to measure in the transient regime, the
modulation frequency of the probe beam has to be much larger than the
acquisition rate of the oscilloscope. In the present experiment, with heat
pulses of the order of minutes, we have used an acquisition rate of 10 Hz and a
modulation frequency of 5 kHz. The surface temperature of the sample has
simultaneously been measured by a thermocouple, placed at a distance of 2 mm
from the detection spot. Since the heating spot at the rear surface with a
diameter of 10 mm is much larger and since the sample is comparatively thin (1
or 2 mm), we can assume that the temperature of the detection spot and that of
the position of the thermocouple are the same.
The main advantage of the probe beam modulation is the improvement of
the signal-to-noise ratio and the elimination of parasitic reflections or
emissions, so that this detection technique can be applied in hostile
environments, where other detectors are blinded. This detection technique also
allows to make measurements in a relatively short time, only limited by the
time constant of the Lock-in amplifier, e.g. with a modulation frequency of 100
kHz and 10 cycles of measurement the response time is only about 1 ms.
| 3. Theory of signal
generation and interpretation |
In a first step, we are concerned with the determination of the
temperature of the detection spot: since the heat transfer time across the
sample is much smaller than the time resolution of the temperature measurement
and since the heating spot is much larger then the detection spot, we can
assume that the temperature is constant over the detection spot, that it only
varies as function of time and can be determined by the equation:
with
q the temperature increase of
the sample, t the time relative to
the beginning of the heating process,  the sample thickness, C =
cr the sample heat capacity per volume unit, Pa the absorbed power, and h the heat loss coefficient.
This coefficient h represents
the sum of free convection heat losses, radiation heat losses, and heat losses
through the sample holder. Although the convection and radiation heat losses
vary with temperature and time, we consider a constant heat loss coefficient h. This assumption is acceptable for
dominant heat losses through the sample holder. For the temperature evolution
we then obtain:
In the second step, for the optical considerations, the sample can be
approximated by a two-layer model with a first layer, the oxide film,
characterized by the thickness d1
and the refraction index n1,
and a second layer, the comparatively thick substrate characterized by the
refraction index n2.
Assuming that the absorption inside the usually dielectric oxide film is
negligible and that the film is isotropic, the reflection coefficient R of the solid sample is given by [11]:
the optical path across the oxide layer;
 the incidence angle and
 defined by Snellius’ refraction law, n0 sin() = n1 sin(). Neglecting polarisation effects for nearly vertical
incidence, we can write
with n0 the air
refraction index. As can be seen in (3) and (4), the reflection coefficient R depends on the optical path
 across the oxide film and thus also on the
film thickness d1, the
incidence angle, the wavelength
l of the probe laser beam, and the refraction indexes, which can vary
with the sample temperature. Here it is worthwhile to mention, that a changed
incidence angle
or of
is equivalent to an increase of the film thickness in the ratio
 of (4).
Figure 2 shows the reflection coefficient R measured for a Silicon sample (n2 = 3.4) as function of the thickness of the SiO2
film (n1 = 1.5) at the laser
beam wavelength of 633 nm and in vertical incidence (curve a). The curve shows
maxima for a zero film thickness and for thickness values of multiples of 218
nm, which are due phase differences of 2p induced by constructive
interference. The minimum of the reflectivity is obtained for a thickness of
109 nm. The reflectivity decreases with the oxide film thickness increasing
from zero to 109 nm, e.g. for a 10 nm thick oxide film the reflectivity
decreases by 1% and for a 1 nm thick film it is less then 0.1%. This means, a
high precision in the reflectivity measurement is required, in order to get a
sensitivity of the order of some nanometers. For a metallic sample, such as
copper, the optical index is represented by a complex number, n (1 + i k), with k the absorption constant and i the imaginary unit, which has to be
taken into account in equ. (3). According to [12], the reflection coefficient R is then given by the norm of
expression (3) with the coefficients r1
and r2 defined by
Figure 2 also shows the influence of
the thickness of a Cu2O oxide film on the reflectivity of a copper
sample (curve b). For the interpretation of the data measured at the probe beam
wavelength of 633 nm the optical properties n1
= 1.91 and k1 = 0.11 have
been used for Cu2O and n2
= 0.62 and k2 = 3.41 for
metallic Cu [10,12]. In contrast to the Si sample, the maxima of the
reflectivity of the copper sample increase with the thickness of the Cu2O
film and for large values the reflectivity of semi-infinite Cu2O
samples is obtained.
Owing to the temperature variation during the experiment, the reflection
coefficient R in principle may vary
also due to the temperature dependence of the refraction index,
with T the actual temperature,
T0 a reference temperature, and
 of the order of
10-4 K-1. For the example of Si, the constant value is
given by
= 15 10-5 K-1 and for Cu
the real part of the refraction index varies with
= 18 10-5
K-1 and the imaginary part varies with 2.13 10-5 K-1.
Introducing the temperature dependence of the complex refraction index
into equ. (6a) and (6b), the complete expression of the reflectivity R, describing both the effects of film
thickness and temperature dependence, can be derived from equ.(3). Theoretical
calculation have shown, however, that the effect of the temperature dependence
is much smaller then the effect of the growing film thickness and can thus be
neglected in the case of transient oxidation. For Silicon this also has been
confirmed experimentally in former measurements [7,8], where we have found that
the temperature coefficient of the reflectance remains constant even for
several hundred degree of temperature increase.
Before investigating transient oxidization, samples with oxide films of
defined thickness have been studied: two silicon samples of 1 mm thickness, one
with its natural oxide film of 2 nm thickness and the other with an oxide film
of 9 nm. These samples have shown good reflection properties, with specular
reflection and without any speckle structure, and thus the profile of the
reflected beam remains Gaussian. Effects of photon-excited charge carriers on
the reflection signal, which may occur on silicon during pulsed or periodic
laser excitation, are negligible in this work due to the long excitation time
scale contributing to complete thermalization of the charge carriers.
Figure 3 presents results of measurements done on the silicon sample
with the 2 nm oxide film. The heating process of the sample starts at the time t = 0 and remains constant during the
whole measurement. The dashed line represents the sample’s surface temperature
measured by thermocouples (right hand side scale). The normalised optical
reflection signal for an incidence angle of 20° (plain line left
hand side scale) has been adjusted to the temperature evolution by using a
temperature coefficient of the reflectance of 2 10-4 K-1.
For the thermoreflectance signal with vertical incidence (fat plain line) a
coefficient of 1.7 10-4 K-1 has been obtained. Here, it
is remarkable, that even a 2 nm thickness of the oxide film can be evaluated by
measurements at two different angles of incidence. Similar results have been
obtained for the silicon sample with the oxide film of 9 nm thickness. The
temperature coefficient of the reflectance deduced from these measurements is 5
10-4 K-1 for the 20° incidence and 4 10-4 K-1
for the perpendicular incidence. Here we can see that for Si the sensitivity of
the method is sufficient to the measure the thickness of oxide films of a few
nanometers.
To study the time evolution of oxidization on copper, Cu samples of 2 mm
thickness have been used, with polished surfaces showing specular reflection.
Figure 4 shows the optical reflectance (fat plain line) observed as function of
the temperature evolution measured by thermocouples (plain line) during a heat
pulse of 420 s. We can observe that the thermoreflectance signal remains
constant during the first 70s after the begin of the heating process. After
70s, the sample has reached the temperature of 100°C, and the oxidization
process starts. At this rather low temperature only Cu2O is formed,
whereas CuO is formed only at temperatures above 250°C [13]. With increasing
oxide layer thickness the reflectance starts to decrease, as shown in Figure 2,
reaching first a relative minimum and then a relative maximum. A second
relative minimum is further observed. Similar observations were reported by
Baufay and al. [10]. The visual inspection shows a periodic change in the
colour of the sample, changing between red and blue. The observed effect is a
typical thin film optical effect.
The time evolution for the extrema allows estimating the evolution of
the thickness of the oxide film (Figure 2): values of the thickness of d
= 57 nm, 128 nm and 220 nm are reached at the time t = 125 s, 203 s and 350 s, respectively. The interpretation of
these data leads to an average variation of the according to a power law d = A t m with m =
3/4, which is faster than the process observed in reference [4], where an
exponent of m = 1/3 was found. This difference can be understood, having in
mind, that in ref [4] the wall temperature was maintained constant, whereas in
the present study the heating power is constant, leading to an increasing
sample temperature.
The fat dashed-dotted line in Figure 4 shows the calculated optical
reflectance and the deduced thickness of oxide film (dotted line) by assuming a
liner increase between the extrema and a power law with m = 1.5 between the
begin of oxidization at t = 70s and the first minimum.
The evolution of the oxide film seems to be rather complex: we observe a
slow growing process during a time interval of 20s after 100°C have been
reached, followed first by a rapid film thickness growth of nearly parabolic
evolution and finally again a slower film thickness growth.
The shape of the theoretical curve of the time evolution of the
reflectance in Figure 5 is in qualitative agreement with the measured data. The
quantitative deviations can be explained by two effects: (i) the measurement is
done on a surface area which is large in comparison with the film thickness,
and thus we measure a convolution of the different thickness values within the
measured spot, which according to [4] are not constant in space ; (ii) the
roughness of the oxide film contribute to a changed optical reflectance which
is not described by equ. (3) and requires a more detailed optical theory.
Another problem is the large spread of values available in literature
for the refraction index, differing from one author to the other, or even
between two measurements of the same author, e.g. in [4] the value of the
refraction index of Cu2O varies from 1.9 to 3.2.
| 5. Conclusions and
perspectives |
These measurements have shown that the modulated optical reflectance
technique is a reliable non-invasive method to investigate oxidization
processes and to measure thin films by remote detection which may even be
applied in non-accessible geometries. In addition, the probe beam modulation
eliminates parasitic reflection and emission, which can disturb measurement
techniques such as infrared radiometry or visible spectrometry. For improved
quantitative interpretation an optical theory is required which considers the
absorption by the oxide film, its roughness effects, and the integrating
effects of the comparatively large probe beam diameter. The achieved
sensitivity allows to resolve thickness values of oxide films of a few
nanometer, e.g. of only 2 nm on Si, and enables in-situ studies of transient
oxidization.
The authors thank J. Pelzl for helpful discussions, contributing to the
success of this experiment. In part, the work has been supported in the frame
of the EU-HCM network
Photothermal Methods.
Figure 1: Schematic of the
measurement system
Figure 2 Optical
reflectance of Si substrate with a SiO2 film (doted line) and of Cu
substrate with a Cu2O film (plain line) versus the film thickness.
Figure 3:
Optical reflectance measured on Silicon with a 2 nm oxide film at vertical
incidence (fat plain line) and under an incidence angle of 20° (plain line),
compared with the temperature measured by thermocouples (dashed line).
Figure 4
Temperature evolution (plain line) and optical reflectance (fat plain line)
measured on a Cu sample during a 420s heating pulse, compared with the
theoretical calculation (fat dotted line). The deduced oxide film thickness
(thin doted line).
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