The features of surface plasmon resonance in gold cluster films
The internal reflection of nanosized gold cluster films was studied using the technique of polarization modulation of electromagnetic radiation in the Kretschmann geometry. We measured the reflection coefficients Rs and Rp of s- and p-polarized radiation, respectively, as well as their polarizati...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2009
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| Цитувати: | The features of surface plasmon resonance in gold cluster films / L.S. Maksimenko, I.E. Matyash, S.P. Rudenko, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 2. — С. 129-134. — Бібліогр.: 13 назв. — англ. |
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Maksimenko, L.S. Matyash, I.E. Rudenko, S.P. Serdega, B.K. 2017-05-30T19:41:52Z 2017-05-30T19:41:52Z 2009 The features of surface plasmon resonance in gold cluster films / L.S. Maksimenko, I.E. Matyash, S.P. Rudenko, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 2. — С. 129-134. — Бібліогр.: 13 назв. — англ. 1560-8034 PACS 73.20.Mf https://nasplib.isofts.kiev.ua/handle/123456789/118687 The internal reflection of nanosized gold cluster films was studied using the technique of polarization modulation of electromagnetic radiation in the Kretschmann geometry. We measured the reflection coefficients Rs and Rp of s- and p-polarized radiation, respectively, as well as their polarization difference ∆R = Rs − Rp, as function of the light incidence angle in the 0.4÷1.6 µm wavelength range. A topological size effect was found; it consists in dependence of the value and sign of curvature of the polarization difference characteristics on the film surface properties. It is shown that the sign of curvature of ∆R characteristics depends on the radiation wavelength λ and indicates resonance interaction with a metal film of either p-polarized radiation only or that of both polarizations. The spectral characteristic of the topological size effect in the resonance interaction is obtained from the condition of isotropic reflection, ∆R = Rs − Rp = 0, and its dependence on the radiation wavelength. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics The features of surface plasmon resonance in gold cluster films Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
The features of surface plasmon resonance in gold cluster films |
| spellingShingle |
The features of surface plasmon resonance in gold cluster films Maksimenko, L.S. Matyash, I.E. Rudenko, S.P. Serdega, B.K. |
| title_short |
The features of surface plasmon resonance in gold cluster films |
| title_full |
The features of surface plasmon resonance in gold cluster films |
| title_fullStr |
The features of surface plasmon resonance in gold cluster films |
| title_full_unstemmed |
The features of surface plasmon resonance in gold cluster films |
| title_sort |
features of surface plasmon resonance in gold cluster films |
| author |
Maksimenko, L.S. Matyash, I.E. Rudenko, S.P. Serdega, B.K. |
| author_facet |
Maksimenko, L.S. Matyash, I.E. Rudenko, S.P. Serdega, B.K. |
| publishDate |
2009 |
| language |
English |
| container_title |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| format |
Article |
| description |
The internal reflection of nanosized gold cluster films was studied using the
technique of polarization modulation of electromagnetic radiation in the Kretschmann
geometry. We measured the reflection coefficients Rs and Rp of s- and p-polarized
radiation, respectively, as well as their polarization difference ∆R = Rs − Rp, as function
of the light incidence angle in the 0.4÷1.6 µm wavelength range. A topological size
effect was found; it consists in dependence of the value and sign of curvature of the
polarization difference characteristics on the film surface properties. It is shown that the
sign of curvature of ∆R characteristics depends on the radiation wavelength λ and
indicates resonance interaction with a metal film of either p-polarized radiation only or
that of both polarizations. The spectral characteristic of the topological size effect in the
resonance interaction is obtained from the condition of isotropic reflection, ∆R = Rs − Rp
= 0, and its dependence on the radiation wavelength.
|
| issn |
1560-8034 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/118687 |
| citation_txt |
The features of surface plasmon resonance in gold cluster films / L.S. Maksimenko, I.E. Matyash, S.P. Rudenko, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 2. — С. 129-134. — Бібліогр.: 13 назв. — англ. |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 2. P. 129-134.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
129
PACS 73.20.Mf
The features of surface plasmon resonance in gold cluster films
L.S. Maksimenko, I.E. Matyash, S.P. Rudenko, B.K. Serdega
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
45, prospect Nauky, Kyiv 03028, Ukraine
Phone: 38-(044) 525-57-78; e-mail: serdega@isp.kiev.ua
Abstract. The internal reflection of nanosized gold cluster films was studied using the
technique of polarization modulation of electromagnetic radiation in the Kretschmann
geometry. We measured the reflection coefficients Rs and Rp of s- and p-polarized
radiation, respectively, as well as their polarization difference ∆R = Rs − Rp, as function
of the light incidence angle in the 0.4÷1.6 µm wavelength range. A topological size
effect was found; it consists in dependence of the value and sign of curvature of the
polarization difference characteristics on the film surface properties. It is shown that the
sign of curvature of ∆R characteristics depends on the radiation wavelength λ and
indicates resonance interaction with a metal film of either p-polarized radiation only or
that of both polarizations. The spectral characteristic of the topological size effect in the
resonance interaction is obtained from the condition of isotropic reflection, ∆R = Rs − Rp
= 0, and its dependence on the radiation wavelength.
Keywords: radiation polarization, plasmon-polariton resonance, gold cluster film,
topological size effect.
Manuscript received 11.02.09; accepted for publication 18.03.09; published online 20.03.09.
1. Introduction
The anomalies of optical properties occur in limited
metal objects (films, clusters, nano-shells, wires etc.)
whose sizes are comparable with the electron free path.
First of all, these anomalies lead to appearance of the
classical size effect [1]. The topological size effect [2]
related to the form of object surface also occurs in that
range of sizes. When both effects occur in the same
object of investigation (say, a rough film as a cluster
structure and its continuous ultrathin underlayer), then it
is difficult to separate the contributions of each of the
reasons for those effects.
It is this situation that takes place when studying
the surface plasmon-polariton resonance (PPR) that is
observed in thin films of some metals (in particular,
gold). The thicknesses of samples where PPR occurs
most clearly depend on the wavelength of the radiation
used and lie within a range of several tens of nanometers
[3]. In thinner films where the concept of thickness is
represented by a mass of deposited substance, PPR
(called the local plasmon resonance [4]) reflects not only
the anomalies of dielectric properties of the material
under consideration [5] but the features of surface
topology as well. In this case, the traditional methods
applied for investigation of metal nanolayers (e.g.,
transmission [6], absorption [7] and luminescence [8])
have limited capabilities for separation of dimensional
features in interaction between the electromagnetic field
of the wave and electron system. Moreover, the
condition of resonance interaction (that requires equality
of the value of dispersion for the wave and plasmon-
polariton [9] and is strictly obeyed in the films with
geometrically flat surface) loses rigor of the orientation
dependence in cluster structures. There, in particular, the
dielectric function becomes spatially- or size-
dependent [10].
Therefore, the objective of this work is, first of all,
investigation of the influence of the properties of a
cluster structure on the polarization characteristics of the
internal reflectance of gold samples. The traditional
opinion is that PPR in such samples manifests itself only
in the dependence of the reflection coefficient Rp of p-
polarized radiation on the angle of light incidence. It will
be shown that the above influence leads also to
dependence of the reflection coefficient Rs of s-polarized
radiation and the polarization difference ∆R = Rs − Rp on
the angle of light incidence.
As to the concept of sample structure as functional
argument (in spite of some indeterminacy of that
concept), the situation becomes simpler because of some
physico-technological reasons. It is well known that,
owing to the growth conditions, a thin metal layer on a
dielectric substrate is a composite that consists of two
components: cluster and continuous uniform ones.
Therefore, one might expect that, by exerting control
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 2. P. 129-134.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
130
over the interrelation between the above components, it
would be possible to obtain a result characterizing their
separate effects on the quantity measured. In our case,
such a quantity is the polarization difference of the
coefficients of internal reflection that is registered with
the polarization modulation (PM) technique.
Application of the above technique for
investigation of PPR in ultrathin gold films is implicit
another part of the problem. It seems expedient for the
following reason. Both internal and external reflections
are characterized with amplitude and phase anisotropies.
For our experiment, the most important is the fact that
generally the values and angular dependences of the
reflection coefficient for s-polarized radiation differ
from the corresponding characteristics of the reflection
coefficient for p-polarized radiation. This distinction is
known as the polarization difference. Being an
experimentally measured quantity, it is a product of the
PM technique because it is formed by periodically
varying in time radiation with orthogonal polarization
azimuths.
The sense of polarization difference is as follows.
After subtraction, the common features of the functions
of the effect under investigation (optical, photoelectric,
magnetooptical etc.) vanish, and the residual contains
the individual features of the terms. In many cases, this
residual is much below the terms. However, it can be
reliably registered with the PM technique owing to
amplification. As has been shown earlier [11],
application of PM for investigation of the features of
total internal reflection attenuated with gold films made
it possible to separate the PPR characteristics against the
background of two nonresonance components. This fact
gives grounds to use the PM technique for investigation
of cluster nanostructures as one more demonstrations of
its detection abilities.
2. The samples and experimental procedure
Our samples were gold (Аu–99.999 %) films prepared
with thermal evaporation in a vacuum (pressure of 10-
3 Pa) from a molybdenum heater onto a substrate kept at
room temperature. Glass plates served as substrates.
They contacted with a glass segment through an
immersion film (glycerol), and their thickness was such
that they formed a semicylinder 4 cm in diameter. The
fixed rate of gold sputtering (1.0 nm/s) enabled us to set
the required values of film thickness by varying the
process duration. More accurate size measurement was
made when studying sample topology with an atomic
force microscope (AFM) NanoScope IIIa (produced by
Digital Instrument, USA). To this end, we used the mode
of periodic contact of film surface with a silicon needle
(rated needlepoint up to 10 nm).
The mass thicknesses d (nm) of the samples under
investigation were 5 (I), 10 (II) and 20 (III). The above
values were chosen from the following considerations.
The samples of type I (samples-I) were freshly prepared
island films. An axonometric AFM-topology of the
sample surface is presented in Fig. 1а. One can see that
the film consists of separate clusters loosely contacting
one another. Their shape was close to a cylinder, with
diameter of 30÷80 nm and height of 5÷25 nm. The
height drop over a 1×1 µm area was 30.24 nm and the
root-mean-square (RMS) roughness was 4.95 nm.
The samples-II in the initial state were a gold film
with continuous surface – see Fig. 1b. It consisted of
grains with fuzzy boundaries; the grain diameter (height)
was 20÷45 nm (0.5÷2 nm). The film was very smooth,
with height drop of 6.78 nm and RMS roughness of
0.91 nm. To transform that film into a cluster one, we
used thermal treatment, by analogy with [12]. The film
was heated in air at a temperature of 230 °С. After
thermal annealing the film structure (Fig. 1b) differed
from that of film-I (Fig. 1a) but quantitatively. The film
material aggregated in separate clusters with irregularly
shaped bases, increased diameter (30÷50 nm) and
heights of 6÷30 nm. The roughness characteristics were
close to those of the initial film-I: height drop of
35.89 nm and RMS roughness of 5.69 nm.
The samples-III (whose initial thickness was
20 nm) were initially smooth, with RMS roughness of
1.91 nm. After heating at the above temperature
(230 °С), both the film appearance and bulk structure
have changed. Although the film mass thickness
remained the same (20 nm), the film became more
porous owing to material aggregation in clusters of
increased size: diameter of 80÷180 nm and height of
18÷25 nm.
(a)
(b)
Fig. 1. AFM-topology of the surfaces of 5 nm (a) and
10 nm (b) gold films.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 2. P. 129-134.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
131
35 40 45 50 55 60 65 70 75 80
-4
-3
-2
-1
0
1
2
3
4
5
6
R
S, R
P, ∆
R
, a
rb
.u
n.
Angle, deg.
1
2
3
30 40 50 60 70 80
-8
-6
-4
-2
0
2
4
6
R
S, R
P, ∆
R
, a
rb
.u
n.
Angle, deg.
1
2
3
(а)
(b)
Fig. 3. The dependences of the reflection coefficients Rp (1),
Rs (2) and polarization difference ∆R (3) on the angle of
light incidence for a 10 nm gold film before (a) and after
thermal treatment (b); light wavelength λ = 1.15 µm.
The optical unit of the installation for investigation
of the PPR features was made in the Kretschmann
geometry. (For its diagram as well as detailed
description of the processes of modulation of radiation
polarization and signal registration, see [11].)
Modulation of polarization was made with the most
appropriate facility based on the photoelastic effect [13].
The quality of the facility was characterized by the
degree of temporal constancy of outgoing radiation
intensity; it was ≅10-4 in relative units. The polarization
difference ∆R = Rs − Rp, as well as the separate
reflection coefficients Rs and Rp were measured with the
PM technique. The AFM measurements of the films
were performed both before and after thermal treatment.
The radiation sources were a He-Ne laser (wavelengths
of 0.63 and 1.15 µm) and diffraction monochromator
with a halogen lamp at the inlet and linear polarizer at
the outlet.
3. Results and discussion
The polarization characteristics of internal reflection for
a sample-I are presented in Fig. 2. The curves 1 and 2
show the reflection coefficients Rp and Rs as function of
the light incidence angle. The curve 1′ (being a typical
characteristic of PPR) shows Rp dependence obtained for
the samples with thickness d = 50 nm that is optimal for
manifestation of the effect.
One can draw the following conclusions from
comparison of the curves. First, the extreme values of all
the three curves lie at the same angle θcr. Second, the
curves have, depending on angle, a typical for PPR dip
at θ > θcr. The above two facts enable one to conclude
that interaction of electromagnetic radiation with the
cluster electron system is of resonance character not only
for p-polarized radiation but for s-polarized radiation as
well. As to the distinctions in the values and extents of
dips of the Rp curves, they are caused exclusively by the
cluster structure of the films (see below).
30 40 50 60 70 80
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
R
S,
R
P,
∆R
, a
bs
. u
n.
Angle, deg.θcr
1
2
3
1′
3'
Fig. 2. The dependences of the reflection coefficients
Rp (1, 1′), Rs (2) and polarization difference ∆R (3, 3′) on the
angle of light incidence for a gold film (1′ − film thickness d =
50 nm; 3′ − d = 10 nm, sample-II after thermal treatment); light
wavelength λ = 1.15 µm.
The curve 3 in Fig. 2 presents the polarization
difference of reflection coefficients, ∆R, for a sample-I
measured directly with the PM technique. Its negative
sign points to the fact that presence of an absorbing
medium at the semicylinder surface is the reason for
“anomalous” reflection of s-polarized radiation in a
sense that, contrary to what you might expect, the
inequality Rs < Rp holds near the critical angle. Presence
of an almost linear section of ∆R curve at θ > θcr reflects
the common features of the dependences Rs(θ) and
Rp(θ).
The measurements for the sample-II were
performed both before and after thermal treatment. The
results of the first measurement are presented in Fig. 3а.
One can see that there is practically no reflection of the
s-polarized radiation, and clear attributes of PPR
interaction can be seen for the р-polarized radiation
only. It should be noted that small Rp values are
observed over a wide range of angles, contrary to the
narrow dip shown by curve 1′ in Fig. 2. Evidently, this
fact is due to film roughness; this is in agreement with
somewhat decreased Rp value in the maximum near the
critical angle.
Thermal treatment has dramatically changed the
surface properties of the film as well as its polarization
characteristics. First of all, the amplitude of reflection of
р-polarized radiation near the critical angle increased,
while the value of the dip at θ > θcr decreased (see
Fig. 3b, curve 1). The most important result of thermal
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 2. P. 129-134.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
132
treatment was that the reflection coefficient for s-
polarized radiation grew manifold, the mass thickness of
the film remaining the same (curve 2), and the resonance
indications appeared in the Rs(θ) curve. The AFM-
topologies of the surfaces of the samples with d = 5 nm
(in the initial state – see Fig. 1) and d = 10 nm (after
thermal annealing) are close in both their appearances
and parameters. This fact may indicate similarity of the
characteristics of the reflection coefficients of the above
samples. The experimental result presented in Fig. 3b
supports the above assumption. All the three
characteristics shown in this Figure practically
completely (except some details) coincide with those
shown in Fig. 2 for the sample with d = 5 nm. To
illustrate, curve 3′ (Fig. 2) that is the polarization
difference for the sample with d = 10 nm after thermal
annealing agrees well with similar curve for a thinner
sample.
The dipole-dipole, or intercluster, interaction has an
impact on the dependence of the form of polarization
characteristics on wavelength. This dispersion is
pronounced most clearly for the function ∆R(θ). They
are presented in Fig. 4 for a sample-I (for the sake of
clearness and convenience of analysis, they are
normalized to the same minimum value). The curve λ =
800 nm stands out of the set of dependences because it is
close to straight line over some angle interval. This
indicates presence of functionally identical curve pieces
in the dependences Rs(θ) and Rp(θ). The experiment
shows that the value λ ≅ 800 nm (to which curve 3
corresponds) is limit value in a sense. The formal
attribute of the threshold character of that curve is that
the characteristics lying on each side of the mentioned
one have opposite signs of curvature in the range of
angles somewhat above the critical one. What is more
important, the value λ ≅ 800 nm for the sample-I is
transitional in that resonance character of interaction
between radiation and sample is inherent to a greater
extent to р-polarized radiation of smaller wavelengths,
while at bigger wavelength, the resonance character of
interaction is inherent to both s- and р-polarizations.
It would seem that such an experimental fact is at
variance with the condition of PPR excitation according
to which only the р-polarized wave energy is transferred
to a surface plasmon-polariton. However, one could
easily imagine a model in which that fact would be
explainable based on a spherical (or close to spherical)
form of a surface that is characteristic of a cluster film.
First, in a cluster of such shape, the electric field vector
is oriented at an angle to its surface for both states of
wave polarization. Second, by definition of PPR
appearance on the spherical surface of a cluster, this
becomes possible in a considerable range of angles
exceeding the critical one. That is, at any angle (from
that range) of light incidence onto the back (working)
surface of the semicylinder, there always exists an angle
relative to a flat area of cluster surface that obeys the
condition of resonance interaction.
All the characteristics of the polarization difference
∆R(θ) obtained for the samples under investigation have
a paradoxical common feature: at some angles, reflection
does not depend on polarization state of the wave. This
manifests itself in intersection of the abscissa axis with
the ∆R(θ) curve within the angle range 0° < θ < 90° and
appearance of the equality Rs = Rp that cannot be
described with the Fresnel formulas in what concerns
either its position in the angular dependence or
especially the number of intersections.
For all the samples studied, there were two
intersections of the abscissa axis with the ∆R(θ) curve.
They lay on each side of the critical angle θcr and
indicated isotropic reflection. One of them (laying at
θ < θcr) was owing to presence of an absorbing medium
on the surface of the totally reflecting prism. Its origin is
as follows. Action of the electric field of s-polarized
wave (that is not restricted with the surface) results in
bigger absorption of the energy of s-polarized wave in
the above medium as compared to that of the р-polarized
wave. The comparative decrease of the reflection
coefficient reduction is the reason for “anomalous”
reflection.
Another isotropic point in the angular dependence
of the polarization difference (laying at θ > θcr) was due
to resonance interaction of radiation with the electron
system of the cluster. Its position on the angle scale
depended on to what extent the cluster shape and size
met the resonance condition for the р-polarized wave (or
both polarizations).
This conclusion is in agreement with those
attributes of the resonance interaction in the
characteristics Rs(θ) and Rp(θ) that are presented in
Fig. 2 (curves 1 and 2). If a film is partially cluster, then
the angle of isotropic reflection has to be sensitive to the
degree of film clusterization because of variation of
interrelation between the intensities of differently
polarized waves that excite resonance interaction. It is
difficult to define the concept of degree of clusterization,
at least quantitatively. Therefore, it is more convenient
to use the characteristic ∆R(θ) of the sample considered
for registration of dispersion of isotropic reflection.
Shown in Fig. 4 are the dependences ∆R(θ) for a
sample-I at different wavelength. One can see that the
angle corresponding to the condition of equality of the
reflection coefficients depends nonmonotonically on the
radiation wavelength. The sample-II after thermal
treatment also demonstrates similar dependences with
nonmonotonic intersection of the abscissa axis. The
characteristic feature of both curves is that the zero-
value point shifts towards total beam grazing due to
positive curvature of the functions ∆R(θ). In this
connection it was of interest to study informativity of the
function of isotropic reflection, θ∆R=0(λ), with our
samples. To this end, we measured the angles θ∆R=0 for
the samples of all three types, both before and after
thermal annealing. The results of our measurements are
presented in Fig. 5. Taking into account that, along with
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 2. P. 129-134.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
133
35 40 45 50 55 60 65 70 75 80
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
∆R
, a
rb
.u
n.
Angle, deg.
450 nm
500 nm
600 nm
800 nm
900 nm
1000 nm
1200 nm
Fig. 4. The dependences of the polarization difference ∆R
on the angle of light incidence for a 5 nm sample; light
wavelength λ = 450; 500; 600; 800; 900; and 1200 nm.
the above measurements, we studied also the
characteristics Rs(θ) and Rp(θ) to determine interrelation
between the intensities of their resonance attributes,
interpretation of the presented results does not involve
difficulties.
The characteristics shown in Fig. 5b as almost
horizontal lines at an angle θ ≅ 85° (samples-I and
samples-II after thermal annealing) indicate possibility
to excite PPR with linearly polarized radiation of
arbitrary azimuth. The characteristic of the sample-III
after thermal treatment demonstrates small changes that
seem to be related to variation of the gold film structure.
Its position near the angle θ ≅ 50° indicates resonance
interaction with р-polarization interaction only. As to the
values of the rest of characteristics at intermediate angles
for λ > 500 nm, they are determined by the value of
contribution to resonance interaction from the s-
polarized radiation.
This conclusion does not refer to all the θ∆R=0(λ)
characteristics at wavelengths λ < 500 nm. In this case,
narrow nonmonotonicity is observed for the samples-I
and samples-II. In any event, the nature of the
characteristics is not related to PPR. This follows from
Fig. 6 presenting the characteristics θ∆R=0(λ) for a
sample-II in the initial state and after thermal treatment.
A comparison of them showed that film restructuring
due to heating made an inessential impact on the
characteristics of polarization difference in that
wavelength range.
The formal reason for the noted features is shift of
the isotropic point lying to the left of the critical angle
θcr. That point, as was noted, is subjected to influence of
the value of extinction coefficient. This is indicated by
the known trends in variation of extinction value that are
related to film thickness or structural perfection.
However, determination of the details of physical origin
of such dispersion remains beyond the scope of the
present problem.
400 500 600 700 800 900 1000
45
50
55
60
65
70
75
80
85
90
5 nm
10 nm
20 nm
Wavelength, nm
θ i, d
eg
.
400 500 600 700 800 900 1000
40
50
60
70
80
θ
i, d
eg
.
5nm
10nm
20nm
Wavelength, nm
(a)
(b)
Fig. 5. The spectral dependences of the angle of isotropic
reflection for samples 5, 10, and 20 nm thick before (a) and
after thermal treatment (b).
400 500 600 700 800 900 1000
45
50
55
60
65
70
75
80
85
90
θ i, d
eg
.
Wavelength, nm
after
before
Fig. 6. The spectral dependences of the angle of isotropic
reflection for a 10 nm sample before and after thermal
treatment.
The last remark concerns the sample-III for which
an inessential effect of film heating was detected by
comparing the dependences θ∆R=0(λ) obtained before and
after thermal annealing. Taking into account the results
of AFM studies of the film, one can conclude that the
reason for such a small effect was decrease of film
roughness owing to material aggregation to bigger bulk
clusters.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 2. P. 129-134.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
134
4. Conclusion
The samples studied in this work demonstrated
polarization characteristics of internal reflections with
some features that cannot be described with the Fresnel
formulas (at least without application of approximations
that take into account surface topology or structural
properties of the whole film bulk). Nevertheless, the
experimental results obtained make it possible to build a
system of sample classification according to certain
features.
One of them is that the form of ∆R(θ) curve
dependence on the wavelength that is expressed with the
sign and value of function curvature enables one to draw
conclusions concerning the degree of film clusterization.
This is based on the fact that the resonance mechanism
of interaction between radiation and the electron system
of clusters takes place not only for р-polarized radiation
(as it occurs in films that are uniform in thickness) but
also for both polarization states (in a certain wavelength
range). The reason for such a peculiarity is finite size of
clusters and their three-dimensional shape. These factors
put restrictions on electron motion under action of the
wave field not only along the normal to the film
(substrate) surface but also parallel to it that is caused by
s-polarization.
Another attribute that is more sensitive to the
surface properties of a film (and even more to its degree
of clusterization) is the characteristic θ∆R=0(λ). Its
essence is that, at some angle θ of light incidence, the
coefficients of reflection for s- and p-polarized radiation
become equal and their polarization difference ∆R =
Rs − Rp vanishes.
The PM technique has resolving power of 0.01°
relative to registration of the angle of isotropic
reflection. Measurements of that angle as function of the
wavelength of radiation used make it possible to obtain
reliable spectral characteristics. From their position in
the coordinate space, θ∆R=0(λ), conclusions were made
concerning (i) interrelation between the intensities of
two polarization states at PPR excitation and (ii) cluster
character of gold films. It was demonstrated with
investigation of gold cluster films that application of the
PM procedure for internal reflection, along with the
developed interpretation of the characteristics of
polarization difference and isotropic reflection, can serve
for testing the topological properties of surfaces of thin
absorbing films.
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