Supplemental Material
Second harmonic generation enhancement at
the percolation threshold
Stefano De Zuani,* Tobias Peterseim, Audrey Berrier, Bruno Gompf,
and Martin Dressel
1. Physikalisches Institut and Research Center SCoPE,
Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
In situ characterization of the gold thin films
In-situ reflectance measurements of the thin gold films were taken during e-beam
evaporation, in order to determine at which thickness the percolation regime occurs.
A scheme of the set up can be seen in Fig. S1a: during the evaporation, the changes of the
reflectance due to the increasing amount of gold on the sapphire substrate are measured
by a near infrared spectrometer in specular reflection at 45°. The light from a halogen
lamp is guided through fibers into the ultra-high vacuum chamber and a similar fiber is
used to collect the specular reflected light and guide it to a near infrared spectrometer.
The evolution of the reflectance with increasing film thickness is shown for few
thicknesses in Fig. S1b.
Fig. S1: (a) Scheme of the in-situ reflectance set-up. (b) Evolution of the reflectance of gold films on a sapphire
substrate when the layers thickness increases: at smallest film thicknesses the gold film is an insulator, it goes
through the percolation around 5 nm and it becomes metallic at larger thicknesses.
The slope of the reflectance curve changes across percolation and gives an indication of
the material modifications. At the beginning of the deposition, when the film consists of a
few well separated particles, it is insulating and its reflectance in the near infrared regime
increases with increasing wavenumber (positive slope). At the percolation threshold,
when a conductive network has just been formed, the reflectance becomes almost
independent of the wavenumber (flat curve). Finally, above the percolation threshold the
films become metallic: the reflectance decreases with increasing wavenumber (negative
slope) and reaches almost 100% for the thickest film (not shown).
Linear properties of the samples: ex-situ spectroscopic ellipsometry and
reflectance measurements
All the produced films were characterized by ex-situ spectroscopic ellipsometry and
reflectance measurements with a Woollam variable angle spectroscopic ellipsometer
(VASE) in the spectral range between 300 nm to 2000 nm with a resolution of 1.5 nm and
angles of incidence varied from 45° to 65° in steps of 10°.
The ellipsometric data were modeled by a general oscillator layer composed of Lorentz
contributions and a Drude component starting at the percolation. We chose here an
isotropic model although a random distribution of metallic nanoparticles can show optical
anisotropy due to the spatial distribution of the particles; however this seems to be only
relevant at smaller wavelengths [S1]. In the spectral frequency region considered here, no
particular difference on the resulting dielectric constants can be noticed between an
isotropic and a uniaxial model. The mean square error (MSE) of the models, used to
obtain the optical constants of the samples was around 3. As additional check to test the
quality of the fit, the reflectance of each of the samples was extracted from the model for
three different angles of incidence (45°, 55°, 65°) and it was compared to the measured
reflectance; the model perfectly reproduces the measured reflectance with an error of
around 3%. The obtained real and imaginary parts of the dielectric constant of gold films
with different thicknesses are shown in Fig. S2.
Fig. S2: Real (a) and imaginary parts (b) of the dielectric function of gold films with increasing thickness
obtained from the modeled ellipsometric data.
As shown in Fig. S2a, in the lowest frequency range up to 5000 cm-1, ɛ1() rises
first with film thickness, reaches a maximum at 5.1 nm and then drops rapidly, becoming
negative above 5.5 nm. This abrupt change in ɛ1(ω) is characteristic for the percolation
threshold where the film becomes metallic and an additional Drude component appears.
The permittivity curves are extrapolated to lower frequencies from the modeled of data in
the measured frequency range, in order to explicit the influence of the Drude term starting
at the percolation threshold. The extrapolation has been made by assuming that no further
resonances are present in the non-measured region below 5000 cm-1. The Drude
contribution can be also seen in Fig. S2b where the value of the imaginary part of the
permittivity ɛ2() shoots up at the lowest frequency region of the spectra (film thickness =
5.3 nm). Two main plasmonic peaks can be also seen in Fig. S2b: as the clusters become
larger, the resonance peaks shift to lower frequencies and they broaden due to an increase
in the size dispersion of the islands. The shift of the most pronounced resonances with
increasing film thickness is shown in Fig. S3 and the evolution of the Drude components
is shown in Table 1.
Fig. S3: (a) Imaginary part of the dielectric constant of the gold film with thickness of 5.4 nm with the Drude
component and the two more pronounced resonances indicated; (b) shift of the most pronounced resonances
with increasing film thickness.
Drude components
Film thickness
ωp/2πc
γ
(nm)
(104 cm-1)
(cm-1)
5.3
0.28
1750
5.4
1.81
3870
5.5
2.68
4439
5.7
4.30
3052
5.8
11.13
1095
6.4
18.78
717
Table 1: Drude components of the thin gold films obtained from a Drude fit of the optical data: ω p is the plasma
frequency and γ denotes the scattering rate.
The plasmon resonances in Fig. S3b shift to lower wavenumber with increasing film
thickness. When the Drude component sets in these resonances do not disappear
immediately but they become weaker and broader so that it is not possible to distinguish
them anymore. At the same time the plasma frequency of the Drude components increases
with film thickness and the films become more and more conductive.
Influence of the laser pulses on the morphology of the thin gold films
Reflectance measurements were carried out before and after laser illumination in order to
check the influence of the high power laser pulses on the film structure. It has been
recently shown that melting of the gold at the position of the hot spots can induce
reshaping of the nanostructures [S2] that in turn can influence the SHG signal. It is
therefore important to check that we operate in a regime where the reshaping is negligible.
Optical characterization is an extremely sensitive method to determine very small
structural changes of the film morphology due to the strong dependence of the plasmon
resonances on shape and size of the clusters. In Fig. S4a, the reflectance spectra of
samples of different thicknesses before and after the SHG experiment at an average power
density of 60 mW/cm2 are shown for an angle of incidence of 45°.
Fig. S4: (a) Reflectance of gold films before (solid line) and after (dashed line) they were illuminated by laser
pulses (1064 nm) with an average power density of 60 mW/cm2, and (b) Ellipsometric angle Ψ measured at the
angle of incidence of 45° of the 5 nm thick gold film before (solid line) and after (dashed line) illumination with
the laser.
As it can be seen from the spectra displayed in Fig. S4a, basically no changes in the
reflectance are observed, which clearly indicates that only very small morphological
changes, if any, are induced by the exposure to the laser pulses. In order to confirm this,
we compared the ellipsometric angle Ψ measured at the angle of incidence of 45° of the 5
nm thick gold film before (solid line) and after (dashed line) illumination with the laser
(Fig. S4b). As we can see the figure confirms the results of Fig. S4a. Only tiny changes
above 800 nm can be observed. The very good agreement of both reflectivity curves in
Fig. S4a is a further proof than the geometrical modifications are negligible. Increasing
the laser power to 225 mW/cm2 leads to slightly larger modifications in the spectra (not
shown), but it was checked that the resulting SHG signal stays constant over time and that
it is not modified by any significant reshaping of the clusters due to material melting that
would cause a closing of the gaps in between the clusters.
Skin depth of the gold thin films
The skin depth δ of gold was calculated using the equation (S1) [S3]:
𝛿=
𝑐
𝜔𝑘
(S1)
Where the extinction coefficient k is extracted from the model of the spectroscopic
ellipsometry data of the 30 nm thick gold film.
Figure S5: Skin depth of gold calculated using the optical constants extracted from the model of the
spectroscopic ellipsometry data of the 30 nm thick gold film.
The figure shows how the skin depth is well above the thickness at which the gold thin
films percolate over the all visible near-infrared frequency range.
*
Author to whom correspondence should be addressed. Electronic mail: stefano.de-zuani@pi1.physik.unistuttgart.de
References
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S3.
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