Optical Characteristics of Directly Deposited Gold Nanoparticle Films

: The manuscript presents the optical properties of directly deposited films of gold nanoparticles (AuNPs) prepared by the Ultrasonic Spray Pyrolysis (USP) technology. Four samples were produced, with AuNP deposition times on the glass substrate of 15 min, 30 min, 1 h and 4 h. The morphological characterisation of the deposited films showed that the size of the first deposited AuNPs was between 10 and 30 nm, while, with a longer duration of the deposition process, larger clusters of AuNPs grew by coalescence and aggregation. The prepared layers were characterised optically with Ultraviolet–visible spectroscopy (UV–vis) and ellipsometry. The ellipsometric measurements showed an increasingly denser and thicker effective thickness of the AuNP layers. The extinction spectra displayed a clear local surface plasmonic resonance (LSPR) signature (peak 520–540 nm), indicating the presence of isolated particles in all the samples. For all AuNP layers, the imaginary part of the parallel and perpendicular components of the anisotropic dielectric function was dominated by a central peak at around 2.2 eV, corresponding to the LSPR of isolated particles, and a high-energy shoulder due to Au interband transitions. It was shown that, as the density of particles increased, the extinction cross-section grew over the whole spectral range where measurements are taken. Thus, the response can be explained with an enhanced electromagnetic response between the AuNPs that can be connected to the increase in particle density, but also by the formation of clusters and irregular structures.


Introduction
Gold nanoparticles (AuNPs) were utilised due to their exceptional chemical and physical properties, with a particular emphasis on their fascinating optical characteristics arising from local surface plasmonic resonance (LSPR) [1][2][3].LSPR is the occurrence of a resonance of the incident electromagnetic field and the plasmon of a particle, which occurs when the frequency of the electromagnetic field is equal to the inherent frequency of oscillation of the cloud of free electrons within the particle.As a result of this resonance, the electronic cloud is excited, generating its own electric field that influences the absorption and scattering of light [4,5].
Thin layers of metallic materials undergo propagating surface plasmon resonance (PSPR), where the plasmon propagates along the surface of the film layer.PSPRs exhibit a continuous dispersion relation, enabling their existence across a broad spectrum of frequencies [6].In contrast, LSPRs are confined to a finite frequency range, due to the constraints imposed by their finite dimensions.The spectral positioning of LSPR is dictated by factors such as the particle's size and shape, along with the dielectric properties of both the metal and the surrounding medium [4][5][6].Notably, LSPR can undergo direct coupling with propagating light, a capability not shared by PSPRs.
In the case of copper, silver and gold, LSPR occurs in the visible light range [4,7].Therefore, these metallic elements are particularly appealing for optical applications, as they enable controlled manipulation of the light's properties.Additionally, gold has a high ionisation potential, and is therefore highly resistant to oxidation and corrosion.This makes it applicable for use in various media and environments, in various biological or chemical conditions, as well as in electronic or aerospace settings, which may not be considered suitable for less corrosion-resistant materials.The occurrence of LSPR opens doors to numerous applications, where the unique optical characteristics of these noble metal nanoparticles can be exploited, such as in sensors [8][9][10][11][12], biomedical applications [13][14][15][16][17][18], advanced optical materials [17,19], where the corrosion resistance of gold is important for signal transmission and monitoring of physical quantities, or photocatalysis [20,21].
The Mie theory allows for the prediction of LSPR in particles.For spherical particles, there are simplified numerical models that assume various oscillations of the electronic cloud known as discrete dipole approximation (DDA), such as dipole and quadrupole oscillations [4].The analytical calculation of LSPR is feasible for spherical particles [3,22], whereas complex particle shapes require complex numerical solutions [4,23].
Analytical and numerical calculations offer a good prediction of the absorption peaks of nanoparticle suspensions, since nanoparticles undergo Brownian motion [5,24,25] and are in contact with other particles for an insignificant amount of time, if any at all, due to the presence of repulsive forces or steric stabilisers.Steric stabilisers are added to nanoparticles ′ suspensions to stabilise the solution and prevent agglomeration and aggregation when the repulsive forces are not sufficient [5,26,27].Stabilisers can also prevent agglomeration and aggregation of nanoparticles, while removing the dispersion media slowly [28][29][30].Without the presence of stabilisers, the nanoparticles agglomerate and aggregate during the removal of the dispersion media, which changes the colour of the gold nanoparticles directly.A similar phenomenon is expected when AuNPs are layered on each other with direct deposition within the reaction chamber of an ultrasound spray pyrolysis (USP) device.No sintering is expected to occur, since the temperatures inside the USP device in the deposition zone are not near the sintering temperature of the AuNPs [30].No direct deposition of AuNPs from an USP process has been observed in the available literature, as this process is used mainly for the production of discrete nanoparticles.Therefore, this research work aims to characterise the optical properties of an AuNPs film prepared by this technology, in order to evaluate the possibility of using USP for coating of the Au layers.This process has a continuous operation for nanoparticle production, which could be used for a high output of Au coatings on glass substrates, if a successful coating is feasible.Overall, the investigated samples displayed narrow-sized distributions, with spectral optical responses essentially defined by the plasmon resonance of isolated particles.At the same time, the magnitude of optical extinction was controlled by the density of particles, regulated by the deposition time.This feature evidences the advantage of the fabrication method in comparison to other bottom-up approaches, in which the morphology, and, hence, optical properties are hard to control.

Gold Nanoparticle Synthesis and Gold Nanoparticle Film Preparation
A USP process was used for producing the AuNPs layer on the glass substrate (Figure 1).The precursor used was Hydrogen tetrachloroaurate (III) trihydrate (HAuCl 4 •3H 2 O, molecular weight: 393.83 g/mol, Glentham Life Sciences, UK), dissolved in deionised water at a concentration of 0.5 g/L Au (1.0 g/L HAuCl 4 •3H 2 O; Au with a molar weight of 196.967 g/mol represents 50% of the weight of Hydrogen tetrachloroaurate (III) trihydrate).The USP process was carried out using a proprietary device from Zlatarna Celje d.o.o., Slovenia [30], consisting of a custom built tube furnace, an ultrasonic generator, a precursor supply system, and a gas washing system for nanoparticle collection.The ultrasonic generator is constructed with a 1.6 MHz piezoceramic membrane for generating the ultrasound (Liquifog II, Johnson Matthey Piezo Products GmbH, Germany), which is submerged in a chamber for the aerosolization of the precursor solution.The generated precursor mist is transported in the tube furnace with nitrogen gas at a rate of 6 L/min.The quartz tube furnace has three heating zones, with a length of 400 mm each and an internal diameter of 35 mm.The tube furnace heating zone temperatures were set at 200, 400 and 400 • C. The hydrogen gas was introduced into the tube between the first and second heating zones at a rate of 6 L/min.The borosilicate glass substrate (Duran Borosilicate glass 3.3 according to ISO 3585, DWK Life Sciences GmbH, Mainz, Germany), with dimensions of 1.5 × 2.5 cm and a thickness of 1 mm, was positioned inside the reaction tube at an angle of 45 • , about 10 cm from the end of the third heating zone.The glass substrate was cleaned with ethanol before use, in order to remove any dust or residues before deposition.The precursor droplets inside the tube furnace undergo droplet evaporation and shrinkage, diffusion of the hydrogen tetrachloroaurate to the droplet centre, reduction with hydrogen gas and final nanoparticle densification, before hitting and depositing a layer of AuNPs on the substrate.Four samples were produced, with AuNP deposition times of 15 min, 30 min, 1 h and 4 h on the glass substrate.
Surfaces 2024, 7, FOR PEER REVIEW 3 precursor supply system, and a gas washing system for nanoparticle collection.The ultrasonic generator is constructed with a 1.6 MHz piezoceramic membrane for generating the ultrasound (Liquifog II, Johnson Matthey Piezo Products GmbH, Germany), which is submerged in a chamber for the aerosolization of the precursor solution.The generated precursor mist is transported in the tube furnace with nitrogen gas at a rate of 6 L/min.The quartz tube furnace has three heating zones, with a length of 400 mm each and an internal diameter of 35 mm.The tube furnace heating zone temperatures were set at 200, 400 and 400 °C.The hydrogen gas was introduced into the tube between the first and second heating zones at a rate of 6 L/min.The borosilicate glass substrate (Duran Borosilicate glass 3.3 according to ISO 3585, DWK Life Sciences GmbH, Mainz, Germany), with dimensions of 1.5 × 2.5 cm and a thickness of 1 mm, was positioned inside the reaction tube at an angle of 45°, about 10 cm from the end of the third heating zone.The glass substrate was cleaned with ethanol before use, in order to remove any dust or residues before deposition.The precursor droplets inside the tube furnace undergo droplet evaporation and shrinkage, diffusion of the hydrogen tetrachloroaurate to the droplet centre, reduction with hydrogen gas and final nanoparticle densification, before hitting and depositing a layer of AuNPs on the substrate.Four samples were produced, with AuNP deposition times of 15 min, 30 min, 1 h and 4 h on the glass substrate.

Morphological Characterisation
A Scanning Electron Microscope, Sirion 400 NC SEM (FEI, Hillsboro, OR, USA), was used for the surface investigations of the prepared layer of AuNPs on the glass substrate.The SEM was equipped with an INCA 350 EDS detector (Oxford Instruments, Abingdon, Oxfordshire, UK) for microchemical analysis.The glass substrates with deposited AuNPs from the USP were coated with carbon, for providing sufficient conductivity for the SEM imaging and EDS analysis.Particle sizes were measured with SEM software and ImageJ (version 1.54h), with at least 500 particles measured for a given sample.

Optical Characterisation
The prepared layers were characterised optically with Ultraviolet-visible spectroscopy (UV-vis) and ellipsometry.
The UV-vis measurements were performed with a Tecan Infinite M200 (Tecan Group Ltd., Männedorf, Switzerland) UV-Vis spectrophotometer, by inserting the sample plates into the light beam path with the following parameters: absorbance range: λ = 400 to 700 nm, no.flashes: 5×.

Morphological Characterisation
A Scanning Electron Microscope, Sirion 400 NC SEM (FEI, Hillsboro, OR, USA), was used for the surface investigations of the prepared layer of AuNPs on the glass substrate.The SEM was equipped with an INCA 350 EDS detector (Oxford Instruments, Abingdon, Oxfordshire, UK) for microchemical analysis.The glass substrates with deposited AuNPs from the USP were coated with carbon, for providing sufficient conductivity for the SEM imaging and EDS analysis.Particle sizes were measured with SEM software and ImageJ (version 1.54h), with at least 500 particles measured for a given sample.

Optical Characterisation
The prepared layers were characterised optically with Ultraviolet-visible spectroscopy (UV-vis) and ellipsometry.
The UV-vis measurements were performed with a Tecan Infinite M200 (Tecan Group Ltd., Männedorf, Switzerland) UV-Vis spectrophotometer, by inserting the sample plates into the light beam path with the following parameters: absorbance range: λ = 400 to 700 nm, no.flashes: 5×.
The samples were investigated by spectroscopic ellipsometry measurements in the spectral range between 0.57 and 3.5 eV with a V-VASE ellipsometer (J.A. Woollam, Lincoln, NE, USA), at incidences of 45 • , 55 • and 65 • .The transmittance measurements at the normal incidence were taken at the same sample point, to increase the reliability of the characterisation results [31].In order to fit the experimental measurements, the layer of gold nanoparticles was modelled using an effective medium approach, i.e., the layer was treated as a homogeneous film, with its optical response completely determined by its effective thickness and effective optical constants.The effective optical constants were modelled using a multiple oscillator model that can take into account the LSPR of the AuNPs and Au interband transitions in the high energy range, as described elsewhere [32].Data fitting was conducted by optimising the parameters describing the sample model through the minimisation of a figure of merit that quantifies the discrepancy between the simulated and experimental data.

Morphological Characterisation
A detailed SEM examination of the samples showed AuNPs deposited in a discontinuous layer across the samples' surfaces (Figure 2).The number of AuNPs was the lowest for the sample with 15 min of deposition, and increased as more time was given for deposition on the glass substrate.As expected, the sample with 4 h of deposition had the highest number of AuNPs, while the nanoparticle sizes were also the biggest for this sample.
The samples were investigated by spectroscopic ellipsometry measurements in the spectral range between 0.57 and 3.5 eV with a V-VASE ellipsometer (J.A. Woollam, Lincoln, NE, USA), at incidences of 45°, 55° and 65°.The transmittance measurements at the normal incidence were taken at the same sample point, to increase the reliability of the characterisation results [31].In order to fit the experimental measurements, the layer of gold nanoparticles was modelled using an effective medium approach, i.e., the layer was treated as a homogeneous film, with its optical response completely determined by its effective thickness and effective optical constants.The effective optical constants were modelled using a multiple oscillator model that can take into account the LSPR of the AuNPs and Au interband transitions in the high energy range, as described elsewhere [32].Data fitting was conducted by optimising the parameters describing the sample model through the minimisation of a figure of merit that quantifies the discrepancy between the simulated and experimental data.

Morphological Characterisation
A detailed SEM examination of the samples showed AuNPs deposited in a discontinuous layer across the samples' surfaces (Figure 2).The number of AuNPs was the lowest for the sample with 15 min of deposition, and increased as more time was given for deposition on the glass substrate.As expected, the sample with 4 h of deposition had the highest number of AuNPs, while the nanoparticle sizes were also the biggest for this sample.The differences between nanoparticle sizes and shapes can be seen in Figure 3. Larger particles were produced as more time was given to the AuNPs' deposition.The AuNPs with 15 min deposition were small, with measured sizes from 10-30 nm, with individual nanoparticles that were somewhat larger, mostly around 60-120 nm.An example of nanoparticle measurements of the sample with 1 h deposition is presented in Figure 4.The smaller nanoparticles were spherical in shape.As the nanoparticle size increased, they Surfaces 2024, 7 373 became increasingly more irregular in shape.With longer deposition times (30 min and 1 h), an increasingly higher number of larger nanoparticles (around 100 nm and up to 200 nm) were present, while the smaller 10-30 nm nanoparticles were still dominating in number.With the longest deposition time of 4 h, the larger particles were more numerous and prevalent on the sample surface as compared to the previous samples.In this sample, the larger, irregularly shaped particles and clusters of these particles were measured up to a value of 380 nm.Therefore, larger deposition times are not reported here, because they resulted in broad and inhomogeneous particle sizes and shape distributions, widening, and quenching the well-defined plasmon resonances of small, isolated particles.There were also dark spots present on the sample's surface (Figures 2iv and 3iv), where nanoparticles were not present, or only very small nanoparticles around 10 nm were present in lower numbers.
The differences between nanoparticle sizes and shapes can be seen in Figure 3. Larger particles were produced as more time was given to the AuNPs′ deposition.The AuNPs with 15 min deposition were small, with measured sizes from 10-30 nm, with individual nanoparticles that were somewhat larger, mostly around 60-120 nm.An example of nanoparticle measurements of the sample with 1 h deposition is presented in Figure 4.The smaller nanoparticles were spherical in shape.As the nanoparticle size increased, they became increasingly more irregular in shape.With longer deposition times (30 min and 1 h), an increasingly higher number of larger nanoparticles (around 100 nm and up to 200 nm) were present, while the smaller 10-30 nm nanoparticles were still dominating in number.With the longest deposition time of 4 h, the larger particles were more numerous and prevalent on the sample surface as compared to the previous samples.In this sample, the larger, irregularly shaped particles and clusters of these particles were measured up to a value of 380 nm.Therefore, larger deposition times are not reported here, because they resulted in broad and inhomogeneous particle sizes and shape distributions, widening, and quenching the well-defined plasmon resonances of small, isolated particles.There were also dark spots present on the sample′s surface (Figures 2iv and 3iv), where nanoparticles were not present, or only very small nanoparticles around 10 nm were present in lower numbers.The EDX analysis of the samples showed the presence of Au, along with elements which were constituents of the glass substrate-Si, O and minor elements of Na, Mg, Ca, Al.The interaction volume of a few µm, from which X-rays are emitted during the EDS analysis, was much larger than the AuNPs′ sizes, resulting in the detection of the glass substrate elements, along with the AuNPs.More importantly, no Cl or other impurities were detected in the samples, which would indicate an incomplete synthesis of the nanoparticles from the chloride precursor, or contamination from other elements during the The EDX analysis of the samples showed the presence of Au, along with elements which were constituents of the glass substrate-Si, O and minor elements of Na, Mg, Ca, Al.The interaction volume of a few µm, from which X-rays are emitted during the EDS analysis, was much larger than the AuNPs ′ sizes, resulting in the detection of the glass substrate elements, along with the AuNPs.More importantly, no Cl or other impurities were detected in the samples, which would indicate an incomplete synthesis of the nanoparticles from the chloride precursor, or contamination from other elements during the synthesis and deposition of the AuNPs.An example of the EDX analysis for a sample with 1 h of AuNPs' deposition is shown in Figure 4; the other samples had similar results.synthesis and deposition of the AuNPs.An example of the EDX analysis for a sample with 1 h of AuNPs' deposition is shown in Figure 4; the other samples had similar results.

Optical Characterisation
The extinction spectra of the samples with USP deposition for 15 min, 30 min, 1 h and 4 h are shown in Figure 5.The spectra display a clear LSPR signature (peak 520-540 nm), indicating the presence of isolated particles in all the samples.The strength of the extinction peak rose with the deposition time, accounting for the increase in the number of deposited particles.In addition to the LSPR peak, the larger deposition times resulted in a progressive increase in extinction in the long-wavelength range, that might be explained by electromagnetic interaction between the particles and the presence of larger/clustered particles, as discussed in Section 4.

Optical Characterisation
The extinction spectra of the samples with USP deposition for 15 min, 30 min, 1 h and 4 h are shown in Figure 5.The spectra display a clear LSPR signature (peak 520-540 nm), indicating the presence of isolated particles in all the samples.The strength of the extinction peak rose with the deposition time, accounting for the increase in the number of deposited particles.In addition to the LSPR peak, the larger deposition times resulted in a progressive increase in extinction in the long-wavelength range, that might be explained by electromagnetic interaction between the particles and the presence of larger/clustered particles, as discussed in Section 4.
In the first step, the ellipsometric measurements were fitted using an isotropic model for the effective optical constants of the AuNPs' layer, leading to a fair agreement with the experimental data, with the multiple oscillator model providing better data fits than the Maxwell-Garnett effective medium theory [33].A significantly better agreement was obtained if the AuNP film was modelled as a uniaxial anisotropic layer, with different effective dielectric functions for light polarised along the plane parallel (ε//) or perpendicular (ε p, the ellipsometric measurements were fitted using an isotropic model tical constants of the AuNPs' layer, leading to a fair agreement with the with the multiple oscillator model providing better data fits than the ffective medium theory [33].A significantly better agreement was obfilm was modelled as a uniaxial anisotropic layer, with different effections for light polarised along the plane parallel (ε//) or perpendicular e′s surface.As an example, the experimental data fits for the sample deposition are shown in Figure 6i-iii.The measurements for the sam-4 h deposition showed very large depolarisation values, probably due and it was not possible to fit them with the current model.NP layers, the imaginary part of both ε//and ε⏊ was dominated by a d 2.2 eV, corresponding to the LSPR of isolated particles, and a highue to Au interband transitions.It should be noted that the LSPR peak d more intense for longer deposition times, which can be explained by ion of nanoparticles in the AuNP layer that gave place to stronger inagnetic interactions [34].In general, both the real and imaginary parts ger values than ε//, which can be explained by the larger polarizability n light is polarised perpendicularly to the sample surface due to the strate and the resulting image effects [35].ective thickness of the AuNP layer for samples deposited at 15, 30 and 7 and 110 nm, suggesting that, as the deposition time increased, the y became denser, but also grew in the vertical dimension.
) to the sample's surface.As an example, the experimental data fits for the sample obtained for 30 min deposition are shown in Figure 6i-iii.The measurements for the sample obtained after 4 h deposition showed very large depolarisation values, probably due to large scattering, and it was not possible to fit them with the current model.In the first step, the ellipsometric measurements were fitted using an isotropic model for the effective optical constants of the AuNPs' layer, leading to a fair agreement with the experimental data, with the multiple oscillator model providing better data fits than the Maxwell-Garnett effective medium theory [33].A significantly better agreement was obtained if the AuNP film was modelled as a uniaxial anisotropic layer, with different effective dielectric functions for light polarised along the plane parallel (ε//) or perpendicular (ε⏊) to the sample′s surface.As an example, the experimental data fits for the sample obtained for 30 min deposition are shown in Figure 6i-iii.The measurements for the sample obtained after 4 h deposition showed very large depolarisation values, probably due to large scattering, and it was not possible to fit them with the current model.
For all the AuNP layers, the imaginary part of both ε//and ε⏊ was dominated by a central peak around 2.2 eV, corresponding to the LSPR of isolated particles, and a highenergy shoulder due to Au interband transitions.It should be noted that the LSPR peak became broader and more intense for longer deposition times, which can be explained by a larger concentration of nanoparticles in the AuNP layer that gave place to stronger interparticle electromagnetic interactions [34].In general, both the real and imaginary parts of ε⏊ displayed larger values than ε//, which can be explained by the larger polarizability of the particle when light is polarised perpendicularly to the sample surface due to the presence of the substrate and the resulting image effects [35].
Finally, the effective thickness of the AuNP layer for samples deposited at 15, 30 and 60 min were 79, 97 and 110 nm, suggesting that, as the deposition time increased, the AuNP film not only became denser, but also grew in the vertical dimension.

Discussion
From the SEM examination, it is seen that the initially deposited AuNPs were small, with sizes of about 10-20 nm.This is the mean particle size resulting from the initial precursor gold concentration of 0.5 g/L.As the aerosol droplets travel through the USP reaction tube, they are evaporated, and the gold salt content is reduced with hydrogen gas and densified into AuNPs at a suitable reaction temperature.Such small particles are not stabilised kinetically in the USP flow stream, and have a relatively high surface energy.As the number of AuNPs increases, and the coverage of the glass substrate becomes greater, coalescence and aggregation occur, forming larger individual particles.In the first stage, these larger individual particles are also spherical, but become increasingly irregu- In the first step, the ellipsometric measurements were fitted using an isotropic model for the effective optical constants of the AuNPs' layer, leading to a fair agreement with the experimental data, with the multiple oscillator model providing better data fits than the Maxwell-Garnett effective medium theory [33].A significantly better agreement was obtained if the AuNP film was modelled as a uniaxial anisotropic layer, with different effective dielectric functions for light polarised along the plane parallel (ε//) or perpendicular (ε⏊) to the sample′s surface.As an example, the experimental data fits for the sample obtained for 30 min deposition are shown in Figure 6i-iii.The measurements for the sample obtained after 4 h deposition showed very large depolarisation values, probably due to large scattering, and it was not possible to fit them with the current model.
For all the AuNP layers, the imaginary part of both ε//and ε⏊ was dominated by a central peak around 2.2 eV, corresponding to the LSPR of isolated particles, and a highenergy shoulder due to Au interband transitions.It should be noted that the LSPR peak became broader and more intense for longer deposition times, which can be explained by a larger concentration of nanoparticles in the AuNP layer that gave place to stronger interparticle electromagnetic interactions [34].In general, both the real and imaginary parts of ε⏊ displayed larger values than ε//, which can be explained by the larger polarizability of the particle when light is polarised perpendicularly to the sample surface due to the presence of the substrate and the resulting image effects [35].
Finally, the effective thickness of the AuNP layer for samples deposited at 15, 30 and 60 min were 79, 97 and 110 nm, suggesting that, as the deposition time increased, the AuNP film not only became denser, but also grew in the vertical dimension.In the first step, the ellipsometric measurements were fitted using an isotropic model for the effective optical constants of the AuNPs' layer, leading to a fair agreement with the experimental data, with the multiple oscillator model providing better data fits than the Maxwell-Garnett effective medium theory [33].A significantly better agreement was obtained if the AuNP film was modelled as a uniaxial anisotropic layer, with different effective dielectric functions for light polarised along the plane parallel (ε//) or perpendicular (ε⏊) to the sample′s surface.As an example, the experimental data fits for the sample obtained for 30 min deposition are shown in Figure 6i-iii.The measurements for the sample obtained after 4 h deposition showed very large depolarisation values, probably due to large scattering, and it was not possible to fit them with the current model.
For all the AuNP layers, the imaginary part of both ε//and ε⏊ was dominated by a central peak around 2.2 eV, corresponding to the LSPR of isolated particles, and a highenergy shoulder due to Au interband transitions.It should be noted that the LSPR peak became broader and more intense for longer deposition times, which can be explained by a larger concentration of nanoparticles in the AuNP layer that gave place to stronger interparticle electromagnetic interactions [34].In general, both the real and imaginary parts of ε⏊ displayed larger values than ε//, which can be explained by the larger polarizability of the particle when light is polarised perpendicularly to the sample surface due to the presence of the substrate and the resulting image effects [35].
was dominated by a central peak around 2.2 eV, corresponding to the LSPR of isolated particles, and a highenergy shoulder due to Au interband transitions.It should be noted that the LSPR peak became broader and more intense for longer deposition times, which can be explained by a larger concentration of nanoparticles in the AuNP layer that gave place to stronger interparticle electromagnetic interactions [34].In general, both the real and imaginary parts of ε nstants of the AuNPs' layer, leading to a fair agreement with the the multiple oscillator model providing better data fits than the e medium theory [33].A significantly better agreement was obas modelled as a uniaxial anisotropic layer, with different effecor light polarised along the plane parallel (ε//) or perpendicular face.As an example, the experimental data fits for the sample sition are shown in Figure 6i-iii.The measurements for the samposition showed very large depolarisation values, probably due was not possible to fit them with the current model.yers, the imaginary part of both ε//and ε⏊ was dominated by a eV, corresponding to the LSPR of isolated particles, and a highu interband transitions.It should be noted that the LSPR peak e intense for longer deposition times, which can be explained by nanoparticles in the AuNP layer that gave place to stronger inic interactions [34].In general, both the real and imaginary parts lues than ε//, which can be explained by the larger polarizability t is polarised perpendicularly to the sample surface due to the and the resulting image effects [35].thickness of the AuNP layer for samples deposited at 15, 30 and 110 nm, suggesting that, as the deposition time increased, the me denser, but also grew in the vertical dimension.
displayed larger values than ε//, which can be explained by the larger polarizability of the particle when light is polarised perpendicularly to the sample surface due to the presence of the substrate and the resulting image effects [35].
Finally, the effective thickness of the AuNP layer for samples deposited at 15, 30 and 60 min were 79, 97 and 110 nm, suggesting that, as the deposition time increased, the AuNP film not only became denser, but also grew in the vertical dimension.

Discussion
From the SEM examination, it is seen that the initially deposited AuNPs were small, with sizes of about 10-20 nm.This is the mean particle size resulting from the initial precursor gold concentration of 0.5 g/L.As the aerosol droplets travel through the USP reaction tube, they are evaporated, and the gold salt content is reduced with hydrogen gas and densified into AuNPs at a suitable reaction temperature.Such small particles are not stabilised kinetically in the USP flow stream, and have a relatively high surface energy.As the number of AuNPs increases, and coverage of the glass substrate becomes greater, coalescence and aggregation occur, forming larger individual particles.In the first stage, these larger individual particles are also spherical, but become increasingly irregular as they grow larger.
Evidence of particles shifting and growing together might be the dark spots observed in the advanced AuNP coverage of the sample with 4 h of deposition time, seen in Figures 2iv and 3iv.These dark spots are zones of particle depletion, as the very small AuNPs shifted towards the larger particles, where they aggregated and became a part of the larger particles, or as a part of clusters of primary nanoparticles.With additional deposition time, these zones would again be filled up with AuNPs until the larger particles form an uninterrupted mesh-like structure, and, finally, a continuous Au layer on the glass substrate.Any other potential influence for particle formation was not considered, as the EDX analysis of the AuNPs showed no impurities in the analysed areas.
The samples with deposited AuNPs had a distinctive red transparent colour, and were increasingly less transparent with additional deposition time (supplementary Figure S1).The sample with 4 h of deposition had a more visibly opaque appearance.The ellipsometric measurements of this sample were also not applicable, due to the large scattering of the produced particles.For the other samples, the ellipsometric measurements showed an increasingly denser and thicker effective thickness of the AuNP layers, in accordance with the described particle growth (Table 1).The chosen parameters (gold concentration in the precursor solution, heating temperatures, gas flows) for the given USP system provided adequate control over the AuNP deposition on the glass substrate.It was determined from previous experimental studies [30] that a gold concentration in the precursor solution of 0.5 g/L Au produces relatively small AuNPs, which is beneficial for an evaluation of their LSPR occurrence, as this optical property is more evident in small nanoparticles.Using higher gold concentrations in the precursor solution, or higher gas and material flows, produces larger AuNPs, or a greater number of nanoparticles, which would cover the glass substrate faster, losing some control over the deposition rates in the conducted experiments.A higher temperature also results in higher particle mobility and agglomeration rates of the particles on the glass substrate.The different factors of using various USP parameters would have to be considered in future studies for their optimisation, in order to provide for a quick deposition of a desired size and thickness of the AuNP layer.In order to understand the evolution of the extinction spectra at normal incidence as a function of the deposition time qualitatively (Figure 5) and the effective dielectric function of the AuNP layer (Figure 6), we performed simulations based on the multiple-particle Mie theory, as described elsewhere [36].In short, the simulations were based in an extension of the Mie theory, in which particles were excited by the incoming radiation and by the field scattered by other particles.We considered 50 nm Au particles embedded in a medium with a refractive index of 1.25 (i.e., the average of an air and glass refractive index) that were distributed randomly in the planar region of 500 nm × 500 nm, as shown schematically in Figure 7 (left).The incoming light was assumed to propagate in the direction perpendicular to the plane of the particles, in order to represent normal incidence measurements.As expected, as the density of the particles increased, the extinction crosssection grew over the whole spectral range where measurements are taken (Figure 7, right panel).Thus, the observed optical response can be explained with an enhanced electromagnetic response between the particles, which can be connected to the increase in particle density, but also by the formation of clusters and irregular structures, as reported in the morphological characterisation.In order to understand the evolution of the extinction spectra at normal incidence as a function of the deposition time qualitatively (Figure 5) and the effective dielectric function of the AuNP layer (Figure 6), we performed simulations based on the multiple-particle Mie theory, as described elsewhere [36].In short, the simulations were based in an extension of the Mie theory, in which particles were excited by the incoming radiation and by the field scattered by other particles.We considered 50 nm Au particles embedded in a medium with a refractive index of 1.25 (i.e., the average of an air and glass refractive index) that were distributed randomly in the planar region of 500 nm × 500 nm, as shown schematically in Figure 7 (left).The incoming light was assumed to propagate in the direction perpendicular to the plane of the particles, in order to represent normal incidence measurements.As expected, as the density of the particles increased, the extinction crosssection grew over the whole spectral range where measurements are taken (Figure 7, right panel).Thus, the observed optical response can be explained with an enhanced electromagnetic response between the particles, which can be connected to the increase in particle density, but also by the formation of clusters and irregular structures, as reported in the morphological characterisation.Finally, it should be noted that the effective optical constants of the Au NP layer turned out to be anisotropic.Although such anisotropy can be expected due to the presence of the substrate and the nearly 2-dimensional arrangement of nanoparticles, it is rarely reported in the literature in cases of similar nanoparticle topologies, such as metal island films, or nanoparticles embedded in dielectric layers.The accurate control over particle size and shape enabled by the fabrication methodology results in narrow plasmon resonances that allow for detection of the inherent anisotropic response associated with the film-onsubstrate geometry.

Conclusions
• The initially deposited AuNPs were small, with sizes of about 10-20 nm.As a higher number of particles were deposited, larger particles were formed and grown through coalescence and aggregation.• The uniaxial anisotropic model showed better agreement with the ellipsometric measurement data compared to the isotropic model.

Figure 1 .
Figure 1.Deposition of AuNPs on the glass substrate with the USP process.

Figure 1 .
Figure 1.Deposition of AuNPs on the glass substrate with the USP process.

Figure 2 .
Figure 2. Low magnification SEM images of the samples with USP deposition of AuNPs for (i) 15 min, (ii) 30 min, (iii) 1 h and (iv) 4 h, showing the nanoparticle coverage on the glass substrate.

Figure 3 .
Figure 3. High magnification SEM images of the samples with USP deposition of AuNPs for (i) 15 min, (ii) 30 min, (iii) 1 h and (iv) 4 h, showing the nanoparticles' morphology.Particle size histograms are included for each deposition time, with calculated mean, Standard Deviation, minimum and maximum values from the SEM image measurements.

Figure 3 .
Figure 3. High magnification SEM images of the samples with USP deposition of AuNPs for (i) 15 min, (ii) 30 min, (iii) 1 h and (iv) 4 h, showing the nanoparticles' morphology.Particle size histograms are included for each deposition time, with calculated mean, Standard Deviation, minimum and maximum values from the SEM image measurements.

Figure 4 .
Figure 4. EDX analysis and particle size measurements for the sample with 1 h of AuNP deposition.

Figure 4 .
Figure 4. EDX analysis and particle size measurements for the sample with 1 h of AuNP deposition.

Figure 5 .
Figure 5. Extinction spectra calculated from the transmittance of the bare (T0) and coated (T) substrate for different deposition times.

Figure 5 .Figure 6 .
Figure 5. Extinction spectra calculated from the transmittance of the bare (T 0 ) and coated (T) substrate for different deposition times.Surfaces 2024, 7, FOR PEER REVIEW 8

Figure 6 . 7 Figure 5 .
Figure 6.Top panel: Fits of the ellipsometric angles ∆ (i), Ψ (ii) and transmittance (iii) spectra for the sample deposited for 30 min.The experimental data are shown by the dots and the fit by the solid lines.The annotated numbers in the ∆ and Ψ spectra indicate the angle of incidence.Bottom panel: The real (εr) and imaginary (εi) parts of the effective dielectric function of the AuNP layer deposited for 15 min (iv), 30 min (v) and 1 h (vi), for both in-plane (ε//) and out of plane (ε

)Figure 5 .
Figure 5. Extinction spectra calculated from the transmittance of the bare (T0) and coated (T) substrate for different deposition times.

Figure 7 .
Figure 7. (left) Random planar distribution of 25 (top), 45 (middle) and 65 Au nanoparticles in a 500 nm × 500 nm region.(right) Extinction spectra at a normal incidence for the simulated distribution of nanoparticles.

Table 1 .
Effective thickness of the deposited AuNP layers from the ellipsometric measurements.