Metallo-Dielectric Colloidal Films as SERS Substrate

Ana L. González, Arturo Santos Gómez and Miller Toledo-Solano

## Abstract

Along this chapter, we probe that the discrete dipole approximation models fairly well the optical response of periodic systems. Herein, we use it to model the reflectance and transmittance, at normal incidence, of colloidal films made of SiO2 spheres. As the thickness increases from 1 to 12 layers, the photonic band gap shifts to the blue tending to the value corresponding to a 3D opal, 442 nm. A film with more than eight layers resembles the bulk properties of a 3D opal. Our results are compared to a real sample. Besides, we show that taking advantage of the wide and asymmetrical absorbance spectrum of an opal with Au NPs is possible to identify the contribution of each component in the overall spectrum, through a deconvolution analysis. Finally, we present the electric field intensity as the content of metal NP increases in a monolayer. We consider NPs one order of magnitude smaller than the silica spheres, and then, 6, 9, and 17 NPs are hosted in the void. Similar average electric field intensities, about 11 times the incident intensity, are obtained with Au and Ag NPs. But, the spots with these intensities cover a bigger area with Ag NPs than with Au NPs.

Keywords: metal nanoparticles, SiO2 spheres, colloidal thin films, discrete dipole approximation, photonic band gap, near field intensity

#### 1. Introduction

A crystal is defined as the solid formed by a long range periodic array of atoms or molecules. Its periodic lattice originates a potential with the same periodicity, and as outcome, the energy levels give rise to allowed and forbidden bands. In consequence, the physical properties of crystals depend on the band structure. For instance, an electromagnetic wave with a frequency in the interval of the forbidden band will be reflected or absorbed by the crystal. In nature, other entities instead of atoms or molecules can conform to ordered arrangements. For example, Tobacco mosaic virus is a virus that infects plants, especially tobacco plant (where its name comes from); it has a rod-shape with the ability of self-assembling naturally creating a bi-dimensional triangular structure. This assembly has been exploited to increase the capacity of batteries [1] and as a template for the fabrication of functional devices [2]. Other periodic structures, found in nature or produced artificially, are the named colloidal crystals. A colloidal crystal is an assembly of colloid particles with a periodic structure. Its bulk properties depend on composition,

particle size, and packing arrangement. Opals are an example of colloidal crystals, in nature and under specific conditions of pressure and temperature; silicon dioxide (SiO2) spheres accommodate in a close-packed array. Probably its most well-known optical property is the constructive interference of light either at its surface or interior producing certain colors as the angle of incident light changes, and this property is named iridescence.

is the discrete dipole approximation (DDA). This method has been widely used to

nanoparticles, human blood, bacteria, and interstellar dust, among others [18–23]. Herein, we place attention to DDA's extended version, proposed by Draine and Flatau, for modeling R and T of infinite 2D periodic systems [24]. Recently, DDA was employed to study R and T of periodic arrays of dielectric and metal

In Figure 1, a section of a bi-dimensional periodic array of solid spheres is exemplified, each one discretized by Ndip dipoles represented by tiny spheres. As an analogy of atoms in a solid crystalline structure, the definition of a convenient unit cell is helpful. The target unit cell (TUC) is the entity located at the origin and that is repeated along the yz plane with an Ly and Lz periodicity. (m,n) is a pair of integers that defines the position of the TUC's replica at m units along the y axis and

The position and dipole moment of the dipole j of the (m,n) TUC replica are

L<sup>y</sup> and L<sup>z</sup> are the vectors that define the periodicity of the array; r<sup>j</sup><sup>00</sup> is the position vector of the j dipole that belongs to the TUC (the one at the origin), and k<sup>0</sup>

The dipole moment p<sup>j</sup><sup>00</sup> of the j dipole in the TUC satisfies the equation

wave at the position rj, and A~ <sup>j</sup>,<sup>k</sup> is a matrix that takes into account the interaction

A section of an infinite bidimensional periodic array of spheres. Each sphere is discretized by an array of Ndip dipoles. r<sup>j</sup>,mn is the position of the j dipole of the target unit cell (TUC) replica located at m units along the y axis

� � �<sup>X</sup> k6¼j

\$<sup>j</sup> � Einc r<sup>j</sup>

2 4

rjmn ¼ r<sup>j</sup><sup>00</sup> þ mL<sup>y</sup> þ nLz, (1)

� � � � for each <sup>j</sup> <sup>¼</sup> 1, … , Ndip, (2)

<sup>A</sup><sup>~</sup> <sup>j</sup>,<sup>k</sup>p<sup>k</sup><sup>00</sup>

3

� � is the field of an incident plane

5, (3)

study the absorbed and scattered light of several systems and materials as

spheres [25].

expressed as

where α

Figure 1.

95

n units along the z axis.

is the incident wave vector.

pjmn ¼ p<sup>j</sup><sup>00</sup> exp i mk<sup>0</sup> � L<sup>y</sup> þ nk<sup>0</sup> � L<sup>z</sup>

Metallo-Dielectric Colloidal Films as SERS Substrate DOI: http://dx.doi.org/10.5772/intechopen.90313

p<sup>j</sup><sup>00</sup> ¼ α

\$<sup>j</sup> is the polarizability tensor, Einc r<sup>j</sup>

and n units along the z axis. Figure taken with permission from Ref. [25].

Artificially, opals can be formed in a liquid medium or during drying/evaporation of particle suspension. Nowadays, it is possible to synthesize them with dielectric spheres of porous silica, polymethyl methacrylate, polystyrene, and others, of diameter of hundreds of nanometers. The main impressive characteristic of artificial opals is its optical response in the visible range [3, 4], and this has technological implications that place them as photonic band gap (PBG) materials. A bidimensional ordered array (thin film) can be used as coatings of several substrates, allowing to optimize or even modify some of the physical and chemical properties of the substrate. Its optical response may depend on the geometry of the periodic array, defects, and thickness. Some artificial opals have been reported with a face centered cubic (FCC) or close-packed hexagonal (HCP) structure with sequences ABCABC and ABAB, respectively [5, 6].

On the other hand, nanocomposite materials often exhibit exceptional properties compared to their constituents. Consequently, the incorporation of metal nanoparticles (NPs) into colloidal crystals is a subject of study that emerges naturally [7]. Some of the methods to achieve the incorporation of the NPs are based on self-assembling, electroplating process, and photolysis [8–10]. The applications of these composite thin films cover catalysis, optical devices, solar cell, and sensors [11–15], among others.

Particularly, composite periodic structures constructed by using colloidal crystals as templates and Au NPs have been tested as surface enhanced Raman scattering (SERS) substrates. These SERS substrates are simple and inexpensive to prepare and, moreover, offer the benefit of being highly stable. However, the SERS enhancement factor (EF) depends on several factors such as the probe molecule, concentration and shape of Au NPs, and thickness of the substrate. One may think that only the NPs in the top layer of the thin film are illuminated by the excitation laser and hence contribute to the SERS signal [16]. Nevertheless, larger SERS signal has been detected using thin composite substrates (less than 10 silica layers) rather than thick ones (more than 10 silica layers), and more surprising is the fact that the SERS enhancement falls down when substrates with a thickness between 1 and 2 mm are used [17]. Therefore, it seems that the SERS EF is thickness dependent, but the origin of this behavior is not completely understood.

This chapter is dedicated to the study of the optical response of colloidal thin films (multilayers of SiO2 spheres), with and without metal nanoparticles. In Section 2, we briefly describe the discrete dipole approximation method to model the reflectance (R), transmittance (T), and near electric field intensity. Section 3 contains an analysis of R and T of colloidal thin films as the thickness increases from 1 to 12 layers of SiO2 spheres. Section 4 focuses on a composite thin film and its role as SERS substrate; first, the absorbance spectra are proposed as a tool to verify the inclusion of Au NP, and second, the near electric field intensity as the amount of Au NP increases is shown.

#### 2. Discrete dipole approximation for periodic targets

Nowadays, there are several methods with their respective numerical implementations to enquire into the optical response of single targets, one of them Metallo-Dielectric Colloidal Films as SERS Substrate DOI: http://dx.doi.org/10.5772/intechopen.90313

particle size, and packing arrangement. Opals are an example of colloidal crystals, in nature and under specific conditions of pressure and temperature; silicon dioxide (SiO2) spheres accommodate in a close-packed array. Probably its most well-known optical property is the constructive interference of light either at its surface or interior producing certain colors as the angle of incident light changes, and this

Artificially, opals can be formed in a liquid medium or during drying/evaporation of particle suspension. Nowadays, it is possible to synthesize them with dielectric spheres of porous silica, polymethyl methacrylate, polystyrene, and others, of diameter of hundreds of nanometers. The main impressive characteristic of artificial opals is its optical response in the visible range [3, 4], and this has technological

implications that place them as photonic band gap (PBG) materials. A

compared to their constituents. Consequently, the incorporation of metal

and, moreover, offer the benefit of being highly stable. However, the SERS enhancement factor (EF) depends on several factors such as the probe molecule, concentration and shape of Au NPs, and thickness of the substrate. One may think that only the NPs in the top layer of the thin film are illuminated by the excitation laser and hence contribute to the SERS signal [16]. Nevertheless, larger SERS signal has been detected using thin composite substrates (less than 10 silica layers) rather than thick ones (more than 10 silica layers), and more surprising is the fact that the SERS enhancement falls down when substrates with a thickness between 1 and 2 mm are used [17]. Therefore, it seems that the SERS EF is thickness dependent,

but the origin of this behavior is not completely understood.

2. Discrete dipole approximation for periodic targets

Nowadays, there are several methods with their respective numerical implementations to enquire into the optical response of single targets, one of them

sequences ABCABC and ABAB, respectively [5, 6].

bidimensional ordered array (thin film) can be used as coatings of several substrates, allowing to optimize or even modify some of the physical and chemical properties of the substrate. Its optical response may depend on the geometry of the periodic array, defects, and thickness. Some artificial opals have been reported with a face centered cubic (FCC) or close-packed hexagonal (HCP) structure with

On the other hand, nanocomposite materials often exhibit exceptional properties

nanoparticles (NPs) into colloidal crystals is a subject of study that emerges naturally [7]. Some of the methods to achieve the incorporation of the NPs are based on self-assembling, electroplating process, and photolysis [8–10]. The applications of these composite thin films cover catalysis, optical devices, solar cell, and sensors

Particularly, composite periodic structures constructed by using colloidal crystals as templates and Au NPs have been tested as surface enhanced Raman scattering (SERS) substrates. These SERS substrates are simple and inexpensive to prepare

This chapter is dedicated to the study of the optical response of colloidal thin films (multilayers of SiO2 spheres), with and without metal nanoparticles. In Section 2, we briefly describe the discrete dipole approximation method to model the reflectance (R), transmittance (T), and near electric field intensity. Section 3 contains an analysis of R and T of colloidal thin films as the thickness increases from 1 to 12 layers of SiO2 spheres. Section 4 focuses on a composite thin film and its role as SERS substrate; first, the absorbance spectra are proposed as a tool to verify the inclusion of Au NP, and second, the near electric field intensity as the amount of

property is named iridescence.

Nanorods and Nanocomposites

[11–15], among others.

Au NP increases is shown.

94

is the discrete dipole approximation (DDA). This method has been widely used to study the absorbed and scattered light of several systems and materials as nanoparticles, human blood, bacteria, and interstellar dust, among others [18–23]. Herein, we place attention to DDA's extended version, proposed by Draine and Flatau, for modeling R and T of infinite 2D periodic systems [24]. Recently, DDA was employed to study R and T of periodic arrays of dielectric and metal spheres [25].

In Figure 1, a section of a bi-dimensional periodic array of solid spheres is exemplified, each one discretized by Ndip dipoles represented by tiny spheres. As an analogy of atoms in a solid crystalline structure, the definition of a convenient unit cell is helpful. The target unit cell (TUC) is the entity located at the origin and that is repeated along the yz plane with an Ly and Lz periodicity. (m,n) is a pair of integers that defines the position of the TUC's replica at m units along the y axis and n units along the z axis.

The position and dipole moment of the dipole j of the (m,n) TUC replica are expressed as

$$\mathbf{r}\_{jmn} = \mathbf{r}\_{j00} + m\mathbf{L}\_{\mathcal{Y}} + n\mathbf{L}\_{\mathfrak{x}},\tag{1}$$

$$\mathbf{p}\_{jmn} = \mathbf{p}\_{j00} \exp\left[i\left(m\mathbf{k}\_0 \cdot \mathbf{L}\_\eta + n\mathbf{k}\_0 \cdot \mathbf{L}\_z\right)\right] \qquad \text{for each } j = 1, \ldots, N\_{dip},\tag{2}$$

L<sup>y</sup> and L<sup>z</sup> are the vectors that define the periodicity of the array; r<sup>j</sup><sup>00</sup> is the position vector of the j dipole that belongs to the TUC (the one at the origin), and k<sup>0</sup> is the incident wave vector.

The dipole moment p<sup>j</sup><sup>00</sup> of the j dipole in the TUC satisfies the equation

$$\mathbf{p}\_{j00} = \overleftarrow{a}\_{j} \cdot \left[ \mathbf{E}\_{\text{inc}} \left( \mathbf{r}\_{j} \right) - \sum\_{k \neq j} \tilde{\mathbf{A}}\_{j,k} \mathbf{p}\_{k00} \right], \tag{3}$$

where α \$<sup>j</sup> is the polarizability tensor, Einc r<sup>j</sup> � � is the field of an incident plane wave at the position rj, and A~ <sup>j</sup>,<sup>k</sup> is a matrix that takes into account the interaction

#### Figure 1.

A section of an infinite bidimensional periodic array of spheres. Each sphere is discretized by an array of Ndip dipoles. r<sup>j</sup>,mn is the position of the j dipole of the target unit cell (TUC) replica located at m units along the y axis and n units along the z axis. Figure taken with permission from Ref. [25].

between the dipole located at r<sup>j</sup><sup>00</sup> and the field induced by the dipoles of the TUC and its replicas at the rkmn positions; for more details, see [24].

If there are Ndip dipoles in the TUC with a similar equation to Eq. (3) existing for each dipole, then, a system of 3Ndip complex coupled equations needs to be solved for p<sup>j</sup><sup>00</sup> values. Once the equation system is solved, then far and near field optical response of the periodic target can be calculated.

Usually, Ndip dipoles are of the order of 10<sup>5</sup> � <sup>10</sup>6; hence, numerical tools are necessary to solve the system of 3Ndip equations. A robust numerical implementation of DDA is the DDSCAT code [26] that assumes an incident plane wave along the positive direction of x axis and a bidimensional target resting on the yz plane. Among other interesting physical quantities, the 2 � 2 scattering amplitude matrix elements Si can be calculated, and consequently, the 4 � 4 scattering intensity matrix elements Sαβ [27].

For the specific case of unpolarized incident light, R and T are related to the Sαβ elements through the next expressions:

$$R = \mathbb{S}\_{11} \quad \text{for } (k\_{\text{ex}} k\_{0\text{x}} < 0), \tag{4}$$

the three-layer six spheres, and so on. A 10 nm separation distance between two

In the visible range, the refractive index of the silica, nSiO2 , is almost constant, and its variations go from 1.48 to 1.45 for wavelengths from 400 to 700 nm [28, 29]. For simplicity and without loss of information, we choose nSiO2 ð Þλ = 1.46. It is noteworthy to mention that in the visible the imaginary part of nSiO2 is negligible compared to the real part. However, in the ultraviolet interval, special care needs to be taken as the imaginary part comes to be significant and it is associated to the

R and T of a thin film composed of N layers, when light comes parallel to the normal of the surface, are shown in Figure 3. As the number of layers increases from 1 to 12, that is, as the film becomes thicker, a maximum of R emerges defining a photonic band, getting sharper around 450 nm. The optical spectrum to the left and right of the PBG is not symmetric because we have chosen the wavelength as the independent variable and not the wave number. The thickness, wavelength of the BG center (λc), width of the BG (ΔBG), effective refractive index of the thin film (neff), and optical path length (L) of each thin film are given in Table 1. Each

The thickness is determined by considering the diameter of the sphere, D, and geometrical aspects of the AB sequence, as is explained next. The base of a tetrahedron is formed by the center of three spheres on a layer A, its height goes from its base to the center of a sphere of layer B, and the last is resting on the void left by the three spheres on layer A. The height of the tetrahedron coincides with the separation distance, d(1 1 1), between two adjacent planes with Miller indices (1 1 1). Then, the thickness of a film with <sup>N</sup> layers is (<sup>N</sup> � 1)d(1 1 1) + <sup>D</sup>, with d(1 1 1) = ffiffiffiffiffiffiffiffiffi

λ<sup>c</sup> is extracted from the calculated R(λ) spectrum, noting that it moves to the blue as the thickness increases, stopping around 444 nm. Latter, we compare this stop value to the λ<sup>c</sup> of a 3D opal, and with experimental results. ΔBG is associated to the full width at the half maximum (FWHM) of the spectrum, and to estimate it, a Gaussian centered at the Bragg peak (the maximum of the R spectrum) was

Reflectance and transmittance of a thin film composed of N layers of 200 nm SiO2 spheres. The incident light

<sup>ð</sup>2=<sup>3</sup> <sup>p</sup> <sup>D</sup>.

adjacent dipoles is used, implying about 4600 dipoles per sphere.

Metallo-Dielectric Colloidal Films as SERS Substrate DOI: http://dx.doi.org/10.5772/intechopen.90313

absorption coefficient.

quantity is estimated as follows:

Figure 3.

97

comes normal to the surface and is unpolarized.

$$T = \mathbb{S}\_{11} \quad \text{for } (k\_{\text{xx}}k\_{0\text{x}} > 0), \tag{5}$$

where ksx and k0<sup>x</sup> are the wave vector components of the scattered light and of the incident light, respectively. Both of them are along the direction of the incident light. The S<sup>11</sup> value is related to Si elements by:

$$\mathbf{S\_{11}} = \frac{1}{2} \left( \left| \mathbf{S\_1} \right|^2 + \left| \mathbf{S\_2} \right|^2 + \left| \mathbf{S\_3} \right|^2 + \left| \mathbf{S\_4} \right|^2 \right). \tag{6}$$
