2. Carriers and plasmon excitations

#### 2.1 Synthesis of ITO NPs

ITO NPs with different Sn contents were fabricated using the chemical thermolysis method with various initial ratios of precursor complexes (C10H22O2)3In and (C10H22O2)4Sn [19]. Indium and tin complexes were thermal heated at 300–350°C for 4 h in a reducing agent, and the mixture was then gradually cooled to room temperature. The resultant mixture produced a pale blue suspension and to which was then added excess ethanol to induce precipitation. Centrifugation and repeated washing were conducted four times using ethanol, which produced dried powders of ITO NPs with a pale blue color. Finally, the powder samples were dispersed in a nonpolar solvent of toluene. Electrophoresis analysis revealed a positive zeta potential of +31 meV for the NPs, which indicated the NPs had non-aggregated states in the solvent due to electrostatic repulsion between NPs. Particle surfaces of the NPs were terminated by organic ligands consisting of fatty acids, which contributed in spatial separation between NPs.

Surface Plasmons in Oxide Semiconductor Nanoparticles: Effect of Size and Carrier Density DOI: http://dx.doi.org/10.5772/intechopen.86999

#### 2.2 Carrier-dependent plasmon absorptions

Optical absorptions and TEM images of ITO NPs with different electron densities (ne) were examined (Figure 1). TEM images revealed that all NP sizes (D) were ca. 36 nm (Figure 2(a–c)). This indicates that the systematic change in the absorption spectra is related to the Sn content. Absorption measurements were performed using a Fourier-transform infrared (FT-IR) spectrometer. A value of n<sup>e</sup> was estimated from the absorption spectra by theoretical calculations. The following equation was used to derive absorption intensity (A) from the experimental data [20]:

$$A = 4\pi k R^3 \text{Im} \left\{ \frac{\varepsilon\_m(\alpha) - \varepsilon\_d}{\varepsilon\_m(\alpha) + 2\varepsilon\_d} \right\} \tag{1}$$

where k = 2π(εd) 1/2ω/c with c representing the speed of light, ε<sup>d</sup> indicates the host dielectric constants of toluene, εm(ω) is the particle dielectric function, and R is

Figure 1.

when confining the collective oscillations of free electrons into NPs. This LSPR effect further provides strong electric fields (E-fields) on NP surfaces, which contribute to surface-enhanced optical spectroscopy [9]. For example, assembled films consisting of ITO NPs have demonstrated optical enhancements of near-IR luminescence and absorption in the IR range [10, 11]. Therefore, optical studies

concerning oxide semiconductor NPs can break new research ground in the area of

An understanding of plasmon damping is very important in order to achieve high-efficiency LSPRs. A number of plasmonic studies of metal NPs have been devoted to investigating the damping processes of LSPRs. For metal NPs, there are two main damping processes, comprising (i) size-dependent surface scattering and (ii) electronic structure-related inter- and intraband damping [12–15]. The damping processes are closely related to the physical properties of the metals. Therefore, understanding of the damping processes of LSPRs in oxide semiconductor NPs is also important for the control of optical properties. Oxide semiconductor NPs are useful plasmonic materials since their LSPR wavelengths can be widely tuned by electron density in addition to particle size [16–18]. Carrier control of LSPRs indicates that oxide semiconductors have an additional means of tuning the optical properties in a manner that is not as readily available for metal NPs. In particular, carrier-dependent damping is a specific feature of the plasmonic response in oxide semiconductor NPs. Precise elucidation of the carrier-dependent damping process including structural size is required for the optical design of plasmonic materials

The purpose of this chapter is to report on the light interactions of size- and carrier-controlled ITO NPs and to discuss their plasmonic applications in the IR range. We introduce size- and carrier-dependent plasmonic responses and provide information for the physical interpretation of optical spectra. A rigorous approach to the analysis of the optical properties allows us to show a quantitative assessment of the electronic properties in ITO NPs. The employments of Mie theoretical calculations, which can describe well the optical properties of metal NPs, are validated in terms of ITO NPs. Finally, we discuss the optical properties assembled films of ITO

ITO NPs with different Sn contents were fabricated using the chemical

(C10H22O2)3In and (C10H22O2)4Sn [19]. Indium and tin complexes were thermal heated at 300–350°C for 4 h in a reducing agent, and the mixture was then gradually cooled to room temperature. The resultant mixture produced a pale blue suspension and to which was then added excess ethanol to induce precipitation. Centrifugation and repeated washing were conducted four times using ethanol, which produced dried powders of ITO NPs with a pale blue color. Finally, the powder samples were dispersed in a nonpolar solvent of toluene. Electrophoresis analysis revealed a positive zeta potential of +31 meV for the NPs, which indicated the NPs had non-aggregated states in the solvent due to electrostatic repulsion between NPs. Particle surfaces of the NPs were terminated by organic ligands consisting of fatty acids, which contributed in spatial separation

thermolysis method with various initial ratios of precursor complexes

plasmonics and metamaterials.

Nanocrystalline Materials

based on oxide semiconductor NPs.

NPs for solar-thermal shielding.

2.1 Synthesis of ITO NPs

between NPs.

56

2. Carriers and plasmon excitations

Absorption spectra of ITO NPs with different electron densities. Doping with Sn contents of 0.02, 1, and 5% into the NPs' induced electron density of 6.3 � 1019 cm�<sup>3</sup> , 5.7 � 1020 cm�<sup>3</sup> , and 1.1 � <sup>10</sup><sup>21</sup> cm�<sup>3</sup> , respectively. Dot lines indicate theoretical calculations based on the modified Mie theory [19].

Figure 2.

TEM images of ITO NPs with electron densities of (a) 6.3 � 1019 cm�<sup>3</sup> , (b) 5.7 � 1020 cm�<sup>3</sup> , and (c) 1.1 � <sup>10</sup><sup>21</sup> cm�<sup>3</sup> [19].

the particle radius. Furthermore, εm(ω) employed the free-electron Drude term with frequency-dependent damping constant, Γ(ω), on the basis that ITO comprised free-electron carriers [20]:

$$\varepsilon\_m(\boldsymbol{\alpha}) = \mathbf{1} - \frac{\boldsymbol{\alpha}\_p^2}{\boldsymbol{\alpha}(\boldsymbol{\alpha} + i\Gamma)} \tag{2}$$

shows metallic behavior. These results indicated that a large amount of free electrons were required to excite highly efficient plasmon excitations. ITO NPs were

Surface Plasmons in Oxide Semiconductor Nanoparticles: Effect of Size and Carrier Density

The two types of damping processes that exist in plasmon excitations of metal NPs are (i) bulk damping and (ii) surface damping. Bulk damping (γB) is related to electron-electron (γe-e), electron-phonon (γe-ph.), and electron-impurity scattering (γe-impurity). These scattering components determine a mean free path (lm) of a free electron. On the other hand, surface scattering is effective when a NP size is smaller

Surface scattering (γs) can be described by γ<sup>s</sup> = AvF/lSC for a small nanoparticle,

surface scattering length (lSC) is defined by lSC = 4 V/S, where V is the volume and S is the surface area of the particle [20]. For our ITO NPs, lSC was calculated as 24 nm, which was longer than the l<sup>m</sup> of ITO (10 nm) [22, 23]. For ITO NPs, no surface scattering was effective because the l<sup>m</sup> of ITO was smaller than lSC. Therefore, it is

Metallic conductivity of ITO NPs is obtained by doping with impurity atoms, suggesting that ITO NPs involve electron-impurity scattering in bulk damping. The spectral features of ITO NPs could be fitted using Mie theory with frequencydependent damping parameter Γ(ω). Figure 4(a) shows absorption spectra of ITO

NPs with the lowest ne, a symmetric absorption spectrum was obtained, while an asymmetric spectrum was obtained for NPs with the highest ne. These spectral features were determined by Γ<sup>H</sup> and ΓL. Figure 4(b) shows the dependence of Γ<sup>H</sup> and Γ<sup>L</sup> on electron density. A difference in Γ<sup>H</sup> and Γ<sup>L</sup> values was found in the high

ing asymmetric LSPR features by broadening in the low photon energy regions. In contrast, the Γ<sup>L</sup> values (70 meV) were the same as those of Γ<sup>H</sup> in the low n<sup>e</sup> region

The carrier-dependent plasmon response is divided into two n<sup>e</sup> regions. Region-I

NPs is not always disturbed by electron-impurity scattering. The spectral features of LSPRs comprise narrow line-widths and symmetric line-shapes. However, absorption intensity is small (Figure 3(a)) since a short mean free path length (l<sup>m</sup> = 3–4 nm) determines the coherence of electron oscillations in the NPs. This situation is due to

insufficient conduction paths. Region-II comprises high n<sup>e</sup> above 10<sup>20</sup> cm<sup>3</sup>

be required to obtain high-efficiency LSPR excitations in the IR range.

which LSPR excitations become more effective with increasing lm, as a result of increased ne. The l<sup>m</sup> value of NPs with the highest n<sup>e</sup> was estimated as 10.7 nm. However, LSPR excitations are influenced by electron-impurity scattering, which

Degenerated metals on doped oxide semiconductors are generally realized by extrinsic and/or intrinsic dopants. However, the carrier screening effect from background cations is weak in contrast to metals with a short screening length (comprising several angstroms) [24]. Electron-impurity scattering dominates the optical properties of LSPRs in the high n<sup>e</sup> region. In this work, the maximum lm in ITO NPs was 10.7 nm. Previous reports have detailed long l<sup>m</sup> values from 14 to 16 nm on ITO films [22, 23]. Control of crystallinity and impurities in ITO NPs will

) and highest (1.1 <sup>10</sup><sup>21</sup> cm<sup>3</sup>

, indicating that LSPRs were independent of electron-impurity

. Electron-impurity scattering is reflected by ΓL, provid-

, in which coherence of electron oscillation in ITO

(3πne)

) n<sup>e</sup> values. For

, in

1/3]. The

suitable for plasmonic materials in the near-IR range.

DOI: http://dx.doi.org/10.5772/intechopen.86999

than lm, which becomes the main damping process in NPs.

considered that ITO NPs are mainly related to bulk damping.

where A is a material constant and v<sup>F</sup> is the Fermi velocity [v<sup>F</sup> = ħ/m\*

2.3 Damping mechanism

NPs with lowest (5.5 <sup>10</sup><sup>19</sup> cm<sup>3</sup>

comprises low n<sup>e</sup> below 10<sup>20</sup> cm<sup>3</sup>

generated the asymmetric line-shapes.

n<sup>e</sup> region above 10<sup>20</sup> cm<sup>3</sup>

below 10<sup>20</sup> cm<sup>3</sup>

scattering.

59

The plasma frequency (ωp) is given by ω<sup>2</sup> <sup>p</sup> <sup>¼</sup> ne=ε∞ε0m<sup>∗</sup> , where <sup>ε</sup><sup>∞</sup> is the highfrequency dielectric constant, ε<sup>0</sup> is the vacuum permittivity, and m\* is the effective electron mass. Fitted absorptions were used with parameter values of ε<sup>d</sup> = 2.03 (n = 1.426 refractive index of the solvent), ε<sup>∞</sup> = 3.8, and m\* = 0.3 m0 to estimate εp(ω).The term Γ(ω) based on electron-impurity scattering can be described by the following relation [21]:

$$
\Gamma(\alpha) = f(\alpha)\Gamma\_L + [\mathbf{1} - f(\alpha)]\Gamma\_H \left(\frac{\alpha}{\Gamma\_H}\right)^{-3/2} \tag{3}
$$

where <sup>f</sup>(ω) can be described by <sup>f</sup>(ω) = [1 + exp{(ω�Γx)/σ}]�<sup>1</sup> . Γ<sup>H</sup> and Γ<sup>L</sup> represent the high-frequency (ω = ∞) and low-frequency (ω = 0) damping, respectively. Γ<sup>X</sup> and σ represent the change-over frequency and width of the function, respectively.

Calculated absorption spectra were very close to the experimental data. ITO NPs doped with Sn content of 0.02, 1, or 5% provided electron density of 6.3 � <sup>10</sup>19, 5.7 � <sup>10</sup>20, and 1.1 � <sup>20</sup><sup>21</sup> cm�<sup>3</sup> , respectively (Figure 1). We summarized the LSPR resonant peak and absorption intensity as a function of n<sup>e</sup> (Figure 3(a)). The LSPR resonant peak gradually showed a redshift from the near-IR to mid-IR range with decreasing ne. Additionally, the absorption intensity decreased markedly with decreasing ne. No plasmon excitation was observed in the low n<sup>e</sup> region below 10<sup>19</sup> cm�<sup>3</sup> . The Mott critical density (Nc) of ITO is estimated as <sup>N</sup><sup>c</sup> = 6 � <sup>10</sup><sup>18</sup> cm�<sup>3</sup> (Figure 3(b)). Below the Mott critical density, the impurity band is not overlapped with the Fermi energy (EF) level. ITO results in a band insulator.

However, the E<sup>F</sup> level combined with the impurity band in the middle n<sup>e</sup> region from 10<sup>19</sup> to 10<sup>20</sup> cm�<sup>3</sup> . At the high n<sup>e</sup> region above 10<sup>20</sup> cm�<sup>3</sup> , the E<sup>F</sup> level is placed in a highest occupied state in the conduction band (CB). As a consequence, ITO

#### Figure 3.

(a) LSPR resonant peak and absorption intensity of ITO NPs as a function of electron density. (b) a schematic picture of electronic structures of ITO with different ranges of electron density.

shows metallic behavior. These results indicated that a large amount of free electrons were required to excite highly efficient plasmon excitations. ITO NPs were suitable for plasmonic materials in the near-IR range.

## 2.3 Damping mechanism

the particle radius. Furthermore, εm(ω) employed the free-electron Drude term with frequency-dependent damping constant, Γ(ω), on the basis that ITO com-

<sup>ε</sup>mð Þ¼ <sup>ω</sup> <sup>1</sup> � <sup>ω</sup><sup>2</sup>

frequency dielectric constant, ε<sup>0</sup> is the vacuum permittivity, and m\* is the effective electron mass. Fitted absorptions were used with parameter values of ε<sup>d</sup> = 2.03 (n = 1.426 refractive index of the solvent), ε<sup>∞</sup> = 3.8, and m\* = 0.3 m0 to estimate εp(ω).The term Γ(ω) based on electron-impurity scattering can be described by the

represent the high-frequency (ω = ∞) and low-frequency (ω = 0) damping, respectively. Γ<sup>X</sup> and σ represent the change-over frequency and width of the function,

Calculated absorption spectra were very close to the experimental data. ITO NPs doped with Sn content of 0.02, 1, or 5% provided electron density of 6.3 � <sup>10</sup>19,

. The Mott critical density (Nc) of ITO is estimated as <sup>N</sup><sup>c</sup> = 6 � <sup>10</sup><sup>18</sup> cm�<sup>3</sup>

resonant peak and absorption intensity as a function of n<sup>e</sup> (Figure 3(a)). The LSPR resonant peak gradually showed a redshift from the near-IR to mid-IR range with decreasing ne. Additionally, the absorption intensity decreased markedly with decreasing ne. No plasmon excitation was observed in the low n<sup>e</sup> region below

(Figure 3(b)). Below the Mott critical density, the impurity band is not overlapped

However, the E<sup>F</sup> level combined with the impurity band in the middle n<sup>e</sup> region

. At the high n<sup>e</sup> region above 10<sup>20</sup> cm�<sup>3</sup>

(a) LSPR resonant peak and absorption intensity of ITO NPs as a function of electron density. (b) a schematic

picture of electronic structures of ITO with different ranges of electron density.

in a highest occupied state in the conduction band (CB). As a consequence, ITO

Γð Þ¼ ω fð Þ ω Γ<sup>L</sup> þ ½ � 1 � fð Þ ω Γ<sup>H</sup>

where <sup>f</sup>(ω) can be described by <sup>f</sup>(ω) = [1 + exp{(ω�Γx)/σ}]�<sup>1</sup>

with the Fermi energy (EF) level. ITO results in a band insulator.

p

ω Γ<sup>H</sup> �3=<sup>2</sup>

, respectively (Figure 1). We summarized the LSPR

ω ωð Þ <sup>þ</sup> <sup>i</sup><sup>Γ</sup> (2)

<sup>p</sup> <sup>¼</sup> ne=ε∞ε0m<sup>∗</sup> , where <sup>ε</sup><sup>∞</sup> is the high-

(3)

. Γ<sup>H</sup> and Γ<sup>L</sup>

, the E<sup>F</sup> level is placed

prised free-electron carriers [20]:

Nanocrystalline Materials

following relation [21]:

5.7 � <sup>10</sup>20, and 1.1 � <sup>20</sup><sup>21</sup> cm�<sup>3</sup>

respectively.

10<sup>19</sup> cm�<sup>3</sup>

Figure 3.

58

from 10<sup>19</sup> to 10<sup>20</sup> cm�<sup>3</sup>

The plasma frequency (ωp) is given by ω<sup>2</sup>

The two types of damping processes that exist in plasmon excitations of metal NPs are (i) bulk damping and (ii) surface damping. Bulk damping (γB) is related to electron-electron (γe-e), electron-phonon (γe-ph.), and electron-impurity scattering (γe-impurity). These scattering components determine a mean free path (lm) of a free electron. On the other hand, surface scattering is effective when a NP size is smaller than lm, which becomes the main damping process in NPs.

Surface scattering (γs) can be described by γ<sup>s</sup> = AvF/lSC for a small nanoparticle, where A is a material constant and v<sup>F</sup> is the Fermi velocity [v<sup>F</sup> = ħ/m\* (3πne) 1/3]. The surface scattering length (lSC) is defined by lSC = 4 V/S, where V is the volume and S is the surface area of the particle [20]. For our ITO NPs, lSC was calculated as 24 nm, which was longer than the l<sup>m</sup> of ITO (10 nm) [22, 23]. For ITO NPs, no surface scattering was effective because the l<sup>m</sup> of ITO was smaller than lSC. Therefore, it is considered that ITO NPs are mainly related to bulk damping.

Metallic conductivity of ITO NPs is obtained by doping with impurity atoms, suggesting that ITO NPs involve electron-impurity scattering in bulk damping. The spectral features of ITO NPs could be fitted using Mie theory with frequencydependent damping parameter Γ(ω). Figure 4(a) shows absorption spectra of ITO NPs with lowest (5.5 <sup>10</sup><sup>19</sup> cm<sup>3</sup> ) and highest (1.1 <sup>10</sup><sup>21</sup> cm<sup>3</sup> ) n<sup>e</sup> values. For NPs with the lowest ne, a symmetric absorption spectrum was obtained, while an asymmetric spectrum was obtained for NPs with the highest ne. These spectral features were determined by Γ<sup>H</sup> and ΓL. Figure 4(b) shows the dependence of Γ<sup>H</sup> and Γ<sup>L</sup> on electron density. A difference in Γ<sup>H</sup> and Γ<sup>L</sup> values was found in the high n<sup>e</sup> region above 10<sup>20</sup> cm<sup>3</sup> . Electron-impurity scattering is reflected by ΓL, providing asymmetric LSPR features by broadening in the low photon energy regions. In contrast, the Γ<sup>L</sup> values (70 meV) were the same as those of Γ<sup>H</sup> in the low n<sup>e</sup> region below 10<sup>20</sup> cm<sup>3</sup> , indicating that LSPRs were independent of electron-impurity scattering.

The carrier-dependent plasmon response is divided into two n<sup>e</sup> regions. Region-I comprises low n<sup>e</sup> below 10<sup>20</sup> cm<sup>3</sup> , in which coherence of electron oscillation in ITO NPs is not always disturbed by electron-impurity scattering. The spectral features of LSPRs comprise narrow line-widths and symmetric line-shapes. However, absorption intensity is small (Figure 3(a)) since a short mean free path length (l<sup>m</sup> = 3–4 nm) determines the coherence of electron oscillations in the NPs. This situation is due to insufficient conduction paths. Region-II comprises high n<sup>e</sup> above 10<sup>20</sup> cm<sup>3</sup> , in which LSPR excitations become more effective with increasing lm, as a result of increased ne. The l<sup>m</sup> value of NPs with the highest n<sup>e</sup> was estimated as 10.7 nm. However, LSPR excitations are influenced by electron-impurity scattering, which generated the asymmetric line-shapes.

Degenerated metals on doped oxide semiconductors are generally realized by extrinsic and/or intrinsic dopants. However, the carrier screening effect from background cations is weak in contrast to metals with a short screening length (comprising several angstroms) [24]. Electron-impurity scattering dominates the optical properties of LSPRs in the high n<sup>e</sup> region. In this work, the maximum lm in ITO NPs was 10.7 nm. Previous reports have detailed long l<sup>m</sup> values from 14 to 16 nm on ITO films [22, 23]. Control of crystallinity and impurities in ITO NPs will be required to obtain high-efficiency LSPR excitations in the IR range.

Figure 4.

(a) Absorption spectra of ITO NPs with ne values of 5.5 1019 and 1.1 1021 cm<sup>3</sup> . (b) Dependence of Γ<sup>H</sup> (●) and Γ<sup>L</sup> (○) on electron density. (c) Mobility (μe) as a function of electron density. The μ<sup>e</sup> (black dots) are compared with those obtained using ionized impurity scattering (IIS) process (black line).

values of n<sup>e</sup> were approximately 1021 cm<sup>3</sup>

indicates a line-width of the (222) peak [25].

DOI: http://dx.doi.org/10.5772/intechopen.86999

size effects of LSPRs in metal NPs as follows.

independent of particle size.

Figure 5.

Figure 6.

lowing relations [26]:

61

The broadening of the absorption spectra was related to the quality factor (Q-factor) of the plasmonic resonance defined by the ratio of peak energy to spectral linewidth of the LSPR peak. This factor provided a good indication of weak electronic damping and efficient E-field generation. Q-factor values of LSPRs with D = 10, 20, and 36 nm NPs were 2.4, 3.3, and 4.5 respectively. The increase in particle size is expected for strong E-field enhancement on the NP surfaces. It was indicated that the Q-factor values in the LSPR peaks were attributed to the electronic and crystalline properties. On the other hand, the LSPR peak positions were

TEM images of ITO NPs with D = 10 nm (a), 20 nm (b), and 36 nm (c) [25].

(a) Size distributions of ITO NPs with particle sizes (D) of 10, 20, and 36 nm. Inset images show TEM images of ITO NPs with different particle sizes. (b) XRD 2q-q pattern of ITO NPs with D = 10, 20, and 36 nm. Δ(2θ)

Surface Plasmons in Oxide Semiconductor Nanoparticles: Effect of Size and Carrier Density

The peak positions of LPRs generally depend on the particle size in the case of metal NPs. The size-dependent absorption spectra of spherical NPs can be calculated precisely using the full Mie equations. These equations can describe well the

An analytical solution to Maxwell's equations describes the extinction and scattering of light by spherical particles. The electromagnetic field produced by a plane wave incident on a homogeneous conducting sphere can be expressed by the fol-

, and μ<sup>e</sup> ranged from 21 to 37 cm<sup>2</sup>

/V.s.

#### 3. Particle size and plasmon excitations

Figure 5(a) shows the size distribution of ITO NPs, revealing that size distribution gradually increased with increasing particle size (D): D = 10 2.2 nm, 20 3.5 nm, and 36 4.3 nm. Figure 6 shows TEM results of the dependency of NPs on particle size. In particular, NPs with D = 36 nm showed well-developed facet surfaces, and NPs were clearly separated from one another due to the presence of organic ligands formed on the NP surfaces. All NP samples showed broad peak characteristic of colloid NPs with a crystalline nature (Figure 5(b)). Patterns were similar to those of standard cubic bixbyite, which had no discernible SnO or SnO2 peak. Besides, the line-width of the (222) peak, Δ(2θ), was narrower for the NPs with D = 36 nm than D = 10 nm. These results reflected differences in crystallinity, size, defects, and strain in the NPs.

The absorption spectra of the NPs with different particle sizes are shown in Figure 7(a). Based on the Mie theory with frequency-dependent damping, the Surface Plasmons in Oxide Semiconductor Nanoparticles: Effect of Size and Carrier Density DOI: http://dx.doi.org/10.5772/intechopen.86999

#### Figure 5.

(a) Size distributions of ITO NPs with particle sizes (D) of 10, 20, and 36 nm. Inset images show TEM images of ITO NPs with different particle sizes. (b) XRD 2q-q pattern of ITO NPs with D = 10, 20, and 36 nm. Δ(2θ) indicates a line-width of the (222) peak [25].

Figure 6. TEM images of ITO NPs with D = 10 nm (a), 20 nm (b), and 36 nm (c) [25].

values of n<sup>e</sup> were approximately 1021 cm<sup>3</sup> , and μ<sup>e</sup> ranged from 21 to 37 cm<sup>2</sup> /V.s. The broadening of the absorption spectra was related to the quality factor (Q-factor) of the plasmonic resonance defined by the ratio of peak energy to spectral linewidth of the LSPR peak. This factor provided a good indication of weak electronic damping and efficient E-field generation. Q-factor values of LSPRs with D = 10, 20, and 36 nm NPs were 2.4, 3.3, and 4.5 respectively. The increase in particle size is expected for strong E-field enhancement on the NP surfaces. It was indicated that the Q-factor values in the LSPR peaks were attributed to the electronic and crystalline properties. On the other hand, the LSPR peak positions were independent of particle size.

The peak positions of LPRs generally depend on the particle size in the case of metal NPs. The size-dependent absorption spectra of spherical NPs can be calculated precisely using the full Mie equations. These equations can describe well the size effects of LSPRs in metal NPs as follows.

An analytical solution to Maxwell's equations describes the extinction and scattering of light by spherical particles. The electromagnetic field produced by a plane wave incident on a homogeneous conducting sphere can be expressed by the following relations [26]:

3. Particle size and plasmon excitations

Figure 4.

Nanocrystalline Materials

60

size, defects, and strain in the NPs.

Figure 5(a) shows the size distribution of ITO NPs, revealing that size distribu-

(●) and Γ<sup>L</sup> (○) on electron density. (c) Mobility (μe) as a function of electron density. The μ<sup>e</sup> (black dots) are

. (b) Dependence of Γ<sup>H</sup>

The absorption spectra of the NPs with different particle sizes are shown in Figure 7(a). Based on the Mie theory with frequency-dependent damping, the

tion gradually increased with increasing particle size (D): D = 10 2.2 nm, 20 3.5 nm, and 36 4.3 nm. Figure 6 shows TEM results of the dependency of NPs on particle size. In particular, NPs with D = 36 nm showed well-developed facet surfaces, and NPs were clearly separated from one another due to the presence of organic ligands formed on the NP surfaces. All NP samples showed broad peak characteristic of colloid NPs with a crystalline nature (Figure 5(b)). Patterns were similar to those of standard cubic bixbyite, which had no discernible SnO or SnO2 peak. Besides, the line-width of the (222) peak, Δ(2θ), was narrower for the NPs with D = 36 nm than D = 10 nm. These results reflected differences in crystallinity,

(a) Absorption spectra of ITO NPs with ne values of 5.5 1019 and 1.1 1021 cm<sup>3</sup>

compared with those obtained using ionized impurity scattering (IIS) process (black line).

$$\sigma\_{ext} = \frac{2\rho}{\left|k\right|^2} \sum\_{l=1}^{m} (2L+1) \left[\text{Re}(a\_L + b\_L)\right] \tag{4}$$

4. Infrared applications for solar-thermal shielding

Recently, plasmonic properties on oxide semiconductors have attracted much attention in the area of solar-thermal shielding. The purpose of our study is to apply

responses have been investigated with regard to transmittance and extinction spectra of composites and films using oxide semiconductor NPs. IR shielding properties by transmittance and absorption properties have mainly been discussed [27–30]. Reports concerning reflective performances in assemblies of NPs have yet to appear in spite of the desire for thermal shielding to cut IR radiation, not by absorption, but

Assemblies of Ag and Au NPs can produce high E-fields through plasmon coupling between NPs in the visible range and are utilized in surface-enhanced spectroscopy [31, 32]. The high E-fields localized between NPs are very sensitive to interparticle gaps [33]. A gap length down to distances less than the size of a NP causes remarkable enhancements in E-fields. Surfactant- and additive-treated NPs are effective strategies that can be employed to obtain small interparticle gaps between NPs, which can be developed into one-, two-, and three-dimensional assemblies of NPs [34]. In particular, optical applications based on NPs have the benefit of large-area fabrications with lower costs to make NP assemblies attractive for industrial development. In this section, we report on the plasmonic properties of assembled films comprising ITO NPs (ITO NP films) and their solar-thermal applications in the IR range [35]. Both experimental and theoretical approaches were employed in an effort to understand the plasmonic properties of the NP films. The IR reflectance of the NP films was analyzed on the basis of variations in particle size and electron density. The investigation focused in particular on E-field interactions in order to determine how the NP films affected high IR reflectance. This behavior is discussed in terms of the physical concept of plasmonic hybridization, which further clarified the impor-

the plasmonic properties of assembled films of ITO NPs. To date, IR optical

Surface Plasmons in Oxide Semiconductor Nanoparticles: Effect of Size and Carrier Density

4.1 High reflections in the IR range

DOI: http://dx.doi.org/10.5772/intechopen.86999

through reflection properties.

Figure 8.

63

films with different electron densities.

tance of interparticle gaps for high IR reflectance.

(a) Reflectance spectra of ITO NP films with different electron densities of 1.1 <sup>10</sup><sup>21</sup> cm<sup>3</sup> (○), 8.7 <sup>10</sup><sup>19</sup> cm<sup>3</sup> (□), and <sup>&</sup>lt; 1019 cm<sup>3</sup> (Δ). (b) Reflectance as a function of NP film thickness of ITO NP

where k is the incoming wave vector and L are integers representing the dipole, quadrupole, and higher multipoles of the scattering. In the above equations, a<sup>L</sup> and b<sup>L</sup> are represented by the following parameters, composed of the Riccati-Bessel functions ψ<sup>L</sup> and χ<sup>L</sup> [26]:

$$b\_L = \frac{\left\|\boldsymbol{\nu}\_L(m\boldsymbol{\kappa})\boldsymbol{\nu}\_L'(\boldsymbol{\kappa}) - m\,\boldsymbol{\nu}\_L'(m\boldsymbol{\kappa})\boldsymbol{\nu}\_L(\boldsymbol{\kappa})}{\left\|\boldsymbol{\nu}\_L(m\boldsymbol{\kappa})\boldsymbol{\chi}\_L'(\boldsymbol{\kappa}) - m\,\boldsymbol{\nu}\_L'(m\boldsymbol{\kappa})\boldsymbol{\chi}\_L(\boldsymbol{\kappa})}\right\|}\tag{5}$$

$$a\_L = \frac{m\,\psi\_L(m\mathbf{x})\psi\_L'(\mathbf{x}) - \psi\_L'(m\mathbf{x})\psi\_L(\mathbf{x})}{m\,\psi\_L(m\mathbf{x})\,\mathcal{X}\_L'(\mathbf{x}) - \psi\_L'(m\mathbf{x})\mathcal{X}\_L(\mathbf{x})} \tag{6}$$

Here, m ¼ n~=nm, where n~ ¼ nR þ inI is the complex refractive index of the metal and n<sup>m</sup> is the refractive index of the surrounding medium. Additionally, x = kmr, where r is the radius of the particle. It should be noted that k<sup>m</sup> = 2π/λ<sup>m</sup> is defined as the wavenumber in the medium rather than the vacuum wavenumber. Peak positions of absorption spectra of ITO NPs were estimated using the full Mie theory (black line in Figure 7(b)). The dielectric constants were taken from the ellipsometric data of an ITO film with an electron density of 1.0 � <sup>10</sup><sup>21</sup> cm�<sup>3</sup> . The estimated peak positions remained almost unchanged with particle sizes below 120 nm and then slightly redshifted to longer wavelengths with particle sizes above 120 nm. That is, ITO NPs with particle sizes below 40 nm had no high-order plasmon mode and were mainly dominated by light absorptions. These results differed largely from those of metal NPs. LSPR properties of ITO NPs could be fully described using Mie theory in the quasi-static limit.

#### Figure 7.

(a) Absorption spectra of ITO NPs with different sizes comprising (a) 10 nm, (b) 20 nm, and (c) 36 nm. (d) LSPR peak energy as a function of particle size. A black line represents using Eqs. (4)–(6) [25].
