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

Oxide semiconductors have received much attention for potential use in optoelectronic applications such as transparent electrodes, transistors, and emitting devices. Recently, new functionalities of oxide semiconductors have been discovered such as localized surface plasmon resonances (LSPRs), which show highefficiency plasmon excitations in the infrared (IR) range using different structures such as nanorods, nanoparticles (NPs), and nanodots. In this chapter, we introduce optical properties of carrierand size-dependent LSPRs in oxide semiconductor NPs based on In2O3: Sn (ITO). In particular, systematic examinations of carrierand size-dependent LSPRs reveal the damping mechanisms on LSPR excitations of ITO NPs, which play an important role in determining excitation efficiency of LSPRs. Additionally, the control of carrier and size in the ITO NPs contribute toward improving solar-thermal shielding in the IR range. The high IR reflectance of assembled films of ITO NPs is due to three-dimensional plasmon coupling between the NPs, which is related to electron carriers and particle size of ITO NPs. This chapter provides new information concerning structural design when fabricating thermal-shielding materials based on LSPRs in oxide semiconductor NPs.


Introduction
Metals (such as Au and Ag) have been utilized for the majority of plasmonic materials in the visible range. Recently, oxide semiconductors have attracted much attention for use as potential new plasmonic materials. In particular, ZnO: Ga and In 2 O 3 : Sn (ITO) are known for use as transparent electrodes due to their metallic conductivity. These oxide semiconductors show surface plasmon resonances (SPRs) in the infrared (IR) range [1,2]. Propagated SPRs can be excited on metal surfaces using a prism-coupling technique such as a Kretschmann-type attenuated total reflection (ATR) system [3]. Our research group has investigated the optical properties of SPRs excited on ZnO: Ga and ITO film surfaces from the viewpoint of physical characteristics such as field strength and penetration depth [4][5][6]. On the other hand, subwavelength materials such as nanorods, nanoparticles (NPs), and nanodots are capable of supporting localized surface plasmon resonances (LSPRs), which can be directly excited by incident light in the absence of a prism-coupling method [7,8]. Above all, LSPRs confined to NPs can lead to light at the nanoscale 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 plasmonics and metamaterials.
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][13][14][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][17][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 based on oxide semiconductor NPs.
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 NPs for solar-thermal shielding.

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 (C 10 H 22 O 2 ) 3 In and (C 10 H 22 O 2 ) 4 Sn [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.

Carrier-dependent plasmon absorptions
Optical absorptions and TEM images of ITO NPs with different electron densities (n e ) 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 e was estimated from the absorption spectra by theoretical calculations. The following equation was used to derive absorption intensity (A) from the experimental data [20]: where k = 2π(ε d ) 1/2 ω/c with c representing the speed of light, ε d indicates the host dielectric constants of toluene, ε m (ω) is the particle dielectric function, and R is 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 Â 10 19 cm À3 , 5.7 Â 10 20 cm À3 , and 1.1 Â 10 21 cm À3 , respectively. Dot lines indicate theoretical calculations based on the modified Mie theory [19]. the particle radius. Furthermore, ε m (ω) employed the free-electron Drude term with frequency-dependent damping constant, Γ(ω), on the basis that ITO comprised free-electron carriers [20]: The plasma frequency (ω p ) is given by ω 2 p ¼ ne=ε ∞ ε 0 m * , where ε ∞ is the highfrequency dielectric constant, ε 0 is the vacuum permittivity, and m* is the effective electron mass. Fitted absorptions were used with parameter values of ε d = 2.03 (n = 1.426 refractive index of the solvent), ε ∞ = 3.8, and m* = 0.3 m 0 to estimate ε p (ω).The term Γ(ω) based on electron-impurity scattering can be described by the following relation [21]: where f(ω) can be described by f(ω) = [1 + exp{(ωÀΓ x )/σ}] À1 . Γ H and Γ L represent the high-frequency (ω = ∞) and low-frequency (ω = 0) damping, respectively. Γ X 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 Â 10 19 , 5.7 Â 10 20 , and 1.1 Â 20 21 cm À3 , respectively ( Figure 1). We summarized the LSPR resonant peak and absorption intensity as a function of n e (Figure 3(a)). The LSPR resonant peak gradually showed a redshift from the near-IR to mid-IR range with decreasing n e . Additionally, the absorption intensity decreased markedly with decreasing n e . No plasmon excitation was observed in the low n e region below 10 19 cm À3 . The Mott critical density (N c ) of ITO is estimated as N c = 6 Â 10 18 cm À3 (Figure 3(b)). Below the Mott critical density, the impurity band is not overlapped with the Fermi energy (E F ) level. ITO results in a band insulator. However, the E F level combined with the impurity band in the middle n e region from 10 19 to 10 20 cm À3 . At the high n e region above 10 20 cm À3 , the E F level is placed in a highest occupied state in the conduction band (CB). As a consequence, ITO 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.

Damping mechanism
The two types of damping processes that exist in plasmon excitations of metal NPs are (i) bulk damping and (ii) surface damping. Bulk damping (γ B ) is related to electron-electron (γ e-e ), electron-phonon (γ e-ph. ), and electron-impurity scattering (γ e-impurity ). These scattering components determine a mean free path (l m ) of a free electron. On the other hand, surface scattering is effective when a NP size is smaller than l m , which becomes the main damping process in NPs.
Surface scattering (γ s ) can be described by γ s = Av F /l SC for a small nanoparticle, where A is a material constant and v F is the Fermi velocity [v F = ħ/m * (3πn e ) 1/3 ]. The surface scattering length (l SC ) is defined by l SC = 4 V/S, where V is the volume and S is the surface area of the particle [20]. For our ITO NPs, l SC was calculated as 24 nm, which was longer than the l m of ITO ($10 nm) [22,23]. For ITO NPs, no surface scattering was effective because the l m of ITO was smaller than l SC . 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 Â 10 19 cm À3 ) and highest (1.1 Â 10 21 cm À3 ) n e values. For NPs with the lowest n e , a symmetric absorption spectrum was obtained, while an asymmetric spectrum was obtained for NPs with the highest n e . These spectral features were determined by Γ H and Γ L . Figure 4(b) shows the dependence of Γ H and Γ L on electron density. A difference in Γ H and Γ L values was found in the high n e region above 10 20 cm À3 . Electron-impurity scattering is reflected by Γ L , providing asymmetric LSPR features by broadening in the low photon energy regions. In contrast, the Γ L values ($70 meV) were the same as those of Γ H in the low n e region below 10 20 cm À3 , indicating that LSPRs were independent of electron-impurity scattering.
The carrier-dependent plasmon response is divided into two n e regions. Region-I comprises low n e below 10 20 cm À3 , 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 m = 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 e above 10 20 cm À3 , in which LSPR excitations become more effective with increasing l m , as a result of increased n e . The l m value of NPs with the highest n e 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 e region. In this work, the maximum lm in ITO NPs was 10.7 nm. Previous reports have detailed long l m 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 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 SnO 2 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.

Particle size and plasmon excitations
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 values of n e were approximately 10 21 cm À3 , and μ e ranged from 21 to 37 cm 2 /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]:   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 L and b L are represented by the following parameters, composed of the Riccati-Bessel functions ψ L and χ L [26]: Here, m ¼ñ=n m , whereñ ¼ n R þ in I is the complex refractive index of the metal and n m is the refractive index of the surrounding medium. Additionally, x = k m r, where r is the radius of the particle. It should be noted that k m = 2π/λ m 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 Â 10 21 cm À3 . 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.

Infrared applications for solar-thermal shielding 4.1 High reflections in the IR range
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 the plasmonic properties of assembled films of ITO NPs. To date, IR optical 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][28][29][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 through reflection properties.
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 importance of interparticle gaps for high IR reflectance.  shows reflectance spectra of ITO NP films with different electron densities. The assembled ITO NP films were deposited on IR-transparent CaF 2 substrates through a spin-coating technique. The spin-coating conditions comprised sequential centrifugation at (i) 800 rpm for 5 s, (ii) 2400 rpm for 30 s, and (iii) 800 rpm for 10 s. The fabricated NP films were then thermally treated at 150°C in air to evaporate the solvent. Reflectance was enhanced with increasing electron density and reached a value of ca. 0.6 in the NP film with n e = 1.1 Â 10 21 cm À3 . Additionally, reflectance was dependent on film thickness (Figure 8(b)). Reflectance gradually increased with increasing film thickness and was then saturated in film thicknesses above 200 nm. As a result, it is necessary to use NPs with high electron density in order to obtain NP films with high IR reflectance. Figure 9(a) shows reflectance spectra of ITO NP films with different particle sizes. Reflectance gradually increased with increasing particle size, which was dependent on NP film thickness (Figure 9(b)). That is, increasing in particle size contributed to obtain high IR reflectance. Highly efficient solar-thermal shielding played an important role in controlling electron density and particle size. We found that the high IR reflectance was closely related to plasmon coupling between the NPs in the NP films as follows. Figure 10(a) shows experimental and theoretical absorption spectra of ITO NPs dispersed in toluene. The theoretical data was simulated using the finite-difference time-domain (FDTD) method and was close to the experimental data. We observed the formation of a strong electric field (E-field) on the NP surface (inset of Figure 10(a)). The relationship between the E-field and photon energy was further investigated, as shown in Figure 10(b-d). The E-field on the NP surface increased with increasing photon energy. A high E-field was obtained at an LSPR peak position of 1.8 μm. The LSPRs of ITO NPs produced the strong E-field on the NP surface.

Electric field distributions
We evaluated the optical properties of ITO NP films from the viewpoint of electrodynamic simulations based on the finite-difference time-domain (FDTD) method ( Figure 11(a)). The modeled NP layer was assumed to have a hexagonally closepacked (HCP) structure with an interparticle distance (r) of 2 nm along the in-plane (x-y) and out-of-plane (y-z) directions (Figure 11(b and c)). The modeled sample was illuminated with light directed in the z direction from the air side. The E-field was parallel to the x direction. The refractive index (real part: 1.437) of capric acid was used for the medium between the NPs. The dielectric functions of the ITO NPs were obtained from the parameter fitting for the absorption spectra. Figure 11(a) shows the reflectance spectra of ITO NP layers with different particle sizes (D) of 10, 20, and  (a) Simulated reflectance spectra of ITO NP layers at different particle sizes (D). A number of NP layer (N) was set to N = 20 NP layers. (b) and (c) indicate structural diagrams of a simulated NP layers along the inplane (x-y) and out-of-plane (x-z) directions, respectively. The modeled structure was assumed to have a HCP structure with an interparticle distance (r) of 2 nm and was illuminated with light directed in the z direction from the air side. The E-field was parallel to the x direction. 36 nm. The number of the NP layer was set to the N = 20 NP layer. Reflectance clearly enhanced with increasing particle size, which appeared as a result of threedimensional assemblies of ITO NPs, and it was suggested theoretically that increasing particle size contributed to the reflective-type thermal shielding in the IR range.
Plasmon coupling between NPs produces large enhancements of E-fields at interparticle gaps. We typically investigated the E-field distributions at peak-II (0.60 eV) and peak-I (0.208 eV) for a 20 NP layer with D = 36 nm. Figure 12(a and b) shows SEM images of ITO NP films (D = 36 nm) along the in-plane and out-ofplane directions, revealing that the NPs had close-packed structures along both  Images of the E-field distributions and charge vectors at peak-I and peak-II along the x-z directions. Regions delimited by white circles were positioned in the respective bottom parts. An E-field was applied along the x direction. Light was incident along the z direction from the air side.
directions. Figure 13 shows the E-field distributions along the x-z directions. For peak-I, the E-field between the NPs was strongly localized along the x direction when an electric field of light was applied along this direction. In contrast, peak-II displays E-fields along the diagonal directions in the x-z plane in addition to those along the x direction. A difference in the E-field of peak-I and peak-II was clearly found. The FDTD simulations revealed that the two types of reflectance peaks had different mechanisms of plasmon excitations. Therefore, it was indicated that different E-field distributions between the NPs played an important role in producing the IR reflectance in the IR range.

Conclusion
Optical properties of carrier-and size-dependent LSPRs were investigated using dopant-controlled ITO NPs. From systematic correlations between LSPR excitations and electron density, plasmon damping of ITO NPs was closely related to electronimpurity scattering, which was effective with high n e values greater than 10 20 cm À3 . That is, the role of electron carriers in ITO NPs could enhance LSPRs with simultaneous damped plasmon excitations. Changes in particle size also affected the LSPRs in ITO NPs. Increasing particle size altered the magnitude and peak splitting of the resonant reflectance, which covered a wide IR range. As a result, the carrier and size control of ITO NPs led to high solar-thermal shielding. The origin of the high IR reflectance of ITO NP films was clarified by electrodynamic simulations (FDTD). We found that the E-field distributions between the NPs along the in-plane and outof-plane directions played key roles in producing the high IR reflectance. Control of electron carrier and particle size revealed important aspects that should be considered in the area of structural design when fabricating thermal-shielding materials.