anatase TiO2 crystals with 28% {101} and 72% {001} facets [47]. The 9 nm blueshift of absorption edge means a larger bandgap, which is attributed to the different dominant facets exposed. The dependencies of bandgap and exposed surface were also found in other materials [48–50].
2.3.3 Surface Electric Field
For a metal, the surface electric field is oscillating when the light strikes the surface. Light, an electromagnetic wave, oscillates the electric field in a plane perpendicular magnetic field. The electric field's oscillatory patterns would cause a rippling wave pattern in the distribution of electrons, where the resonant oscillation of conduction electrons is called surface plasmon resonance (SPR). The SPR only exists in metals or other electrically conductive materials containing conduction electrons. When the size of the metal crystals shrinks to the nanoscale, which is smaller than the wavelength of the incident light, the surface plasmon is confined to a very small surface rather than the bulk material, known as localized surface plasmon resonance (LSPR). The LSPR frequency affects the light absorption and scattering of metal nanoparticles. How the LSPR frequency is affected by facets (shapes) of a nanoparticle is explained in a later section, but as a consequence, the color of metal nanoparticles will be changed, and it is sensitive to the shape of nanoparticles (with different facets exposed). Based on the Mie theory, it is possible to tune the LSPR spectra of Ag nanocrystals of different shapes, as shown in Figure 2.4 [51].
Figure 2.4 Calculated UV–visible extinction (black), absorption (red), and scattering spectra (blue) of Ag nanocrystals, illustrating the effect of shape on its spectral characteristics, including isotropic sphere (a), anisotropic cubes (b), tetrahedra (c), and octahedra (d), triangular plate (e) and circular disc (f).
Source: Wiley et al. 2006 [51]. Reproduced with permission of American Chemical Society.
(See online version for color figure).
For a faceted semiconductor, the surface electric field is a disparate situation. Besides the variation of the bandgap, the band edge position shifts as a function of different facets due to surface band bending. The different band edge positions provide varying redox potentials of the photogenerated electrons and holes, resulting in spatial separation of charge carriers and the built‐in electric field. In addition, selectively depositing a noble metal as cocatalysts on the surface facets can further enhance the strength of the built‐in electric field. When a single BiVO4 crystal enclosed by {010} and {011} facets was characterized by spatially resolved surface photovoltage spectroscopy (SRSPS), {011} facets exhibited a much higher signal intensity of surface photovoltage than {010} facet [52]. This phenomenon indicated a significant difference in surface band bending between BiVO4{011} and {010} facets. As a consequence, the different band bending will lead to the variation in the spatial distribution of the charge carriers and build an electric field between different facets. By changing the area ratio of (011)/(010) facets of BiVO4 crystal, the surface built‐in electric field varied as well. Such an intrinsic difference in the surface photovoltage between different facets can be further enhanced by selectively depositing cocatalysts, such as MnOx and Pt deposited on faceted BiVO4 crystal, as shown in Figure 2.5 [53].
Figure 2.5 (a) Scanning electron microscopy (SEM) image of a BiVO4 single crystal with Pt photodeposited on {010} facet and MnOx photodeposited on {011} facet. (b) Spatial distribution of the surface photovoltage signals. Pink and green colors correspond to holes and electrons separated toward the external surface, respectively. Schematic band diagrams across the border between the {011} and {010} facets of (c) a bare single BiVO4 photocatalyst particle and of (d) a single BiVO4 photocatalyst particle with MnOx cocatalyst selectively deposited at {011} facets (green line) and with MnOx and Pt nanoparticles selectively deposited at {011} and {010} facets, respectively (dashed pink line).
Source: Zhu et al. 2017 [53]. Reproduced with permission of American Chemical Society. (See online version for color figure.)
2.4 Effects of Facets Engineering
Each facet in a single crystal has different properties. However, combining anisotropic surface properties could dramatically alter the properties of the crystal, especially when the particle size is reduced to the nanoscale and the ratio of surface atoms/bulk atoms is no longer negligible.
2.4.1 Optical Properties
As mentioned previously, the surface electric field of a metal oscillates when the light strikes the surface. The oscillating electric field causes a rippling wave pattern in the spatial distribution of electrons. According to Lenz's law, the wave created by the surface plasmon opposes the electromagnetic wave of the incident light. The oscillating electrons absorb the energy of light and reemit the energy as the reflected light, due to which metals have shiny and reflective surfaces. However, when the particle size becomes very small, the surface plasmon is confined to a very small surface (i.e. LSPR). When the electron cloud is excited at one of the resonance frequencies, light absorption will become stronger. This is how LSPR frequency affects the light absorption of metal nanoparticles. The plasmon frequency is determined by electron density, dielectric constant, and effective mass of an electron. The well‐defined facets of a crystal form different shapes with more symmetries compared with spherical particles [54]. The surface charges tend to accumulate at edges and corners, which further promote surface polarization, i.e. the charge separation between mobile electrons and immobile atoms. Surface polarization determines the frequency and intensity of LSPR as it provides the main restoring force for electron oscillation. Large surface polarization reduces the restoring force, resulting in a redshift of resonance peak, and multiple distinct symmetries may induce several light absorption peaks [55]. Therefore, the same metal nanoparticles with different size and shape may exhibit different colors, indicating diverse light absorption.
The light absorption of semiconductors is quite different from that in metals due to the electronic band structure in semiconductors. Between the VB and CB of semiconductors, no electron states exist in this energy range called the bandgap. In some semiconductors, the minimal energy state of the CB (conduction band minimum, CBM) and the maximal energy state of the VB (valence band maximum, VBM) are situated in the same crystal momentum in the Brillouin zone (direct gap); in other semiconductors, they are not (indirect gap). There is a slight difference in light absorption between these two types of bandgap structure. But it is not necessary to discuss in this chapter. In general, light absorption of a semiconductor is associated with its bandgap. Semiconductors
