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Anisotropic electrical properties of surfaces are logically attributed to the anisotropy of the crystal lattice, which determines the different atomic arrangements and configurations depending on exposed facets. Work function is the minimum energy for valence electrons in the solid to overcome in order to exit into the vacuum [42], which can be defined as

where for elemental metals, E_F is the potential energy of the electrons at the top of the valence band (VB) called the Fermi level, −e is the charge of an electron, and ϕ is the electrostatic potential in vacuum. For elemental metals, work function highly depends on the crystallographic orientation of the surface, as atomic density and electron charge density vary across different facets. The difference of work function between two surfaces of the same metal in different orientation can reach up to 1 eV [43]. For example, work functions of tungsten W{001} facet, W{112} facet, and W{111} facet are 4.56 eV, 4.69 eV, and 4.39 eV, respectively [44]. Work function of polycrystalline Ag is 4.26 eV, but work functions of Ag{100} facet, Ag{110} facet, and Ag{111} facet are 4.64 eV, 4.52 eV, and 4.74 eV, respectively [45]. Furthermore, surface roughness and particle size also have a profound impact on work function.

The electronic structure of semiconductors is different from that of metals because of a bandgap between the conduction band (CB) and the VB. According to the band theory, when a large number of identical atoms assemble to form a solid, the atomic orbitals with discrete energy levels will overlap. Each atomic orbital will split into discrete molecular orbitals with different energies, due to the Pauli exclusion principles stating that it is impossible for two electrons in the solid to have the same values of the four quantum numbers. For example, the VB of TiO₂ is composed of O 2p orbitals, while the CB is composed of Ti 3d orbitals [46]. In the bulk of TiO₂ crystals, no matter in anatase or rutile, there are numerous TiO₆ octahedron units connected to their neighbors by sharing corners and edges in different ways. But at the surface, this periodic arrangement terminates, leading to variation in the coordination of Ti and O atoms. It is reasonable to deduce that the band structure at the surface is more or less different from the band structure in the bulk. A blueshift of light absorption edge was found when comparing the nanosized anatase TiO₂ crystals with 82% {101} and 18% {001} facets with the micrometer‐sized 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].