Surface Potential Barrier Morphology

The SPB experienced by LEED incident electrons traversing the surface region contains two parts [25]  

The shape and the saturation degree of the SPB depend on the surface atomic valence states [26], but the height of the SPB approaches to the muffin-tin inner potential constant of atoms inside the solid, Vq [27]. The real (elastic) and imaginary (inelastic) parts of the SPB take the following forms [27, 28]  

The gradient of the ReV(r) relates to the intensity of the electric field c(r) V[Rey(r)] = —s(r). If p(r) — 0, then the ReV(r) corresponds to a conservative field in which the moving electrons will suffer no energy loss and the spatial variation in the inelastic potential ImV(r) p r) = 0. The ReV(z) transforms at z = Zo from the pseudo-Fermi z function to the l/(z—zo)- lominated classical image potential. Therefore, 

The origin of the image plane, zo, acts as the boundary of the surface region occupied by electrons. If zo varies with the surface coordinates, then the zo(.r, y) provides a contour of the spatial electron distribution, which should be similar to that plotted using STM imaging [29]. 

At the dipole site, zim Zom - -3.425, a a while in the atomic vacancy or ion positions, zim zom — 1-75 Bohr radii due to the strong localization of electrons at the surface. The SPB increases its degree of saturation with the outward shift of the image plane zo- This means that formation of metal dipoles shifts the electron clouds outwardly and enhances the density of the shifted electronic clouds. 

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Chemisorption roughens the surface potential barrier and morphology by formation of ions, dipoles, and missing vacancies. 

In the phase-space treatment the situation is very similar. However, rather than study the morphology of the potential energy surface, we must focus on the total energy surface. The geometry of this surface, which is defined on phase space instead of coordinate space, can also be characterized by its stationary points and their stability. In this treatment, the rank-one saddles play a fundamental result. They are, in essence, the traffic barriers in phase space. For example, if two states approach such a point and one passes on one side and the other passes on the other side, then one will be reactive and the other nonreactive. Once the stationary points are identified, then the boundaries between the reactive and nonreactive states can be constructed and the dynamical structure of phase space has been determined. As in the case of potential energy surfaces, saddles with rank greater than one occur, especially in systems with high symmetry between outcomes, as in the dissociation of ozone. 

However, experimental ]V curves often deviate from the ideal /scl- In these cases, the measured current /inj is injection limited caused by a nonohmic contact or poor surface morphology. When the MO interface is nonohmic, carrier injection can be described by the Richardson-Schottky model of thermionic emission the carriers are injected into organic solid only when they acquire sufficient thermal energy to overcome the Schottky barrier ((()), which is related to the organic ionization potential (/p), the electron affinity (AJ, the metal work function (O, ), and the vacuum level shift (A) [34,35]. Thus, the carrier injection efficiency (rj) can be calculated by the following equation ... 

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