Electron image-potential states

If the tunneling current is from the surface to the tip, the STM images the density of occupied states. If the potential is reversed, the current flows in the other direction, and one images the unoccupied density of states, as the reader can easily understand from Fig. 7.19. This figure also illustrates a necessary condition for STM there must be levels within an energy e-V from the Fermi level on both sides of the tunneling gap, from and to which electrons can tunnel In metals, such levels are practically always available, but when dealing with semiconductors or with adsorbed molecules, this condition may be a limitation. A second condition is that the sample possesses conductivity perfect electrical insulators cannot be measured with STM. 

This one-dimensional escape probability can be compared with the three-dimensional expression (168). The observed escape probability for a distribution of initial distances between electrode and electron is the average of that distribution over all escape probabilities given by eqn. (178). Under steady-state photostimulation of the cathode, an electric current flows between cathode and anode and the current is proportional to the escape probability of these electrons from their image potential. As in the three-dimensional (Onsager) case, the field dependence of the electric current may be used to estimate the range of photoejected electrons from the cathode. However, these photoejected electrons have... 

First of all, the existence of the surface establishes a certain correlation between different electronic states, particularly between incident and reflected electrons. In addition there are electron density variations both within the surface and along the surface normal. Since the screening radius increases with decreasing electron density, it is obviously unrealistic to third of a spherical potential hole accompanying its electron in the immediate surface region, where the electron density drops very rapidly to zero. At the very lowest densities, in particular, the potential must somehow go over in continuous fashion into the classical image potential applying far away from the metal surface. Finally, from the dynamic nature of these interactions it follows that the problem must be dealt with self-consistently each electron contributes to the holes of all the other electrons in a manner dependent on the detailed features of its own potential hole. 

Grimes, C.C. and Brown, T.R. (1974). Direct spectroscopic observation of electrons in image-potential states outside liquid helium, Phys. Rev. Lett. 32, 280-283. 

Amongst the optical techniques there are also the more traditional methods such as the ellipsometry, electroreflectance and particularly, surface plasmons, where experimental and theoretical advances have made it possible to offer a picture of the surface electronic states of the metal in some selected cases, such as the silver (111) phase. We should mention here the measurement of image potential induced surface states by electroreflectance spectroscopy. In this case, besides the normal surface... 

The barrier Vois superimposed on this potential. Several cases can be distinguished. (1) An electron in the vapor space is approaching a liquid with Vq > 0. The electron is attracted by the image potential but it cannot enter the liquid due to the barrier presented by Vq. Surface states are formed. An example of this is liquid helium (see Section 6.8). (2) An electron is approaching a liquid with Vq > 0 in the vapor space. In this case, the electron transfer is readily effected. (3) An electron is in the liquid approaching the liquid/vapor interface. It is repelled by the image potential. If in addition, Vq < 0, then a barrier for electron transfer exists which the electrons have to overcome by thermal activation. If Vq > 0, then in principle electron transfer should... 

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