Image-force lowering

The image force lowering of the barrier results from the field produced by an electron and will be absent when there is no electron present in the... 

In a metal-semiconductor junction, the electrons approaching the interface also experience an image-force lowering of the barrier. A negative charge at a distance x... 

Clearly, the image-force lowering increases through a square root dependence with the electric field. The resulting effective barrier for electron escaping the metal can be expressed as... 

Figure 8.3 Ideal metal n-type semiconductor contacts under (a) equilibrium and (b) forward and (c) reverse biases. Also shown is the image-force lowering of the barrier.

The MBA provides another simple explanation of why the image potential is not observable. According to Eq. (2.42), as long as the integral of the distortion potential is a constant (that is, the shaded area in Fig. 2.8 remains constant while varying the tip-sample distance), the effect of distortion is a constant independent of the barrier thickness. Therefore, the effect of barrier lowering due to image force is not observable. 

Fig. 8. The change in surface tension at low electrolyte concentrations (the Jones-Ray effect). Circles Experimental data from Ref. [33]. Curve (1) predicted surface tension for the simple model which accounts for OH adsorption and only ion hydration effects for electrolyte ions, within the Poisson-Boltzmann approach. Curve (2) predicted surface tension when image forces are also included in the model. As noted in Section 3, the image forces cannot be neglected at concentration lower than 0.01 M.

The upper sign corresponds to a water-dielectric , and the lower one to a water-conductor type of interface. Equation (7) shows that a charge located next to a conductor will be attracted by its own image, and dielectrics in aqueous solutions will repel it. For a review of statistical-mechanical models of the double layer near a single interface we refer to [7], and here we would like only to illustrate how the image forces will alter the ion concentration and the electrostatic potential distribution next to a single wall. At a low electrolyte concentration the self-image forces will mostly dominate, and the ion-surface interaction will only be affected by the polarization due... 

For the operation of contact mode AFM under liquid there are only few details that differ from operation in air. The imaging forces can often be controlled much more precisely if the adhesion is lower due to the absence of capillary forces. Hence the adjustment of the setpoint requires more attention and can be done with much more precision. The adjustment can be based on acquired force-displacement curves (see below, Fig. 3.39). Setpoint deflection values close to the out of contact deflection yield minimized normal forces [82-84],... 

Quite a large number of systems have been studied and most of the current-voltage curves follow the thermionic emission model [12,16]. Frequently, there is some difference in the slope for example, instead of a theoretical slope of 60 mV per decade in current, slopes of 70-75 mV were found. This deviation may either be due to an image-force-induced lowering of the barrier or to tunneling through the space charge layer, as has been quantitatively studied for Au/Si barriers [28]. These two effects have been treated in detail by Sze [16]. 

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