Tunnelling of electrons

STM is based on the tunneling of electrons between the surface and a very sharp tip [36,49]. As explained in the Appendix, the cloud of electrons at the surface is not entirely confined to the surface atoms but extends into the vacuum (this effect causes the electric dipole layer at the surface that contributes to the work function). When an extremely fine tip (see Fig. 7.18) approaches the surface to within a few angstroms, the electron clouds of the two start to overlap. A small positive potential... 

Figure 7.18 Scanning tunneling microscopy is based on the tunneling of electrons between the surface and an atomically sharp tip positioned at a few angstroms above the surface. The tunneling current depends sensitively on the distance s between the tip and the surface. An image of the surface is obtained by scanning the tip horizontally over the surface. A control system keeps the tunneling current and therefore the distance between tip and surface constant the scans are a plot of the vertical position of the piezoelectrically driven tip versus its horizontal position.

Field emission is the emission of electrons from a solid under an intense electric field, usually at ambient temperatures. It occurs by the quantum mechanical tunneling of electrons through a potential barrier (Fig. 13.1). This leads to an exponential dependence of emission current density J on the local electric field, as given by the Fowler Nordheim equation,... 

Image formation Tunneling of atomic electrons into sample which is a tip Tunneling of electrons between the probing tip and sample... 

A typical example of a special state is as follows. Electron transfer reactions at an atom are aided by vibrations that equilibrate the interatomic distances that differ for the two oxidation states. Thus a low-energy, high-amplitude vibration is desirable. The vibration could have the further function that it provided a time-dependent fluctuation of the redox potential. As I and Goldanskii in this volume have pointed out, this allows a precise matching of the redox potential of one redox couple with another leading to tunneling of electrons. 

Figure 3.44. Dissociation of 02 adsorbed on Pt(lll) by inelastic tunneling of electrons from a STM tip. (a) Schematic ID PES for chemisorbed Of dissociation and illustrating different types of excitations that can lead to dissociation, (b) Schematic picture of inelastic electron tunneling to an adsorbate-induced resonance with density of states pa inducing vibrational excitation (1) competing with non-adiabatic vibrational de-excitation that creates e-h pairs in the substrate (2). (c) Dissociation rate Rd for 0 as a function of tunneling current I at the three tip bias voltages labeled in the figure. Solid lines are fits of Rd a IN to the experiments with N = 0.8, 1.8, and 3.2 for tip biases of 0.4, 0.3, and 0.2 V, respectively and correspond to the three excitation conditions in (a). Dashed lines are results of a theoretical model incorporating the physics in (a) and (b) and a single fit parameter. From Ref. [153].

The theoretical model developed to explain these experiments is based on inelastic tunneling of electrons from the tip into the 2ir adsorbate resonance that induces vibrational excitation in a manner similar to that of the DIMET model (Figure 3.44(b)). Of course, in this case, the chemistry is induced by specific and variable energy hot electrons rather than a thermal distribution at Te. Another significant difference is that STM induced currents are low so that vibrational excitation rates are smaller than vibrational de-excitation rates via e-h pair damping. Therefore, coherent vibrational ladder climbing dominates over incoherent ladder climbing,... 

All this material is described in introductory textbooks of physics and chemistry. However, it is interesting to recall the headlines here because the veiy first application to a chemical theme of the ideas of waves in quantum mechanics was to explain how electrons were emitted from, or accepted by, electrodes. This was the achievement of Ronald Gurney,1 the first physical electrochemist, and much of this chapter is based on developments that sprang from his seminal paper of 1931. In this paper, he related electric currents across the electrode solution interface to the tunneling of electrons through energy barriers formed between the electrode and the ions or molecules in the first layer next to the electrode (possessing electronic states ). 

A lively subsection in applications of quantum theory to transitions at electrodes concerns the tunneling of electrons through oxide films. This work has been led by Schmickler (1980, 1996), who has used a quantum mechanical approach known as resonance tunneling to explain the unexpected curvature of Tafel lines for electron transfer through oxide-covered electrodes (Fig. 9.21). 

The picture begins to come somewhat into focus. Starting off with some basic mechanics of electrons, one was able to define the quantum mechanical condition for the tunneling of electrons from a metallic donor to electron acceptors through an electron-energy barrier. The tunneling condition could be expressed in terms of an energy barrier for ion movement, e.g., the movement of protons toward the metal in the reaction ... 

In some cases the statistical mechanical concept of entropy changes makes it conceivable that relations exist between A/f° and AS° or between A2/ and A S for a number of reactions. As a special case, reactions involving the tunneling of electrons between ions of different valence states may serve as an example for the possibility that a tunnel effect may account for the occurrence of compensation effects. 

It is more probable that the phenomenon consists of a tunneling of electrons into the metal. We shall first consider the case of an unbound neutral atom or molecule near a surface, choosing H for simplicity. Since electronic motion is much faster than that of nuclei, we may consider the... 

Molecular superconductors are of more immediate practical interest. Experimental evidence indicates superconductivity is incipient at 30 K, a temperature above the critical temperature for other known materials. Superconductors have a major potential use in providing two distinguishable states associated with tunneling of electron pairs through a... 

The presence of the region of weak dependence of the conductivity of alloyed semiconductors on temperature can be explained by tunneling of electrons from one impurity centre to another, unoccupied centre. The necessary condition of the impurity conductivity is the partial filling of the impurity levels. At low temperatures this conduction can be maintained only by semiconductor compensation, i.e. by the simultaneous presence of donor and acceptor impurities. In the case, for instance, of the n-type semiconduc-... 

Fig. 1. Schematic view of the nanomechanical GMR device a movable dot with a single electron level couples to the leads due to tunneling of electrons, described by the tunneling probability amplitudes TL,n(t)), and due to the exchange interaction whose strength is denoted by JL,n(t). An external magnetic field H is oriented perpendicular to the direction of the magnetization in the leads (arrows).

Fig. 27 Processes involved in the transport characteristics in figure 26. ei = ei,CT, 62 = 62,(7, The red line indicates electron resonant-tunnelling, a) The first conductance peak, b) The second conductance peak, c) The pseudo-peak of conductance, d) The first current maximum, and the red line indicates resonant tunnelling of electrons, e) The second current maximum for electron resonant tunnelling, f) The dip of conductance.

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