Electronic tunneling model

Electron-tunneling Model. Several models based on quantum mechanics have been introduced. One describes how an electron of the conducting band tunnels to the leaving atom, or vice versa. The probability of tunneling depends on the ionization potential of the sputtered element, the velocity of the atom (time available for the tunneling process) and on the work function of the metal (adiabatic surface ionization, Schroeer model [3.46]). 

Later, the kinetics of the ITL of /i-irradiated vitreous solutions of Ph2 in methylcyclohexane was studied [55] over a much wider time interval (10 6 -103 s). Within this whole time interval the kinetics of ITL was found to obey one and the same hyperbolic law, i.e. eqn. (7) with m 1. These results are difficult to interpret in terms of conventional kinetic models, but are easy to account for in terms of the electron tunneling model. Indeed, as shown in Chap. 4, the drop in the intensity of recombinational luminescence in the case of the tunneling mechanism of recombination obeys the equation... 

Figure 5.6 Cyclic voltammograms obtained for a spontaneously adsorbed [Os(bpy)2 4-tet Cl]+ monolayer on a 5 pm radius gold microdisk electrode where the scan rate is 1333 V s 1. The theoretical fits to the data, using a non-adiabatic electron tunneling model at electrolyte pH values of 0.9 and 6.0, are denoted by O and , respectively. In both cases, k is 27 kj mol-1, while k° is 1.1 x 103 and 1.1 x 104 s 1 at pH values of 0.9 and 6.0, respectively. Reprinted with permission from D. A. Walsh, T. E. Keyes, C. F. Hogan and R. J. Forster, ]. Phys. Chem., 105, 2792 (2000). Copyright (2000) American Chemical Society...

This type of motion, where the electron is chemically forbidden in certain regions of space, resembles the tunneling mechanism in physics, first discovered in radioactive nuclear decays. Since the term tunneling has been an accepted name for decades, there is no reason to adopt another name. However, the original tunneling model is a qualitative model. In ordinary quantum chemical calculations, there is no simple way to calculate tunneling barriers for the electron and there is also no reason to do so. Quantitative results can be obtained with the help of molecular orbital (MO) methods. The electron tunneling model is based on the overlap between the D and A wave functions and this still holds true in MO models. 

In an attempt to simplify the foregoing discussions, only a select few models are covered. This starts, for historical reasons, with a brief overview of the Local Thermal Equilibrium model. This is covered in Section 3.3.2.I. The Bond Breaking model is then discussed in Section 3.3.2.2, followed by the Electron Tunneling model in Section 3.3.2.3. For completeness sake, the Kinetic Emission model is presented in Section 3.3.2.4 as this appears to be responsible for the production of multiply charged atomic ions from the elements hghter than Phosphoras. Although many other models have also been put forward, only these are covered as the latter three, in particular, represent those currendy accepted for the respective systems described. 

Lastly, many of the concepts used in the bond-breaking model show similarities to both the LTE formalism and the electron tunneling model. In the case of the LTE formalism, this is noted as the bond-breaking concept reproduces the same Boltzmann-like exponential dependence on the ionization potential. As for the electron tunneling model, the dependence of the neutralization probability of the outgoing ion on the work-function is similar to the effect the energy of the trapped electron in the cation vacancy site has on the neutralization of the departing cation. 

Figure 3.40 Pictorial illustration (energy diagram) describing the neutralization of a positive ion on departing a condncting or semiconducting surface as surmised by the electron tunneling model. Note The direction of electron transfer, as represented by the large arrow, is defined primarily by the positions of the Fermi edge (Ep) and the ionization level at a distance at which the interaction occnrs (zj- The probability, on the other hand, is defined by the width of the ionization level (2A) at as well as the emission velocity normal to the snrface (Vj ).

The strongest evidence for the validity of the concepts used in the electron tunneling model is noted in the change of secondary ion yield observed when either of the above restrictions (/< or EA > work-function of a substrate is reduced such that the Fermi edge rises above the ionization level of electropositive elements such as Cs (this has an ionization level that is above the position of the Fermi edge of most all substrates), then complete neutralization of the departing Cs ions should then occur. 

Electron tunneling model A model describing atomic secondary ion emission... 

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