Spatially resolved tunneling spectroscopy

The most extensively used theoretical method for the understanding of the MIM tunneling junction is the time-dependent perturbation approach developed by Bardeen (1960). It is sufficiently simple for treating many realistic cases, and has been successfully used for describing a wide variety of effects (Duke, 1969 Kirtley, 1982). 

A schematic diagram of the Bardeen approach is shown in Fig. 1.20. Instead of trying to solve the Schrodinger equation of the combined system. 

Bardeen considers two separate subsystems first. The electronic states of the separated subsystems are obtained by solving the stationary Schrodinger equations. For many practical systems, those solutions are known. The rate of transferring an electron from one electrode to another is calculated using time-dependent perturbation theory. As a result, Bardeen showed that the amplitude of electron transfer, or the tunneling matrix element M, is determined by the overlap of the surface wavefunctions of the two subsystems at a separation surface (the choice of the separation surface does not affect the results appreciably). In other words, Bardeen showed that the tunneling matrix element M is determined by a surface integral on a separation surface between the two electrodes, z = zo. 

The 8 function in this equation indicates that only the states with the same energy level in both electrodes can tunnel into each other. 

The tunneling current can be evaluated by summing over all the relevant states. At any finite temperature, the electrons in both electrodes follow the Fermi distribution. With a bias voltage V, the total tunneling current is 

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The high lateral resolution down to the atomic scale is the special merit of scanning tunneling microscopy and spectroscopy. Spatially resolved measurements at T — 10 K with a W tip coated with approximately 10 ML Fe were performed on a sample prepared by depositing 10 ML of Gd on the W(llO) substrate held at 530 K. This preparation procedure leads to partially coalesced Gd islands with a Gd wetting layer on the W(llO) substrate. 

From a methodological point of view, of particularly interest have been improvements in the chemical sensitivity of STM and AFM characterization. This is especially desirable for electrochemists, as electrochemical environments prevent the combined characterization by other surface techniques, as are frequently used for composition determinations in vacuum. Tunneling spectroscopy measurements to obtain 7 y and d//dV y relationships may provide a certain degree of information regarding the electronic structure of the substrate surface and adsorbed molecules [77], and the use of ionic liquids of large electrochemical windows is favorable in this respect. One major enhancement would be to complement SPM with other spatial, time- and energy-resolved surface in-situ techniques. For example, a combination of scanning electrochemical microscopy and atomic force microscopy... 

Time-resolved spectroscopy investigations of GaP N crystals indicate the presence of exciton energy transfer over distances of at least 100 A The interaction causing the energy transfer is too strong to be explained by a resonant dipole-dipole mechanism and a tunneling process made possible by the large spatial extent of the exciton wavefunction has been proposed. 

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