Elastic tunneling

Elastic tunneling spectroscopy is discussed in the context of processes involving molecular ionization and electron affinity states, a technique we call orbital mediated tunneling spectroscopy, or OMTS. OMTS can be applied readily to M-I-A-M and M-I-A-I -M systems, but application to M-A-M junctions is problematic. Spectra can be obtained from single molecules. Ionization state results correlate well with UPS spectra obtained from the same systems in the same environment. Both ionization and affinity levels measured by OMTS can usually be correlated with one electron oxidation and reduction potentials for the molecular species in solution. OMTS can be identified by peaks in dl/dV vs bias voltage plots that do not occur at the same position in either bias polarity. Because of the intrinsic... 

Keywords Inelastic Elastic Tunneling Spectroscopy Orbital mediated Vibrational Electronic Ionization levels Affinity levels... 

The second issue of interest is the temperature dependence of elastic tunneling spectroscopy. Because the bands are intrinsically wide, spectra measure at 5 K are similar in line shape to those measured near 300 K. In any case, the integrated normalized intensities,... 

The take-home message here is that conductivity measurements in single-molecule junctions are difficult to analyze without the support of quantum mechanical calculations that include the metal electrodes. This is very much the domain of specialists, and the simple rules discussed for analyzing elastic tunneling spectra in other junction types generally do not apply for metal-single-molecule-metal junctions. 

The tunnel current which flows from one metal to the other when a potential difference is applied across the junction is mainly due to elastic tunneling. However, if the adsorbed molecules on the junction have a characteristic vibrational mode of energy hv, then an inelastic process can occur when ev hv. 

Thus far the discussion has centered on elastic tunneling, but consideration of inelastic processes may offer additional analytical opportunities. An energy scale of the relevant phenomena is presented in Table 2. Inelastic tunneling was first observed in metal-oxide-metal junctions. It was immediately developed as a technique for photon-free vibrational spectroscopy (lETS) where the tunneling electrons dissipate energy by coupling to vibra-... 

It is not always possible to discern non-elastic tunneling on the background of elastic tunneling. For example, when it proves possible, Fig. 14 shows the dependence of d2J/d V2 on V for the tunnel junction bearing H20 molecules as impurity. Tunnel spectroscopy is, at present, one of the powerful methods of studying the vibrational spectra of molecules in condensed media. 

Fig. 56. Current component due to direct elastic tunnelling for a semiconductor with varying Ld values. The LD values are given against each plot.

Figure 20. Elastic tunneling of an electron between two metal phases separated by vacuum (rectangular barrier). Shown are the wave functions of a free electron propagating in a direction perpendicular to the interface. The wave function decays exponentially in the vacuum. The tunneling probability is related to the amplitude of the free electron wave functions (see section 6).

Figure 25a. Electron exchange between a metal and a simple redox system in solution under conditions of electrochemical equilibrium, =, u(Ox/Red). The energy distribution of the occupied and empty electron levels in the metal and in the redox system are depicted. Elastic tunneling occurs between occupied and empty levels on both sides of the interface. The rate of exchange is maximal at around the Fermi-level as indicated by the length of the arrows.

Here, ka and kc are the electrochemical rate constants (cm s ) and CRed and cox are the concentrations of the redox ions just outside the electrochemical double layer. The anodic current is due to electron transfer from the reduced species to the empty states in the working electrode, the cathodic current is due to transfer from an occupied electron level in the metal to an unoccupied level corresponding to the oxidized species. We evaluate the electrochemical rate constants by taking into account all elastic tunneling events between the energy levels in the metal, g E), and those in the electrolyte, given by Wox E)cox and IFRed(F)cRed. The procedure is similar to that described in Section 4.6.2. Thus ... 

Schultze and Haga (249) attributed the 120 mV slope at low overpotentials to a direct elastic tunneling mechanism and the lower slope of 60 mV at high... 

Figure 2, lETS results for a control sample (no organic material present on the alumina layer). Note the rising background from elastic tunneling processes, (See Table I for peak assignments). 

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