Current-bias voltage relation

We focus on the electronic conductivity of molecular monolayers and on single molecules enclosed between a pair of metallic electrodes. We address specifically in situ STM of redox (bio)molecules but concepts and formalisms carry over to other metallic nanogap configurations. Importantly, in addition to the substrate and tip, a third electrode serves as reference electrode [42-44] (Figure 2.2). This allows electrochemical potential control of both substrate and tip. The three-electrode configuration is the basis for two kinds of tunneling spectroscopy unique to electrochemical in situ STM. One is the current-bias voltage relation as for STM in air or vacuum, but with the notion that the substrate (over)potential is kept constant. The other is the current-overpotential relation at constant bias... 

Similar tunneling spectroscopic features are associated with the current-bias voltage relations, i.e. new electronic conduction channels open when the redox level is brought to cross into the energy region between the Fermi levels of the substrate and tip electrodes. The spectroscopic current-bias... 

The current-bias voltage relations can be written in parametric form... 

Additional information with respect to the mechanism of the grain boundary resistance can be obtained from temperature- and voltage-dependent impedance measurements. The grain boundary semicircle varies, for example, considerably with the applied dc bias (Fig. 39a). The current-voltage relations calculated from such bias-dependent impedance measurements are thus non-linear. In the logarithmic plot (Fig. 39b) it can be seen that the low bias regime exhibits a non-linearity factor a (= d og(I/A)/d og(U/ V)) of almost one (ohmic behavior), while at a bias value of about 0.35 V this factor changes to a x 2. 

This form discloses an immediate general implication in Eqs. 2.9)-(2.12), namely a pronounced ( spectroscopic ) maximum in the tunneling current-overpotential relation (at given bias voltage). For the symmetric configuration of Eq. (2.12), the maximum appears at the overpotential... 

Figure 8-9. Top Tunneling current/overpotential correlations of the two osmium complexes in Fig. 8-8. Constant bias voltage Vnas (= E,tp-Esubstrate) -015 V 0.1 M NaC104 and 0.1 M HCIO4. Bottom Effect of the bias voltage on the peak maximum (relative to the equilibrium potential of the surface-immobilized complexes, E ) of the tunneling current/overpotential relations, cf eqns. (8-21) and (8-22). Data from refs. 134 and 135.

In practical terms, a topographical experiment begins by positioning the tip properly in relation to a sample. The tip is then moved in the z-direction to adjust the sample-to-tip distance, which must not exceed a few tenths of a nanometer. A small bias voltage is then applied between the sample and the tip. As the tip approaches the surface, a tunneling current guides the final positioning in the z-direction. The... 

Figure 5.3 shows the drain current of PEI/starch functionalized HEMT sensors measured exposed to different CO2 concentration ambients. The measurements were conducted at 108°C and a fixed source-drain bias voltage of 0.5 V. The current increased with the introduction of CO2 gas. This was due to the increase in net positive charges on the gate area, thus inducing electrons in the 2DEG channel. The response to CO2 gas has a wide dynamic range from 0.9% to 40%, as shown in Fig. 5.4. Higher CO2 concentrations were not tested because there is little interest in these for medical-related applications. The response times were in the order of 100 s. The signal decay time was slower than the rise time, and was due to the longer time required to purge CO2 from the test chamber.

The nature of the barrier to charge transfer at the metal-oxide interface is open to speculation. Assuming semiconducting properties for the Pt-oxide layer, this additional barrier may simply represent the nonlinear resistance of a metal-semiconductor junction, i.e., resistance of a diode biased in the conduction direction. For high bias voltages, the current-voltage relation for such a junction may be expressed by an equation of the form of Eq. (31). 

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