Differential conductance, applied voltag

By definition, a molecular transport junction consists of a molecule extended between two macroscopic electrodes. The nature of the molecule, the environment (whether it is solvated or not), the electrode s shape and composition, the temperature, the binding of the molecule to the electrodes, and the applied field are all variables that are relevant to the measurement, which is usually one of differential conductance, defined as the derivative of the current with respect to voltage. 

Fig. 14.7. Tunneling spectra with the varying-gap method. Raw data for (a) the differential conductivity, and (b) the current, as a function of bias voltage (at the sample). The applied variation in tip-sample separation is shown in (c). The total conductivity //V is shown in (d), with no broadening (solid curve) and with broadening of AV =1 V (dashed curve). (Reproduced from M4rtensson and Feenstra, 1989, with permission.)...

Fig. 4 Differential conductance dl/dV versus applied voltage V at 100 K. The differential conductance manifests a clear peak structure. Good reproducibility can be seen from the six nearly overlapping curves. Peak structures were observed in four samples measured at low temperatures although details were different from sample to sample. Subsequent sets of I-V measurements can show a sudden change, possibly due to conformational changes of the DNA. The inset shows an example of two typical I-V curves that were measured before and after such an abrupt change. Switching between stable and reproducible shapes can occur upon an abrupt switch of the voltage or by high current (from [14], with permission Copyright 2000 by Nature Macmillan Publishers Ltd)...

Fig. 35. Temperature dependence of the differential conductance d//dV versus bias voltage V of a resonant tunneling diode with a (Ga,Mn)As emitter. No magnetic held is applied (Ohno et al. 1998). (b) Calculated resonant tunneling spectra as a function of the exchange energy NqP (Akiba et al. 2000b).

The electronic density of states of SWNTs have been brought into evidence with STM measurements which revealed structures which are consistent with the calculated density of states [125,127], In particular, the measured separation between, and the shapes of the peaks in measured differential conductivity versus applied bias voltage closely resemble calculated densities of states. 

Fig. 5.24. Differential conductance dl/dV as a function of bias voltage of an AI-AI2O3 - amorphous Ge tunneling diode (after Osmun and Fritzsche (1970)). At low temperatures the resistance of the a-Ge electrode becomes comparable with the tunnel resistance. The bias voltage across the oxide barrier is then smaller than the applied bias shown here.

Fig. 5.3-11 Left differential conductance as a function of the applied voltage for a 49-period superlattice at 20 K. Right schematic model to explain the 48 negative peaks in the differential conductance, (a) Zero bias (b) ground-state resonanttunneling conduction (c) first field localization, where resonant tunneling between the ground state and an adjacent excited state takes place (d) expansion of the high-field region by one additional quantum well. (After [3.62])...

What is usually measured experimentally is the so called differential conductance, given by the derivative of the current with respect to applied voltage ... 

Figure 8.7. Left density of states at a metal-superconductor contact the shaded regions represent occupied states, with the Fermi level in the middle of the superconducting gap. When a voltage bias V is applied to the metal side the metal density of states is shifted in energy by e V (dashed line). Right differential conductance d//dV as a function of the bias voltage eV at T = 0 (solid line) in this case the measured curve should follow exactly the features of the superconductor density of states AtT > 0 (dashed line) the measured...

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC>2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

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