Current-bias relation

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. 

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... 

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... 

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... 

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.

Figure 5. Current bias (E-EJ relation for a clean 0.1M NaCl surface—O and for a surface with a monolayer of distearoyl lecithin at a surface pressure of 30.4 dynes/cm at 20°C—(A).

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). 

In STM, a sharp metal tip is positioned sufficiently close to a conductive sample that a measurable current (pA-nA) due to quantum mechanical tunneling of electrons between states in the tip and sample flows when a bias voltage (usually less than 1 V) is applied to the gap. - The magnitude of the tunneling current is related to the densities of electronic states near the Fermi level in the tip/sample gap, and depends exponentially on the tip/sample separation distance as follows ... 

An additional limit to the size of a passive array relates to the current which flows in an OLED when it is under reverse bias [189]. When a given pixel is turned on in the array, there are many possible parallel paths for the current, each involving two diodes in reverse bias and one forward. Hence, as the number of rows and columns increases, there is a higher level of background emission from non-selected pixels that limits the contrast ratio of the array. As a result, the contrast degrades as N increases. 

IN 1989, A PANEL CONVENED BY THE NATIONAL SCIENCE FOUNDATION examined introductory college chemistry courses and concluded that the historic bias of chemistry curricula toward small-molecule chemistry, generally in the gaseous and liquid states, is out of touch with current opportunities for chemists in research, education, and technology (i). Moreover, the report noted that the attractiveness of chemistry and physics for undergraduate majors could be enhanced by greater emphasis on materials-related topics which would help students better relate their studies to the real world. ... 

Figure 11.10. NW smart pixels, (a) Schematic of an integrated crossed NW FET and LED and the equivalent circuit, (b) Shows SEM image of a representative device, (c) Plots of current and emission intensity of the nanoLED as a function of voltage apphed to the NW gate at a fixed bias of -6V. (d) EL intensity versus time relation when a voltage applied to NW gate is switched between 0 and +4V for a fixed bias of -6V. [Reprinted with permission from Ref. 59. Copyright 2005 Wiley-VCH Verlag.]...

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