Junction differential conductance

Figure 11. Experimental and predicted differential conductance plots of the double-island device of Figure 10(b). (a) Differential conductance measured at 4.2 K four peaks are found per gate period. Above the threshold for the Coulomb blockade, the current can be described as linear with small oscillations superposed, which give the peaks in dljdVj s- The linear component corresponds to a resistance of 20 GQ. (b) Electrical modeling of the device. The silicon substrate acts as a common gate electrode for both islands, (c) Monte Carlo simulation of a stability plot for the double-island device at 4.2 K with capacitance values obtained from finite-element modeling Cq = 0.84aF (island-gate capacitance). Cm = 3.7aF (inter-island capacitance). Cl = 4.9 aF (lead-island capacitance) the left, middle and right tunnel junction resistances were, respectively, set to 0.1, 10 and 10 GQ to reproduce the experimental data. (Reprinted with permission from Ref [28], 2006, American Institute of Physics.)...

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. 1.21. Tunneling spectroscopy in classic tunneling junctions, (a) If both electrodes are metallic, the HV curve is linear, (b) If one electrode has an energy gap, an edge occurs in the HV curve, (c) If both electrodes have energy gaps, two edges occur. A "negative differential conductance" exists. (After Giaever and Megerle, 1961).

Figure 25 Differential conductance of a sandwich-type tunnel junction of Y-Ba-Cu-0(123) Tc = 60 K, formed with native oxide and a Pb counter electrode. Ref. 89.

Fig. 2. Measurement of G(V, B) for a 2 pm junction. Light shows positive and dark negative differential conductance. A smoothed background has been subtracted to emphasize the spectral peaks and the finite-size oscillations. The solid black lines are the expected dispersions of noninteracting electrons at the same electron densities as the lowest ID bands of the wires, ui) and li). The white lines are generated in a similar way but after rescaling the GaAs band-structure mass, and correspondingly the low-voltage slopes, by a factor of 0.7. Only the fines labeled by a, b, c, and d in the plot are found to trace out the visible peaks in G(V,B), with the fine d following the measured peak only at V > —10 mV.

Enormous progress has been achieved in the experimental realization of such nano-devices, we only mention the development of controllable single-molecule junctions [8]-[22] and scanning tunneling microscopy based techniques [23]— [44]. With their help, a plethora of interesting phenomena like rectification [18], negative differential conductance [9,35], Coulomb blockade [10,11,15,16,21, 23], Kondo effect [11,12], vibrational effects [10,13,14,16,21,25,31-33,35,36], and nanoscale memory effects [34,39,40,42,44], among others, have been demonstrated. 

Fig. 30 Differential conductance of a symmetric junction (rj = 0.5, Er = El) at different molecule-to-lead coupling, from El/iuo = 0.1 (lower curve) to El/wo = 10 (upper curve), /ujq = 1, e0/u>o = 2. Voltage is in the units of fko0/e.

Fig. 31 Differential conductance of an asymmetric junction (77 = 0, Fr = 20Fr) at different molecule-to-lead coupling, from Fr/wo = 0.2 (lower curve) to Fr/iv0 = 4 (upper curve), X/ujo = 2, eo/oJo = 5. The voltage is in the units of hiao/e...

Fig. 32 Differential conductance at different molecule-to-STM coupling (see the text), from asymmetric junction with Fl/wo = 0.025, Fr/wo = 0.5 and 77 = 0.2 (lower curve, blue thick line) to symmetric junction with Fl/w0 = Fr/wo = 0.5 and 77 = 0.5 (upper curve, red thick line), X/ujo = 1, eo/wo = 2. Voltage is in the units of hjJo/e...

In conclusion, at weak molecule-to-lead (tip, substrate) coupling the usual vibronic side-band peaks in the differential conductance are observed at stronger coupling to the leads (broadening) these peaks are transformed into step-like features. A vibronic-induced decreasing of the conductance with voltage is observed in high-conductance junctions. The usual IETS feature (in-... 

Figure 6 Differential conductance of the break junction made of a polycrystalline Rbj C o pellet (dots). The continuous line is a three parameter fit using a modified BCS formula for the density of states. The dashed line was obtained by including an additional leakage conductance at zero bias and the voltage dependence of the transmission function of the...

Fig. 17.8 Current/ (full Hne) and differential conduction g(4>) = dl/d (dotted line) displayed as a function of voltage for a junction characterized by a single resonance state.

If a semiconductor element with negative differential conductance is operated in a reactive circuit, oscillatory instabilities may be induced by these reactive components, even if the relaxation time of the semiconductor is much smaller than that of the external circuit so that the semiconductor can be described by its stationary I U) characteristic and simply acts as a nonlinear resistor. Self-sustained semiconductor oscillations, where the semiconductor itself introduces an internal unstable temporal degree of freedom, must be distinguished from those circuit-induced oscillations. The self-sustained oscillations under time-independent external bias will be discussed in the following. Examples for internal degrees of freedom are the charge carrier density, or the electron temperature, or a junction capacitance within the device. Eq.(5.3) is then supplemented by a dynamic equation for this internal variable. It should be noted that the same class of models is also applicable to describe neural dynamics in the framework of the Hodgkin-Huxley equations [16]. 

Fig. 24 (a) Diagram of NW with triple junctions on Au electrodes, (b) Comparison of I-V characteristic curves of pristine and treated single P3MT NWs with various numbers of serial junctions, (c) Voltage dependence of differential conductance between pristine and treated single P3MT NWs with various numbers of junctions. (Reproduced with permission from [62]. Copyright 2011 Wiley-VCH.)... 

In order to obtain devices with negative differential conductance, Kunze and Kowalsky (1988) have used ytterbium as a film gate. The low work function of Yb compared to the electron affinity of InAs increases the surface field. And, the low resistive tuimel junction serves as ohmic contact to the inversion layer. 

Throughout this chapter we will also refer to the conductance of the junction, which is properly the differential conductance and is defined as ... 

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