Current controlled negative resistance

The picture completely changes if we reach a current-controlled negative-differential-resistance (NDR) regime. As a consequence of NDR the current distribution decays into filaments. In the simplest model two parameters are needed. One is the breakdown field, or threshold field, for growth of a filament F, and the other is the channel field Pch (Zeller, 1987 Wiesmann and Zeller, 1986). The contraction into filaments leads to the situatibn that a local field enhancement becomes self-enhanced and propagating at the tip of the filament. If V > then the filament will reach the counter-electrode and breakdown will occur. 

A discussion will be given of electronic currents through sandwich structures of the type tantalum (or other substrate metal)/oxide film/metal counterelectrode. The thickness of the oxide film has varied from 25 to 5000 A. The counterelectrode has usually been deposited on the oxide by evaporation, but pressure contacts, mercury droplets, and electroless plating have also been used. The behavior of the system metal/oxide/electrolytic solution is more difficult to interpret and little can be added to a previous article. Even with the simple metal/insulator/metal system there is disagreement about which mechanisms control the current under the various conditions of temperature, thickness, and field. However, recent work has clarified the picture with regard to the choice of mechanisms, and experimental results are beginning to accumulate. Some effects, such as the negative resistance, which has been observed with films which have been subjected to a preliminary breakdown, can be explained only very tentatively. 

Breakdown in general implies a current-controlled (S-shaped) negative differential resistance region. As a consequence, the current distribution becomes filamentary in nature. 

Generally, irrespective of the technique for which they are used, electrochemical cells are constructed in a way which minimizes the resistance of the solution. The problem is particularly accentuated for those techniques which require high current flows (large-scale electrolysis and fast voltammetric techniques). When current flows in an electrochemical cell there is always an error in the potential due to the non-compensated solution resistance. The error is equal to / Rnc (see Chapter 1, Section 3). This implies that if, for example, a given potential is applied in order to initiate a cathodic process, the effective potential of the working electrode will be less negative compared to the nominally set value by a amount equal to i Rnc. Consequently, for high current values, even when Rnc is very small, the control of the potential can be critical. 

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