Coulomb staircase

In particular, considering a ballistic model for the charge transport through a dot, it was possible to demonstrate that the current through it should be represented as a series of equidistant peaks whose positions correspond to the steps in the coulomb staircase. 

All of the theoretical work proposed during the past 10 years forces experimental researchers to develop real systems to observe the described phenomena. In reality, only a year after the very first work of Averim and Likharev, the first measurements of the coulomb blockade and the coulomb staircase phenomena were published. 

A few months later, the observation of the coulomb blockade appeared (Fulton and Dolan 1987). In the case of a coulomb staircase, only one additional mouth was required (Earner and Ruggiero 1987). 

On the other hand, even in particle systems the coulomb blockade (Van Bentum et al. 1988a) and the coulomb staircase (Van Bentum et al. 1988b) were observed, some nonlinear effects were observed in the current-voltage characteristics (Wilkins et al. 1989), and behavior related to the quantized energy levels inside the particles was described (Crom-mie et al. 1993, Dubois et al. 1996). 

However, the main research result from those years was the discovery of the room-temperature single-electron phenomenon. In the 1990s, STM experiments on liquid crystal had shown a very weak staircase (Nejoh 1991) only one year later, the clear observations of the coulomb blockade and the coulomb staircase were demonstrated on gold nanoparticles (Shonenberger et al. 1992a) and the role of system symmetry on the appearance of these two phenomena was outlined (Shonenberger et al. 1992b). 

Finally, it was possible to build up the first stand-alone room-temperature singleelectron junction by depositing a semiconducting particle directly onto the tip of a very sharp electrode, avoiding in this case the use of an STM microscope, and it was possible to observe the coulomb staircase in such a system (Facci et al. 1996). 

Nevertheless, the appearance of regions with negative resistance is generally not typical for the coulomb staircase phenomenon. However, several articles reported similar features both theoretically (Beenakker 1991, Stone et al. 1992, Prigodin et al. 1993) and experimentally (Reed et al. 1988). 

Asymmetry of the structure is one of the basic parameters responsible for the coulomb staircase phenomenon (Shonenberger et al. 1992b). As we have said previously, it is absolutely necessary to have an asymmetrical system in order to observe stephke V-I characteristics. 

Other sensor applications can be considered if some sensitive biological molecules (such as antibodies or receptors) are attached to the nanogranule. If, for example, an antibody molecule is attached to it, then the granule is placed between two electrodes, and single-electron current flows between them. The step value of the coulomb staircase depends on the capacity of the junctions. When the antibody molecule binds specific antigen, the capacity value will be changed, and, therefore, the step value of the VH characteristics will also change. 

The tip-particle distance, using (Vbias = 1 V, /tmmei = 1 nA) as tunnel parameters does not correspond to that needed to observe the Coulomb staircase. The particle-substrate distance is fixed by the coating with dodecanethiol. Hence the two tunnel junctions are characterized by fixed parameters. Similar Coulomb blockade behavior has been observed [58,59]. 

Andres RP, Bein T, Dorogi M, Feng S, Henderson JI, Kubiak JP, Mahony W, Osifchin RG, Reifenberger R (1996) Coulomb Staircase at room temperature in a self-assembled molecular nanostructure. Science 272 1323-1325... 

The small size of nanoelectrodes also makes possible the detection of discrete electron transfer events. Fan and Bard have recently shown cou-lombic staircase response using electrodes of nanometer dimensions [63], Ingram and co-workers have also shown coulombic staircase response, in their case while studying colloids and collections of colloids [64]. Fan and Bard have also applied nanoelectrodes to achieve high-resolution electrochemical imaging and single-molecule detection [65]. 

Now, let us consider the current-volt age curve of the differential conductance (Fig. 7). First of all, Coulomb staircase is reproduced, which is more pronounced, than for metallic islands, because the density of states is limited by the available single-particle states and the current is saturated. Besides, small additional steps due to discrete energy levels appear. This characteristic... 

This chapter is organized into sections corresponding to various electrochemical characteristics of nanometallic particles. The introduction gives a brief idea of the basics of colloids together vith related literature. Subsequently, the electrochemistry with nanoparticles and ensembles of nanoelectrodes is explained followed by the electrochemical coulomb staircase behaviour of monolayer-protected nanometallic clusters. The investigation of nanoparticles using techniques based on combinations of different spectroscopic and electrochemical techniques is then reviewed. Sensors and electrocatalysis form the next sections and finally a summary and perspectives are given. 

Murray has demonstrated that soluble metallic clusters exhibit coulomb staircase-type behaviour [102]. The ionic space charge formed around the dissolved MFCs is reported to contribute to its capacitance, upon charging of the metal core. It is well known that small metal particles exhibit double layer charging (capacitive charging) properties in liquid electrolytes [104]. The sub-attofarad capacitance associated with the MFCs leads to charging of the tiny capacitor by single electron processes in potential intervals of A V that surpass ke T where is the Boltzmann constant and T is the temperature [102, 105]. 

D.K., and First, P.N. (1997) 28 kDa alkanethiolate-protected Au dusters give analogous solution electrochemistry and STM Coulomb staircases. Journal of the American Chemical Society, 119, 9279-9280. 

Andreas, R.P. Bein, T. Dorogi. M. Feng, S. Henderson, J.I. Kubiak, C.P. Mahoney, W. Osifchin. R.G. Reifen-berger. R. Coulomb staircase at room temperature in a self-assembled molecular nanostructure. Sience 1996, 272. 1323. 

These peculiarities of metal nanopartides do not, however, eliminate charging effects in them. Both, theoretical and experimental investigations have shown that the fundamental results of SET still hold true qualitatively. For example, the current-voltage characteristic of a double-barrier junction with a quantum dot (QD) possesses at low temperature, as well as the Coulomb staircase, a fine structure due to energy quantization inside the Q D. Nevertheless, the interpretation of these results is comphcated by the fact that the characteristic time RyC becomes as short as the characteristic time of the energy relaxation inside the QD, and consequently the... 

The I(V) characteristics of these devices showed a resistance of 700MQ at room temperature, and dear Coulomb staircases with a gap of 160 mV at 4.2 K (Figure 5.47a). 

R. Reifenberger Coulomb staircase at room temperature in a self-assembled molecular nanostructure, Science 272,1323-1325 (1996)... 

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