Single electron tunnelling

The results discussed in Sections 3.1-3.3 turned out as very valuable with respect to the knowledge about the transition from bulk metal to molecule. The most important method, however, to gain direct information from individual metal nanoparticles on their inner electronic life is the tunnelling spectroscopy. The method is based on the single-electron tunnelling (SET) through an intermediate island between two metal electrodes as is indicated in Figure 10. 

Grabert H, Devoret MH (1972) Single electron tunneling. Plenum, New York... 

Li B, Zeng C, Zhao J, Yang J, Hou JD, Zhu Q (2006) Single-electron tunneling spectroscopy of single C60 in double-barrier tunnel junction. J Chem Phys 124 064709-064720... 

Porath D, Millo O (1997) Single electron tunneling and level spectroscopy of isolated Cgo molecules. J Appl Phys 81 2241... 

For noninteracting electrons the transition rates are determined by the single-electron tunneling rates, and are nonzero only for the transitions between the states with the number of electrons different by one. For example,... 

The important point is, that the leads are actually in the equilibrium mixed state, the single electron states are populated with probabilities, given by the Fermi-Dirac distribution function. Taking into account all possible single-electron tunneling processes, we obtain the incoming tunneling rate... 

To proceed, we introduce the following Hamiltonian, describing single electron tunneling and charging of the nanosystem state... 

At finite bias voltage we find new manifestations of the interplay between single-electron tunneling and resonant free-particle tunneling. 

Taking into account all possible single-electron tunneling processes, we obtain the incoming tunneling rate... 

E The heme group may not be too deeply buried inside the enzyme. Single electron tunneling jumps greater than about 20 A do not happen, although much can be done (Heller and Delgani, 1987) to facilitate successive jumps. 

A preliminary result from measurements based on the atom beam interferometry of the Cesium atom has also been reported [37]. The He atom fine structure will become another source of high precision a when the current theoretical work is completed [38,39,40,41,42]. fo js fortunate that so many independent ways are available for obtaining high precision a. Precision of some measurements may exceed 1 in 108 in the near future. Even higher precision might be achieved by techniques based on the atom interferometry [43] and the single electron tunneling [44]. 

T. Ohgi and D. Fujita, Consistent Size Dependency of Core-Level Binding Energy Shifts and Single-Electron Tunneling Effects in Supported Gold Nanoclusters, Phys. Rev. B 66, 115410-115415 (2002). 

Saville, G.F., Goodkind, J.M. and Platzman, P.M. (1993). Single-electron tunneling from bound states on the surface of liquid helium, Phys. Rev. Lett. 70, 1517-1520. 

Apart from their interesting structures, molecular clusters are intensively studied because of their physical properties. It has been shown for transition-metal clusters that small uniform particles of a certain size show interesting electronic, size-dependent effects (quantum size effects). In Au55(PR3)i2Cl6 a few electrons are trapped in a metallic state and single electrons tunnel between the cluster units. (SET, single electron tunneling).Such effects have yet to be observed in main-... 

For these very thin oxide films (d < 10 nm), single electron tunnel processes... 

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