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In 1923 L. de Broglie [24] introduced a new fundamental hypothesis
that particles may
also have the characteristics of waves. Schrödinger expressed this
hypothesis 1926 in a definite form which is now known as the Schrödinger
wave equation. The continuous nonzero nature of its solution, the wave
function which
represents an electron or particle, implies an ability to penetrate
classically forbidden regions and a probability of tunneling from one
classically allowed region to another. Fowler and Nordheim [33]
explained in 1928 the main features of electron emission from cold metals by
high external electric fields on the basis of tunneling through a triangular
potential barrier. Conclusive experimental
evidence for tunneling was found by L. Esaki in 1957 [26]
and by I. Giaever in 1960. Esaki's tunnel diode had a large impact on the
physics of semiconductors, leading to important developments such as
the tunneling spectroscopy, and to increased understanding of tunneling
phenomena in solids.
L. Esaki [27], I. Giaever [41] and B. Josephson
[59] received 1973 the Nobel prize for their work
about tunneling in semiconductors, superconductors and theoretical predictions
of the properties of a supercurrent through a tunnel barrier, respectively.
The concept of resonant tunneling in double barriers was first introduced
by R. Davis and H. Hosack [21]. At about the same time C. Neugebauer
and M. Webb [90] and some years later H. Zeller and I. Giaever
[110] and J. Lambe and R. Jaklevic [73] studied granular
films. They observed a current suppression at low bias voltage, which is
today known as the Coulomb blockade. It took almost two decades until in 1985 D. Averin and
K. Likharev [8] formulated the
`orthodox' theory of single-electron tunneling
or short SET, which quantitatively describes important charging effects such
as Coulomb blockade and Coulomb oscillations. The orthodox theory makes the following assumptions: It
neglects dimensions and shapes of islands. Thus it is a zero-dimensional
model. The tunnel process is assumed to be instantaneous. Actually the
tunnel
time, the duration an electron spends below a barrier, is of the magnitude of
10^{-14} s [47]. Charge redistributions after a tunnel
event are also assumed to be instantaneous. In addition
energy spectra in leads and
islands are taken to be continuous. The main result of the orthodox theory
is that the rate of a tunnel event strongly depends on the change in
free energy the event causes.

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*Christoph Wasshuber*