Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 17

This additional energy is equal to e 2 =2C in metallic islands, where C is the
capacitance between the island and the surrounding medium, and leads to a gap
of e 2 =C in the electron energy spectrum at the Fermi level since, in addition to
electrons, holes need the same additional energy e 2 =2C to tunnel in or out of the
island. The Coulomb blockade phenomenon is observed when e 2 =C k B T ,which
implies low temperatures, and when the electron number on the island is constant.
The last condition is fulfilled if e 2 =C is much larger than the lifetime broadening
„ =,where denotes the electronic lifetime. Alternatively, in terms of an effective
RC time, this requirement can be written as R h=e 2 , which means that the
island is decoupled from the reservoirs through tunneling barriers with much larger
resistances in comparison to the quantum resistance.
As displayed in Fig. 1.16 b, c, in the presence of Coulomb blockade, an electron
can tunnel into a metallic island only if a large enough bias is applied, V>e=C,
which overcomes the charging energy. As a result, in the I V characteristic of
the island, the current has very low values around zero bias. On the contrary, when
V D e=C a single electron from one lead can tunnel in the island, leading to an
increase of the Fermi energy in the island by e 2 =C, and a subsequent tunneling event
is forbidden by the opening of another energy gap, unless the applied bias raises to
V>3e=Cor the additional electron in the island tunnels out of it. Summarizing,
the average electron number in the island augments with one whenever the voltage
increases with 2e=C. As a consequence of these correlated tunneling events into
and out of the island, the net current increases, and the I V characteristic
acquires a staircase shape when the two junctions differ significantly ( Ferry and
Goodnick 2009 ).
The Coulomb blockade phenomenon in ballistic semiconductor islands can be
treated in an analogous manner except that the quantization of energy must be
included in the model (size quantization effects are not relevant in metallic clusters
because the conditions for ballistic transport are not satisfied, in general). In this
case, the additional energy needed to add an electron to the island is e 2 =C C E,
where E is the difference between the energies of adjacent discrete quantum
states.
The single-electron Coulomb blockade phenomenon is caused by the discrete-
ness of electric charge that can be transferred to and from a conducting island
connected through thin barriers to electron reservoirs. On the contrary, resonant
tunneling devices are based on the discreteness of resonant energy levels in a
quantum well coupled to electron reservoirs through thin barriers. The Coulomb
blockade effect controls precisely the (small) number of electrons in the island and is
employed in low-power switching devices that are essential for an increased level of
circuit integration. In general, single-electron devices based on Coulomb blockade
have an additional control of the electric charge in the island via a gate electrode,
which leads to periodic current oscillations through the leads as the gate voltage is
modified.