Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

36 J.M. Elzerman et al.
a b c d
µ( N+ 1)
µ S µ( N)
µ D
µ( N-1)
E add
Γ L
µ( N+ 1)
µ( N )
Γ R
eV SD
µ( N )
∆E
µ( N+ 1)
µ( N)
Fig. 7. Schematic diagrams of the electrochemical potential of the quantum dot
for different electron numbers. (a) No level falls within the bias window between
µS and µD, sotheelectronnumberisfixedatN − 1 due to Coulomb blockade.
(b) Theµ(N) level is aligned, so the number of electrons can alternate between N
and N − 1, resulting in a single-electron tunneling current. The magnitude of the
current depends on the tunnel rate between the dot and the reservoir on the left,
ΓL, andontheright, ΓR. (c) Both the ground-state transition between N − 1and
N electrons (black line), as well as the transition to an N-electron excited state
(gray line) fall within the bias window and can thus be used for transport (though
not at the same time, due to Coulomb blockade). This results in a current that is
different from the situation in (b). (d) The bias window is so large that the number
of electrons can alternate between N − 1, N and N + 1, i.e. two electrons can tunnel
onto the dot at the same time
electrons on the dot remains fixed and no current flows through the dot. This
is known as Coulomb blockade.
Fortunately, there are many ways to lift the Coulomb blockade. First,
we can change the voltage applied to the gate electrode. This changes the
electrostatic potential of the dot with respect to that of the reservoirs, shifting
the whole “ladder” of electrochemical potential levels up or down. When a level
falls within the bias window, the current through the device is switched on. In
Fig. 7b µ(N) is aligned, so the electron number alternates between N − 1and
N. This means that the Nth electron can tunnel onto the dot from the source,
but only after it tunnels off to the drain can another electron come onto the
dot again from the source. This cycle is known as single-electron tunnelling.
By sweeping the gate voltage and measuring the current, we obtain a trace
as shown in Fig. 8a. At the positions of the peaks, an electrochemical potential
level is aligned with the source and drain and a single-electron tunnelling
current flows. In the valleys between the peaks, the number of electrons on
the dot is fixed due to Coulomb blockade. By tuning the gate voltage from
one valley to the next one, the number of electrons on the dot can be precisely
controlled. The distance between the peaks corresponds to EC + ∆E, and can
therefore give information about the energy spectrum of the dot.
A second way to lift Coulomb blockade is by changing the source-drain
voltage, VSD (see Fig. 7c). (In general, we keep the drain potential fixed, and
change only the source potential.) This increases the bias window and also
“drags” the electrochemical potential of the dot along, due to the capacitive
coupling to the source. Again, a current can flow only when an electrochemical