14.4 Quantum Dots
417
(a)
-0.5
0.5
-0.55
-0.6
1.0
2
0
G
(b)
Fig. 14.26 a Conductivity (Coulomb oscillations) and b current–voltage diagram at different gate voltages (Coulomb
staircase, shifted vertically for better readability) of a tunnel junction with a quantum dot as in Fig. 14.25. Adapted from
[1386], reprinted with permission, ©1991, SpringerNature
Fig. 14.27 Chemical
potentials of source and
drain and of a quantum dot
in between them. a, b, and
c show the sequence for a
variation of the gate voltage
and visualize the origin of
the Coulomb oscillations
(see Fig. 14.26a). d, e and f
visualize a variation of the
source–drain voltage and
the origin of the Coulomb
staircase (cf. Fig. 14.26b)
C G (V G − V S ), we find (C = C G + C S + C D ),
V S =
1
C
(Q + C G V G + C D V SD )
(14.20)
V D =
1
C
(−Q − C G V G + (C − C D ) V SD ) .
(14.21)
Now, if for a given pair of (V G , V SD ) in a diagram like Fig. 14.28b the current is Coulomb-blocked
and low, then it is for all voltages with the same charge Q on the dot and either the same V S or
V D . The derivatives of (14.20) and (14.21) yield the slopes ∂ V SD /∂ V G = γ 1 = −C G /C D and γ 2 =
+C G /(C G + C S ), respectively, that defined the borders of the diamond in the schematic stability
diagram as depicted in Fig. 14.29. We note that such analysis is allowed when |V S |, |V D | | e/2C
and the quantum dot circuit can be treated as a system of capacitors (inset in Fig. 14.25a). Changing
Q to Q − e requires V G to increase by e/C G for the same V S,D , yielding the periodicity of the stability
diagram.
Single electron tunneling (SET) circuits [1387] are investigated with respect to metrology for a
novel ampere standard [1389].
417
(a)
-0.5
0.5
-0.55
-0.6
1.0
2
0
G
(b)
Fig. 14.26 a Conductivity (Coulomb oscillations) and b current–voltage diagram at different gate voltages (Coulomb
staircase, shifted vertically for better readability) of a tunnel junction with a quantum dot as in Fig. 14.25. Adapted from
[1386], reprinted with permission, ©1991, SpringerNature
Fig. 14.27 Chemical
potentials of source and
drain and of a quantum dot
in between them. a, b, and
c show the sequence for a
variation of the gate voltage
and visualize the origin of
the Coulomb oscillations
(see Fig. 14.26a). d, e and f
visualize a variation of the
source–drain voltage and
the origin of the Coulomb
staircase (cf. Fig. 14.26b)
C G (V G − V S ), we find (C = C G + C S + C D ),
V S =
1
C
(Q + C G V G + C D V SD )
(14.20)
V D =
1
C
(−Q − C G V G + (C − C D ) V SD ) .
(14.21)
Now, if for a given pair of (V G , V SD ) in a diagram like Fig. 14.28b the current is Coulomb-blocked
and low, then it is for all voltages with the same charge Q on the dot and either the same V S or
V D . The derivatives of (14.20) and (14.21) yield the slopes ∂ V SD /∂ V G = γ 1 = −C G /C D and γ 2 =
+C G /(C G + C S ), respectively, that defined the borders of the diamond in the schematic stability
diagram as depicted in Fig. 14.29. We note that such analysis is allowed when |V S |, |V D | | e/2C
and the quantum dot circuit can be treated as a system of capacitors (inset in Fig. 14.25a). Changing
Q to Q − e requires V G to increase by e/C G for the same V S,D , yielding the periodicity of the stability
diagram.
Single electron tunneling (SET) circuits [1387] are investigated with respect to metrology for a
novel ampere standard [1389].