14.4 Quantum Dots
419
Fig. 14.30 a Schematic sample geometry for side-gated In 0.05 Ga 0.95 As/Al 0.22 Ga 0.68 As disk-shaped quantum dot. b
Coulomb oscillations in the current versus gate voltage at B = 0 T observed for a D = 0.5 µm disk-shaped dot. c
Addition energy versus electron number for two different dots with D = 0.50 and 0.44 µm. Adapted from [1391]
Fig. 14.31 a Schematic layer sequence of epitaxial structure comprising a n-AlGaAs/GaAs heterointerface with a twodimensional electron gas and a layer of InAs/GaAs quantum dots. b and c are corresponding band diagrams with no gate
bias and gate voltage below the critical value, respectively. d Experimental dependence of drain current on gate voltage
in a split-gate structure at a drain source voltage of 10 µV. Inset: Dependence of valley current on temperature (squares)
with theoretical fit. Reprinted with permission from [1392], ©1997 AIP
E 21 = 00|W ee |00 =
2
0 (r
1
e ) W ee (r
1
e , r
2
e ) )
2
0 (r
2
e ) d
3 r
1
e d
3 r
2
e ,
(14.23)
where W ee denotes the Coulomb interaction of the two electrons and 0 the ground state (single
particle) electron wavefunction. The matrix element gives an upper bound for the charging energy
since the wavefunctions will rearrange to lower their overlap and the repulsive Coulomb interaction.
For lens-shaped InAs/GaAs quantum dots with radius 25 nm a charging energy of about 30 meV has
been predicted.
419
Fig. 14.30 a Schematic sample geometry for side-gated In 0.05 Ga 0.95 As/Al 0.22 Ga 0.68 As disk-shaped quantum dot. b
Coulomb oscillations in the current versus gate voltage at B = 0 T observed for a D = 0.5 µm disk-shaped dot. c
Addition energy versus electron number for two different dots with D = 0.50 and 0.44 µm. Adapted from [1391]
Fig. 14.31 a Schematic layer sequence of epitaxial structure comprising a n-AlGaAs/GaAs heterointerface with a twodimensional electron gas and a layer of InAs/GaAs quantum dots. b and c are corresponding band diagrams with no gate
bias and gate voltage below the critical value, respectively. d Experimental dependence of drain current on gate voltage
in a split-gate structure at a drain source voltage of 10 µV. Inset: Dependence of valley current on temperature (squares)
with theoretical fit. Reprinted with permission from [1392], ©1997 AIP
E 21 = 00|W ee |00 =
2
0 (r
1
e ) W ee (r
1
e , r
2
e ) )
2
0 (r
2
e ) d
3 r
1
e d
3 r
2
e ,
(14.23)
where W ee denotes the Coulomb interaction of the two electrons and 0 the ground state (single
particle) electron wavefunction. The matrix element gives an upper bound for the charging energy
since the wavefunctions will rearrange to lower their overlap and the repulsive Coulomb interaction.
For lens-shaped InAs/GaAs quantum dots with radius 25 nm a charging energy of about 30 meV has
been predicted.