Using randomly distributed charges to create quantum dots

Using a combination of modeling and tunneling spectroscopy, we investigate how electrostatic potential fluctuations generated by randomly distributed ionized donors close to a quantum well can produce deep and strongly confined quantum-dot-like potential minima with a rich spectrum of zero-dimensional electronic energy levels. We consider different types of random distribution of donors and how the electronic properties can be controlled and investigated in appropriately designed double barrier resonant tunneling diodes.

Figure 1

(Color online) Distributions of positively charged donors close to a QW in a GaAs/AlAs $p\text{−}i\text{−}n$ RTD. (a) Distribution for diffusive charge. (b) A uniform and random “charged slab” distribution. (c) A $\delta$ layer of ionized donors.

Figure 2

(Color online) Numerical simulation of the electrostatic potential created by randomly distributed nanoclusters of ${\text{Mn}}_{\text{i}}$ ions for (a) $d=20\text{nm}$, (b) 15 nm, and (c) 10 nm. Parts (d), (e), and (f) represent corresponding Fock-Darwin-type energy spectra of electrons confined in the potential minima in the area indicated by a square. In figure (f), the three lowest energy states at low $B$ are labeled $1s$ and $2p_{x,y}$.

Figure 3

(Color online) (a) Numerical simulation of the electrostatic potential for an elongated quantum dot. (b) Energy spectra of the QD shown in part (a). (c) Probability to find a QD whose cross-section in the $\left(x,y\right)$ plane is approximated by an ellipse with axis ratio ${\omega }_2/{\omega }_1$ $\left({\omega }_2\ge {\omega }_1\right)$.

Figure 4

(Color online) Numerical simulation of the electrostatic potential created by (a) a uniform “slab” and (b) a $\delta$ layer distribution of ${\text{Mn}}_{\text{i}}$ donors. Parts (c) and (d) represent corresponding energy spectra of electrons confined in the potential minima.

Figure 5

(Color online) (a) Electrostatic potential profile along $x$ for $d=0.5$, 1, 2, 4, 10, 15, 20, 30, 40, and 60 nm. For clarity the curves are shifted along the vertical axis. The thicker line, corresponding to $d=15\text{nm}$, is shown in part (b) together with a parabolic fit around the minimum.

Figure 6

(a) and (b) $I\left(V\right)$ at zero magnetic field $\left(T=4.2\text{K}\right)$ for two mesa diodes. The corresponding gray scale plots of the differential conductivity as a function of $V$ and $B$ parallel to $z$ are shown in (c) and (d), respectively.