Quantum Dots

QDs are nanostructures electrostatically or structurally isolated from the outside in which electrons are confined. Typically QDs consist of a few hundreds to a few millions of atoms, but only a small number of electrons (<100) are free. Depending on electron confinement, it is possible to distinguish between planar QDs, vertical QDs, and self-assembled QDs.

2.1. Planar Quantum Dots

The first experiments with semiconductor QDs were made with planar structures by patterning several Schottky metal gates above the surface of a two-dimensional electron gas (2DEG) which isolates electrostatically a small region and form a planar quantum dot (PQD) [7, 19-25] (for a more exhaustive list see, e.g., [26]). An example of such structure is depicted on Figure 2. By applying a negative bias on the top gate, electrons are repelled and a small island is isolated at the center of the 2DEG, at the n+GaAs/AlGaAs

Top Gate

Figure 2. Schematic diagram of a PQD showing the gates and different material layers.

Back Gate

Figure 2. Schematic diagram of a PQD showing the gates and different material layers.

interface. A back gate allows one to change the dot confinement and thus the number of electrons inside the dot.

PQDs have two main characteristics. (i) The current flows in the 2DEG plane; (ii) the tunnel barrier are created electrostatically which has an advantage: their height is controllable. However, electrostatic barriers are weak (a few meV high) and thick (~100 nm). Moreover they have variable shape which is strongly influenced by the gate voltage. That makes PQDs quite sensitive to external perturbations.

2.2. Vertical Quantum Dots

In vertical quantum dots (VQDs), the zero-dimensional region is sandwiched vertically between a double resonant tunneling barrier made of heterostructure layers, and lateral confinement is achieved by a combination of deep mesa etching and electrostatic depletion [8, 9, 11, 27-37]. The dot confinement is controlled by a Schottky gate that is deposited on top of the mesa [30] or is wrapped around it [31]. VQD atomiclike properties were first evidenced by Ashoori, by capacitance spectroscopy measurements [8, 29, 30]. Later, in addition to the quantum features mentioned above, spin effects were clearly observed by Tarucha in experiments with a device similar to the one depicted in Figure 3 [9, 11, 31, 34, 35].

The main characteristics of VQD are: (i) the current flows vertically, perpendicularly to the 2DEG plane; (ii) the tunnel

undoped AlGaAs undoped InGaAs Schottky gate

Figure 3. Schematic diagram of Tarucha's VQD. Adapted with permission from [11], S. Tarucha et al., Phys. Rev. Lett. 77, 3613 (1996). © 1996, American Institute of Physics.

undoped AlGaAs undoped InGaAs Schottky gate

Figure 3. Schematic diagram of Tarucha's VQD. Adapted with permission from [11], S. Tarucha et al., Phys. Rev. Lett. 77, 3613 (1996). © 1996, American Institute of Physics.

barriers are high (>100 meV) and thin (~10 nm) because they are due to the large bandgap material such as GaAs, but then, they are not electrically tunable. VQDs are therefore less sensitive to external fluctuations.

The most popular device made with PQDs and VQDs is the single-electron transistor (SET) in which the QD replaces the inversion channel of conventional MOSFETs [38]. Potential applications for SETs are metrology [39, 40], optical detectors [16], and ultradense digital logic circuits [15]. However, due to their high sensitivity to random background charges, SETs future is not clear [6].

2.3. Self-Assembled Quantum Dots

In PQDs and VQDs, electrostatic confinement leads typically to dimensions around 100 nm, and structural confinement is of the order of 10 nm. The eigenlevel separation of a rectangular box of such dimensions is about 1 meV. To prevent quantum effects from being smeared out by thermal fluctuations, experiments with PQDs and VQDs are conducted at very low temperature, typically below 1 K [7, 11].

When a few monolayers of InAs are grown on a GaAs substrate, the lattice mismatch between the two materials induces a strain which leads to the breakdown of a 2D layered structure and the emergence of randomly distributed self-crystallized islands called self-assembled quantum dots (SAQDs) on the GaAs substrate [41-44] (for a more complete list of references see, e.g., Jiang [45]). The confinement in SAQDs is determined by the conduction band offset between InAs and GaAs and is therefore much stronger than in PQDs and VQDs. This leads to pyramidal or lens-shape structures with sizes of approximately 100 A. Pyramidal QDs are very promising structures for laser applications [46-49] because of their spectral purity, relative insensitivity to temperature, low current threshold, and high differential gain [50, 51]. However, they are relatively small to be addressed individually by electrical means, which constitutes an important drawback for electronic applications.

Even more promising candidates for room temperature devices are the so called "silicon nanocrystal s" which consist of 50 A diameter spherical silicon particles embedded in silicon dioxide [52-55]. Here the eigenlevel separation is typically about 100 meV [56]. Several groups have fabricated flash memories based on nanocrystal s which surpass classical CMOS devices in terms of retention time and power consumption.

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