The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered. (Less)

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Electronic structure of quantum dots

The physics of mesoscopic electronic systems has been explored for more than 15 years. Mesoscopic phenomena in transport processes occur when the wavelength or the coherence length of the carriers becomes comparable to, or larger than, the sample dimensions. One striking result in this domain is the quantization of electrical conduction, observed in a quasi-one-dimensional constriction formed between reservoirs of two-dimensional electron gas. The conductance of this system is determined by the number of participating quantum states or 'channels' within the constriction; in the ideal case, each spin-degenerate channel contributes a quantized unit of 2e^2/h to the electrical conductance. It has been speculated that similar behaviour should be observable for thermal transport in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results. Here we report the observation of a quantized limiting value for the thermal conductance, G_(th), in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predictions for phonon transport in a ballistic, one-dimensional channel: at low temperatures, G_(th) approaches a maximum value of g_0 = π^2k^2BT/3h, the universal quantum of thermal conductance.

Measurement of the quantum of thermal conductance

The ongoing miniaturization of solid state devices often leads to the question: “How small can we make resistors, transistors, etc., without changing the way they work?” The question can be asked a different way, however: “How small do we have to make devices in order to get fundamentally new properties?” By “new properties” we particularly mean those that arise from quantum mechanics or the quantization of charge in units of eeffects that are only important in small systems such as atoms. “What kind of small electronic devices do we have in mind?” Any sort of clustering of atoms that can be connected to source and drain contacts and whose properties can be regulated with a gate electrode. Practically, the clustering of atoms may be a molecule, a small grain of metallic atoms, or an electronic device that is made with modern chip fabrication techniques. It turns out that such seemingly different structures have quite similar transport properties and that one can explain their physics within one relatively simple framework. In this paper we investigate the physics of electron transport through such small systems.

Electron Transport in Quantum Dots

We investigate the thermal conductivity of silicon nanowires based on molecular dynamics (MD) simulations. The simulated thermal conductivities of nanowires with square cross sections are found to be about two orders of magnitude smaller than those of bulk Si crystals in a wide range of temperatures (200–500 K) for both rigid and free boundary conditions. A solution of the Boltzmann transport equation is used to explore the possibility of explaining the MD results based on boundary scattering.

Molecular dynamics simulation of thermal conductivity of silicon nanowires

The technology of high‐resolution focused ion beams has advanced dramatically in the past 15 years as focusing systems have evolved from laboratory instruments producing minuscule current densities to high current density tools which have sparked an important new process: direct micromachining at the micrometer level. This development has been due primarily to the exploitation of field emission ion sources and in particular the liquid‐metal ion source. Originally developed in the early 1960’s as a byproduct of the development of electrostatic rocket engines, the liquid‐metal ion source was adapted for focused beam work in the late 1970’s, when it was demonstrated that submicrometer focused ion beams could be produced with current densities greater than 1 A cm−2. Ions can be produced with liquid‐metal ion sources from elements including Al, As, Au, B, Be, Bi, Cs, Cu, Ga, Ge, Fe, In, Li, P, Pb, Pd, Si, Sn, and Zn. In the past decade, focused ion beam systems with liquid‐metal ion sources have had a signific...

High‐resolution focused ion beams

A scanning ion beam lithography system has been used for the rework of chromium‐on‐glass mask plates to repair defects in the VLSI circuit pattern. By using submicrometer diameter beams of gallium and of gold ions to sputter selected areas of the mask, both clear and opaque areas have been generated on the substrate.

Application of a focused ion beam system to defect repair of VLSI masks

Strong image contrast from ion channelling has been observed in gold specimens in a high-resolution scanning ion microscope. This contrast is seen to persist after sputtering, and this effect has been used to investigate simultaneously the comparative sputtering rates of different crystal faces. The specimen is scanned with a finely focused probe o f gallium ions from a liquid-metal field-ion source [1] in a two-lens ionoptical system [2]. The ion probe liberates secondary electrons for imaging. Material is also removed from the specimen as sputtered neutral atoms, and the surface layer becomes disordered. As imaging and surface modification of the specimen occur in the same instrument, changes in the surface and comparative sputtering rates can be observed directly, for precisely selected regions of the specimen. The present work was undertaken to investigate the interdependence of directional effects on the sputtering rate and the secondary-electron emission from materials, both of which are affected by ion

Channelling ion image contrast and sputtering in gold specimens observed in a high-resolution scanning ion microscope

Focused ion beam repair techniques for clear and opaque defects in masks

Freestanding wires of submicrometer width and with lengths up to 40 μm have been fabricated from single‐crystal GaAs and Si for studies of quantum transport. Fabrication techniques are described, and the low‐temperature properties for semiconductors and metals such as AuPd are compared. Fabrication of three‐terminal freestanding GaAs metal–semiconductor field effect transistor structures is demonstrated.

Fabrication of submicrometer freestanding single‐crystal gallium arsenide and silicon structures for quantum transport studies

The authors report on experiments, and their analysis, on electron heating effects in 3.2 mu m long free-standing fine wires (triangular cross-section with approximately=0.5 mu m side) of single-crystal GaAs doped at 1017 cm-3. The data can be used to extract a thermal conductivity that has a linear temperature dependence, consistent with a contribution from electrons and/or one-dimensional phonons they show that the electronic contribution dominates.

J. R. A. Cleaver

Papers

Application of a focused ion beam system to defect repair of VLSI masks

Channelling ion image contrast and sputtering in gold specimens observed in a high-resolution scanning ion microscope

Focused ion beam repair techniques for clear and opaque defects in masks

Fabrication of submicrometer freestanding single‐crystal gallium arsenide and silicon structures for quantum transport studies

Electron heating effects in free-standing single-crystal GaAs fine wires