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)

/pdf/electronic-structure-of-quantum-dots-c4uhdr9l0b.pdf

Electronic structure of quantum dots

Progress in semiconductor technology has enabled the fabrication of structures so small that they can contain just one mobile electron. By varying controllably the number of electrons in these 'artificial atoms' and measuring the energy required to add successive electrons, one can conduct atomic physics experiments in a regime that is inaccessible to experiments on real atoms.

Electrons in artificial atoms

I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

/pdf/quantum-transport-in-semiconductor-nanostructures-1n3dkljf6x.pdf

Quantum Transport in Semiconductor Nanostructures

Publisher Summary Quantum transport is conveniently studied in a two-dimensional electron gas (2DEG) because of the combination of a large Fermi wavelength and large mean free path. Semiconductor nanostructures are unique in offering the possibility of studying quantum transport in an artificial potential landscape. This is the regime of ballistic transport in which scattering with impurities are neglected. The chapter presents a self-contained account of these three novel transport regimes in semiconductor nanostructures. The study of quantum transport in semiconductor nanostructures is motivated by more than scientific interest. The fabrication of nanostructures relies on sophisticated crystal growth and lithographic techniques that exist because of the industrial effort toward the miniaturization of transistors. Conventional transistors operate in the regime of classical diffusive transport, which breaks down on short length scales. The discovery of novel transport regimes in semiconductor nanostructures provides options for the development of innovative future devices.

/pdf/quantum-transport-in-semiconductor-nanostructures-3vpunw3uta.pdf

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 observe the magnetic-field-induced bifurcation of quantum levels into surface states and bulklike Landau States. The disruption of the electric field quantization by a magnetic field is most dramatic for electrons bound in two dimensions perpendicular to the magnetic field. The interplay between competing spatial and magnetic quantization mechanisms results in a pronounced and complex level splitting. The observed splitting of zero-dimensional energy levels depends critically on the size of the quantum dots, and can be explained with a calculated single-particle energy spectrum.

Zeeman bifurcation of quantum-dot spectra.

We have observed fractional quantization of very few electrons confined in a semiconductor quantum dot using capacitance spectroscopy. The number of electrons per dot varies from 0 to about 40 as a function of bias on the quantum capacitors. The capacitance spectra have clear minima at gate voltages and magnetic fields, where the filling factors are 1/3 and 2/3. These measurements may allow direct comparison with few‐particle calculations.

Fractional states in few‐electron systems

We have devised and demonstrated a novel technique for fabricating structures with nanometer scale features in semiconductor heterostructures. The technique is based on definition of nanometer scale patterns by submicron trenches in a GaAs‐AlGaAs heterostructure. The depletion of free carriers below the trenches gives rise to very strong electrostatic confinement. This technique avoids the complications associated with the use of negative resist materials and lift‐off techniques while minimizing the time required to expose densely packed patterns. Aharonov–Bohm rings fabricated using this technique exhibit interference oscillation larger than any reported previously.

Submicron trenching of semiconductor nanostructures

This paper demonstrates a submicron trenching technique for defining low‐dimensional electron systems in GaAs/GaAlAs heterostructures for transport measurements. A variety of electron systems can be defined between trenches as narrow as 200 nm etched into a suitable heterostructure. The use of narrow trenches gives the advantages of high resolution, simplicity, and flexibility, and also avoids the complications associated with negative resists and lift‐off techniques. Using the trenching technique, we have fabricated Aharonov–Bohm ring devices with a Schottky gate over the entire ring. At 0.4 K, these devices exhibit clear interference effects which are dependent on the gate bias.

W. Hansen

Papers

Zeeman bifurcation of quantum-dot spectra.

Fractional states in few‐electron systems

Submicron trenching of semiconductor nanostructures

Fabrication of GaAs/GaAlAs transport devices using a deep submicron trench etching technique

Hansen, Smith, and Lee reply.