Semiconductor “quantum dots” refer to nanometer-sized, giant (103–105 atoms) molecules made from ordinary inorganic semiconductor materials such as Si, InP, CdSe, etc. They are larger than the traditional “molecular clusters” (~1 nanometer containing ≤100 atoms) common in chemistry yet smaller than the structures of the order of a micron, manufactured by current electronic-industry lithographic techniques. Quantum dots can be made by colloidal chemistry techniques (see the articles by Alivisatos and by Nozik and Mićić in this issue), by controlled coarsening during epitaxial growth (see the article by Bimberg et al. in this issue), by size fluctuations in conventional quantum wells (see the article by Gammon in this issue), or via nano-fabrication (see the article by Tarucha in this issue).

The study of nanometer-sized semiconductor crystals has been advancing at a rapid pace. Much of the interest in these materials stems from the fact that their physical and chemical properties can be systematically tuned by variation of the size, according to increasingly well-established scaling laws. This article describes colloidal semiconductor nanocrystals belonging to the II-VI and III-V families, and outlines strategies for obtaining electrical access to such dots.

If an inorganic cluster exceeds a certain size—generally in the 10s of unit cells—then it will likely possess a bonding geometry characteristic of a bulk phase. Above this critical size, the nature of the chemical bonds in the cluster remains fixed as a function of the size, but the total number of atoms—or the surface to volume ratio—changes smoothly. This leads to a slow extrapolation of the properties for ideal nanocrystals toward bulk values with increasing size, according to the scaling laws. The ability to control systematically the properties of inorganic materials by variation of size and shape is an important development with many implications for how materials should be processed and assembled.

Many scaling laws have been investigated, including the size variation of bandgap, charging energy, magnetization reversal, and melting. Study of the scaling laws reveals lessons for how to make nanocrystals. This article focuses on the properties of colloidal semiconductor nanocrystals, how to make them, and ways of gaining electrical access to them. Advances in metal, magnetic, and structural nanomaterials are also occurring. Semiconductor dots produced by other processing techniques in the articles by Bimberg, Gammon, and Tarucha in this issue.

Quantization effects in semiconductor structures were first demonstrated in the early 1970s in III-V quantum wells; these structures consisted of a thin epitaxial film of a smaller bandgap (Eg) semiconductor (e.g., GaAs, Eg = 1.42 eV) sandwiched between two epitaxial films of a larger bandgap semiconductor (e.g., Al0.3Ga0.7As, Eg = 2.0 eV). The conduction- and valence-band offsets of the two semiconductor materials produce potential barriers for electrons and holes, respectively. The smaller bandgap semiconductor constitutes the quantum-well region and the larger bandgap material the potential barrier region. If the film of the smaller bandgap material is sufficiently thin (thickness less than the de-Broglie wavelength of the charge carriers, which typically requires thicknesses less than about 300 Å for III-V semiconductors), then the charge carriers are confined in one dimension by the potential barriers, and quantization of the energy levels for both electrons and holes can occur (Figure 1).

The development and application of semiconductor light-emitting and laser diodes has been a huge success during the last 30 years in key areas of modern technology like communications, recording, and printing. Still there is ample room for improvement through combination of the atomlike properties for zero-dimensionally localized carriers in quantum dots (QDs) with state-of-the-art semiconductor-laser technology. Low, temperature-insensitive threshold current; high gain; and differential gain have been predicted since the early 1980s.

In the past two decades, the fabrication of QDs has been attempted using colloidal techniques (see the article by Nozik and Mićić in this issue), patterning, etching, and layer fluctuations (see the article by Gammon in this issue). However a break-through occurred recently through the employment of self-ordering mechanisms during epitaxy of lattice-mismatched materials (see the next section) for the creation of high-density arrays of QDs that exhibit excellent optical properties, particularly high quantum efficiency, up to room temperature. The zero-dimensional carrier confinement and subsequent atomlike electronic properties have a drastic impact on optical properties (see the section on Spectroscopy). Also intimately connected is the applicability of QDs as a novel gain medium in state-of-the-art laser diodes with superior properties (see the section on Lasers).

Progress made in the growth of “free-standing” (e.g., colloidal) quantum dots (see also articles in this issue by Nozik and Mićić, and by Alivisatos) and in the growth of semiconductor-embedded (“self-assembled”) dots (see also the article by Bimberg, Grundmann, and Ledentsov in this issue) has opened the door to new and exciting spectroscopic studies of quantum structures. These have revealed rich and sometimes unexpected features such as quantum-dot shape-dependent transitions, size-dependent (red) shifts between absorption and emission, emission from high excited levels, surface-mediated transitions, exchange splitting, strain-induced splitting, and Coulomb-blockade transitions. These new observations have created the need for developing appropriate theoretical tools capable of analyzing the electronic structure of 103–106-atom objects. The main challenge is to understand (a) the way the one-electron levels of the dot reflect quantum size, quantum shape, interfacial strain, and surface effects and (b) the nature of “many-particle” interactions such as electron-hole exchange (underlying the “red shift”), electron-hole Coulomb effects (underlying excitonic transitions), and electron-electron Coulomb (underlying Coulomb-blockade effects).

Interestingly, while the electronic structure theory of periodic solids has been characterized since its inception by a diversity of approaches (all-electron versus pseudopotentials; Hartree Fock versus density-functional; computational schemes creating a rich “alphabetic soup,” such as APW, LAPW, LMTO, KKR, OPW, LCAO, LCGO, plane waves, ASW, etc.), the theory of quantum nano-structures has been dominated mainly by a single approach so widely used that I refer to it as the “Standard Model”: the effective-mass approximation (EMA) and its extension to the “k · p” (where k is the wave vector and p is the momemtum). In fact, speakers at nanostructure conferences often refer to it as “theory” without having to specify what is being done. The audience knows.

Currently spectroscopists are studying many semiconductor quantum-dot (QD) systems in great detail because of their scientific and technological importance. However as in all nanostructure systems in which significant confinement energies exist, size fluctuations lead to inhomogeneous broadening of the spectral lines. This blurring of the spectra severely reduces the amount of information obtainable from spectroscopy. The finding has initiated an effort to isolate optically and study spectroscopically individual QDs. Studies involving individual QDs in most QD systems have been published. Here the results of a series of experiments are reviewed on GaAs QDs defined by interface fluctuations in narrow GaAs quantum wells. These experiments demonstrate the elegance and potential of single-QD spectroscopy.

An example of single-QD photoluminescence (PL) spectroscopy appears in Figure 1. The spectra shown were obtained at a temperature of 6 K by successively reducing the size of the laser spot on a GaAs quantum-well sample through the use of small apertures in a metal mask. The bottom trace is a PL spectrum obtained with a macroscopic laser spot diameter of 25μm. The spectrum shows two broad peaks corresponding to the recombination of excitons in parts of the quantum well that are either 10 or 11 monolayers wide (2.8 or 3.1 nm). The spectrum is strongly inhomogeneously broadened as shown most directly by a reduction in the aperture size. The relatively broad lines break up into a decreasing number of extraordinarily narrow PL spikes as the aperture is reduced to submicroscopic dimensions. These PL spikes arise from excitons localized in individual QD potentials. Remarkably the linewidth decreases from several meV in the ensemble-averaged spectrum (25-μm aperture) to 10s of μeV in the single QD spectra, corresponding to an effective improvement in resolution of two orders in magnitude. By probing individual QDs, it becomes possible to resolve directly a number of phenomena that previously were hidden in the inhomogeneous linewidth.

Recent advances in nanofabrication technologies have enabled us to fabricate semiconductor quantum dots in which electrons are three-dimensionally confined. These quantum dots are often referred to as artificial atoms since their electronic properties—for example the ionization energy and discrete excitation spectrum—resemble those of real atoms. Electrons bound to a nucleus potential encounter sufficiently strong effects of quantum-mechanical confinement and mutual Coulomb interactions that they are well arranged in ordered states, and this leads to the arrangement of atoms in the periodic table. It is well known in atom physics that the threedimensional spherically symmetric potential around atoms gives rise to the shell structure 1s, 2s, 2p, 3s, 3p,…. The ionization energy has a large maximum for atomic numbers 2, 10, 18,…. Up to atomic number 23, these shells are filled sequentially. Hund's rule determines whether a spin-down or a spin-up electron is added. This article describes how closely we can approach the electronic properties of real atoms through the use of semiconductor quantum dots.

Both the effects of quantum confinement and Coulomb interaction become strong in quantum dots when the dot size is comparable to the electron wavelength and contains just a few electrons. The consequence of these factors on transport have only recently been studied in vertical-dot devices, which contain a dot located between source and drain contacts by means of heterostructure tunnel barriers because the few-electron regime is only accessible in the vertical-dot device. Studies include transport measurements through submicron resonant tunneling devices and submicron gated resonant-tunneling devices, and capacitance measurements on submicron double-barrier structures. However quantum-dot devices usually contain some disorder—for instance because of impurities or when the shape of the dot is irregular—which readily causes sample specific inhomogeneity in the electronic properties. Clean quantum dots, in the form of regular disks, have only recently been fabricated in a semiconductor heterostructure (Figure 1), and have been used to study the atomlike properties of artificial atoms.