Transport in Quantum Dots: Observation of Atomlike Properties
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Quantum Dots: Observation of Atomlike Properties Seigo Tarucha
Introduction 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.1'2 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 wellknown in atom physics that the threedimensional spherically symmetric potential around atoms gives rise to the shell structure Is, 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.3 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 MRS BULLETIN/FEBRUARY 1998
tunneling devices 4 9 and submicron gated resonant-tunneling devices,10"14 and capacitance measurements on submicron double-barrier structures. 1516 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.17'18 In this circular disk, electrons are strongly confined in the vertical direction and are parabolically confined in the lateral direction. This system has a high degree of rotational symmetry, which leads to sets of degenerate singleparticle states equally spaced by ho}0 where hco0 is the parabolic confinement energy (h is the Planck constant divided by 2TT, and wo is the characteristic frequency of a parabolic potential). These single-particle states can be consecutively filled with noninteracting electrons. For the actual filling of electrons in the dot however, this single-particle picture can be significantly modified by electron-electron interactions. Neverthe-
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