Molybdenum disulfide (MoS(2)) of single- and few-layer thickness was exfoliated on SiO(2)/Si substrate and characterized by Raman spectroscopy. The number of S-Mo-S layers of the samples was independently determined by contact-mode atomic force microscopy. Two Raman modes, E(1)(2g) and A(1g), exhibited sensitive thickness dependence, with the frequency of the former decreasing and that of the latter increasing with thickness. The results provide a convenient and reliable means for determining layer thickness with atomic-level precision. The opposite direction of the frequency shifts, which cannot be explained solely by van der Waals interlayer coupling, is attributed to Coulombic interactions and possible stacking-induced changes of the intralayer bonding. This work exemplifies the evolution of structural parameters in layered materials in changing from the three-dimensional to the two-dimensional regime.

We model, in an elementary way, the excited electronic states of semiconductor crystallites sufficiently small (∼50 Å diam) that the electronic properties differ from those of bulk materials. In this limit the excited states and ionization processes assume a molecular-like character. However, diffraction of bonding electrons by the periodic lattice potential remains of paramount importance in the crystallite electronic structure. Schrödinger’s equation is solved at the same level of approximation as used in the analysis of bulk crystalline electron-hole states (Wannier excitons). Kinetic energy is treated by the effective mass approximation, and the potential energy is due to high frequency dielectric solvation by atomic core electrons. An approximate formula is given for the lowest excited electronic state energy. This expression is dependent upon bulk electronic properties, and contains no adjustable parameters. The optical f number for absorption and emission is also considered. The same model is applied to the problem of two conduction band electrons in a small crystallite, in order to understand how the redox potential of excess electrons depends upon crystallite size.

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Optical transitions in carbon nanotubes are of central importance for nanotube characterization. They also provide insight into the nature of excited states in these one-dimensional systems. Recent work suggests that light absorption produces strongly correlated electron-hole states in the form of excitons. However, it has been difficult to rule out a simpler model in which resonances arise from the van Hove singularities associated with the one-dimensional band [corrected] structure of the nanotubes. Here, two-photon excitation spectroscopy bolsters the exciton picture. We found binding energies of approximately 400 millielectron volts for semiconducting single-walled nanotubes with 0.8-nanometer diameters. The results demonstrate the dominant role of many-body interactions in the excited-state properties of one-dimensional systems.