Louis E. Brus

Electron–electron and electron‐hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state

We model, in an elementary way, the excited electronic states of semiconductor crystallites sufficiently small (∼ 50 A 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. Schrodingers 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 salvation 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.

Anomalous Lattice Vibrations of Single- and Few-Layer MoS2

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.

A simple model for the ionization potential, electron affinity, and aqueous redox potentials of small semiconductor crystallites

Large semiconductor crystals have intrinsic electronic properties dependent upon the bulk band structure. As the crystal becomes small, a new regime is entered in which the electronic properties (excited states, ionization potential, electron affinity) should be strongly dependent upon the electron and hole in a confined space. We address the possibility of a shift in the photochemical redox potential of one carrier, as a function of crystallite size. As a semiquantitative guide, one might expect a shift on the order of h2/8em*R2 due to the kinetic energy of localization in the small crystallite. We model the elementary quantum mechanics of a charged crystallite using (a) the effective mass approximation, (b) an electrostatic potential for dielectric polarization, and (c) penetration of the carrier outside the crystallite in a cases of small effective mass. Shifts of several tenths of an eV appear possible in crystallites of diameter 50 A. The carrier charge density reside near the crystallite surface if ...

Quantum crystallites and nonlinear optics

This is a review and analysis of the optical properties of quantum crystallites, with principal emphasis on the electro-optic Stark effect and all optical third order nonlinearity. There are also introductory discussions on physical size regimes, crystallite synthesis, quantum confinement theory, and linear optical properties. The experiments describe CdSe crystallites, exhibiting strong confinement of electrons and holes, and CuCl crystallites, exhibiting weak confinement of the exciton center of mass. In the CdSe system, neither the Stark effect nor the third order nonlinearity is well understood. The Stark shifts appear to be smaller than calculated, and field inducted broadening also occurs. The third order nonlinearity is only modestly stronger than in bulk material, despite theoretical prediction. Unexpectedly large homogeneous widths, due to surface carrier trapping, in the nominally discrete crystallite excited states appear to be involved. The CuCl system shows far narrower spectroscopic homogeneous widths, and corresponds more closely to an ideal quantum dot in the weak confinement limit. CuCl also exhibits exciton superradiance at low temperature. Surface chemistry and crystallite encapsulation are critical in achieving the predicted large Stark and third order optical effects in II-VI and III-V crystallites.

Tuning the graphene work function by electric field effect.

We report variation of the work function for single and bilayer graphene devices measured by scanning Kelvin probe microscopy (SKPM). By use of the electric field effect, the work function of graphene can be adjusted as the gate voltage tunes the Fermi level across the charge neutrality point. Upon biasing the device, the surface potential map obtained by SKPM provides a reliable way to measure the contact resistance of individual electrodes contacting graphene.

DRYING-MEDIATED SELF-ASSEMBLY OF NANOPARTICLES

Systems far from equilibrium can exhibit complex transitory structures, even when equilibrium fluctuations are mundane. A dramatic example of this phenomenon has recently been demonstrated for thin-film solutions of passivated nanocrystals during the irreversible evaporation of the solvent. The relatively weak attractions between nanocrystals, which are efficiently screened in solution, become manifest as the solvent evaporates, initiating assembly of intricate, slowly evolving structures. Although certain aspects of this aggregation process can be explained using thermodynamic arguments alone, it is in principle a non-equilibrium process. A representation of this process as arising from the phase separation between a dense nanocrystal ‘liquid’ and dilute nanocrystal ‘vapour’ captures some of the behaviour observed in experiments, but neglects entirely the role of solvent fluctuations, which can be considerable on the nanometre length scale. Here we present a coarse-grained model of nanoparticle self-assembly that explicitly includes the dynamics of the evaporating solvent. Simulations using this model not only account for all observed spatial and temporal patterns, but also predict network structures that have yet to be explored. Two distinct mechanisms of ordering emerge, corresponding to the homogeneous and heterogeneous limits of evaporation dynamics. Our calculations show how different choices of solvent, nanoparticle size (and identity) and thermodynamic state give rise to the various morphologies of the final structures. The resulting guide for designing statistically patterned arrays of nanoparticles suggests the possibility of fabricating spontaneously organized nanoscale devices.

Luminescence properties of CdSe quantum crystallites: Resonance between interior and surface localized states

We use time‐, wavelength‐, temperature‐, polarization‐resolved luminescence to elucidate the nature of the absorbing and ‘‘band edge’’ luminescing states in 32 A diameter wurtzite CdSe quantum crystallites. Time‐resolved emission following picosecond size‐selective resonant excitation of the lowest excited state shows two components—a temperature insensitive 100 ps component and a microsecond, temperature sensitive component. The emission spectrum, showing optic phonon vibrational structure, develops a ∼70 wave number red shift as the fast component decays. Photoselection shows the slow component to be reverse polarized at 10 K, indicating this component to be the result of a hole radiationless transition. The 100 ps emitting state is repopulated thermally as temperature increases from 10 to 50 K. All available data are interpreted by postulating strong resonant mixing between a standing wave molecular orbital delocalized inside the crystallite and intrinsic surface Se lone pair states. The apparent excit...

Quantum confinement in size-selected, surface-oxidized silicon nanocrystals

The dynamics and spectroscopy of silicon nanocrystals that emit at visible wavelengths were analyzed. Size-selective precipitation and size-exclusion chromatography cleanly separate the silicon nanocrystals from larger crystallites and aggregates and provide direct evidence for quantum confinement in luminescence. Measured quantum yields are as high as 50 percent at low temperature, principally as a result of efficient oxide passivation. Despite a 0.9—electron-volt shift of the band gap to higher energy, the nanocrystals behave fundamentally as indirect gap materials with low oscillator strength.

Atmospheric Oxygen Binding and Hole Doping in Deformed Graphene on a SiO2 Substrate

Using micro-Raman spectroscopy and scanning tunneling microscopy, we study the relationship between structural distortion and electrical hole doping of graphene on a silicon dioxide substrate. The observed upshift of the Raman G band represents charge doping and not compressive strain. Two independent factors control the doping: (1) the degree of graphene coupling to the substrate and (2) exposure to oxygen and moisture. Thermal annealing induces a pronounced structural distortion due to close coupling to SiO2 and activates the ability of diatomic oxygen to accept charge from graphene. Gas flow experiments show that dry oxygen reversibly dopes graphene; doping becomes stronger and more irreversible in the presence of moisture and over long periods of time. We propose that oxygen molecular anions are stabilized by water solvation and electrostatic binding to the silicon dioxide surface.

Electronic structure and bonding in icosahedral C60

Abstract The Huckel molecular orbital theory for non-planar conjugated organic molecules has been applied to study the electronic structure and properties of the proposed icosahedral geometry of C60. The results support the suggestion that C60 may be the first example of a spherical aromatic molecule. The molecule is calculated to have a stable closed shell singlet ground electronic state.