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Showing papers on "Silicon published in 2002"


Journal ArticleDOI
07 Nov 2002-Nature
TL;DR: The synthesis of core–multishell structures, including a high-performance coaxially gated field-effect transistor, indicates the general potential of radial heterostructure growth for the development of nanowire-based devices.
Abstract: Semiconductor heterostructures with modulated composition and/or doping enable passivation of interfaces and the generation of devices with diverse functions. In this regard, the control of interfaces in nanoscale building blocks with high surface area will be increasingly important in the assembly of electronic and photonic devices. Core-shell heterostructures formed by the growth of crystalline overlayers on nanocrystals offer enhanced emission efficiency, important for various applications. Axial heterostructures have also been formed by a one-dimensional modulation of nanowire composition and doping. However, modulation of the radial composition and doping in nanowire structures has received much less attention than planar and nanocrystal systems. Here we synthesize silicon and germanium core-shell and multishell nanowire heterostructures using a chemical vapour deposition method applicable to a variety of nanoscale materials. Our investigations of the growth of boron-doped silicon shells on intrinsic silicon and silicon-silicon oxide core-shell nanowires indicate that homoepitaxy can be achieved at relatively low temperatures on clean silicon. We also demonstrate the possibility of heteroepitaxial growth of crystalline germanium-silicon and silicon-germanium core-shell structures, in which band-offsets drive hole injection into either germanium core or shell regions. Our synthesis of core-multishell structures, including a high-performance coaxially gated field-effect transistor, indicates the general potential of radial heterostructure growth for the development of nanowire-based devices.

2,022 citations


Journal ArticleDOI
17 May 2002-Science
TL;DR: These results demonstrate that the chemical stability of silicon NCs could enable their use as redox-active macromolecular species with the combined optical and charging properties of semiconductor quantum dots.
Abstract: Reversible electrochemical injection of discrete numbers of electrons into sterically stabilized silicon nanocrystals (NCs) (∼2 to 4 nanometers in diameter) was observed by differential pulse voltammetry (DPV) in N , N ′-dimethylformamide and acetonitrile. The electrochemical gap between the onset of electron injection and hole injection—related to the highest occupied and lowest unoccupied molecular orbitals—grew with decreasing nanocrystal size, and the DPV peak potentials above the onset for electron injection roughly correspond to expected Coulomb blockade or quantized double-layer charging energies. Electron transfer reactions between positively and negatively charged nanocrystals (or between charged nanocrystals and molecular redox-active coreactants) occurred that led to electron and hole annihilation, producing visible light. The electrogenerated chemiluminescence spectra exhibited a peak maximum at 640 nanometers, a significant red shift from the photoluminescence maximum (420 nanometers) of the same silicon NC solution. These results demonstrate that the chemical stability of silicon NCs could enable their use as redox-active macromolecular species with the combined optical and charging properties of semiconductor quantum dots.

969 citations


Journal ArticleDOI
TL;DR: In this article, the size control of SiO/SiO2 superlattices with an upper limit of the nanocrystal sizes of 3.8, 2.5, and 2.0 nm was investigated.
Abstract: Phase separation and thermal crystallization of SiO/SiO2 superlattices results in ordered arranged silicon nanocrystals. The preparation method which is fully compatible with Si technologies enables independent control of particle size as well as of particle density and spatial position by using a constant stoichiometry of the layers. Transmission electron microscopy investigations confirm the size control in samples with an upper limit of the nanocrystal sizes of 3.8, 2.5, and 2.0 nm without decreasing the silicon nanocrystal density for smaller sizes. The nanocrystals show a strong luminescence intensity in the visible and near-infrared region. A size-dependent blueshift of the luminescence and a luminescence intensity comparable to porous Si are observed. Nearly size independent luminescence intensity without bleaching effects gives an indirect proof of the accomplishment of the independent control of crystal size and number.

764 citations


Journal ArticleDOI
TL;DR: In this paper, the nanoelectrochemistry of silver nanowires in an aqueous HF solution containing silver nitrate was used to construct large-area silicon nanowire arrays.
Abstract: Large-area silicon nanowire arrays have been prepared on a silicon wafer without the use of a template The simple method, which can be carried out near room temperature, involves the nanoelectrochemistry of silver nanowires in an aqueous HF solution containing silver nitrate This technique may be generally applicable to other semiconductors and metals The Figure shows nanodendritic silicon wires

734 citations


Journal ArticleDOI
TL;DR: Al2O3 films with thicknesses ranging from 30 to 3540 A were grown in a viscous flow reactor using ALD with trimethylaluminum and water as the reactants as mentioned in this paper.

689 citations


MonographDOI
22 Feb 2002

675 citations


Journal ArticleDOI
TL;DR: In this article, a single-walled nanotube transistor is used to construct a nonvolatile charge-storage memory element operating at room temperature, which can be reversibly written, read, and erased at temperatures up to 100 K.
Abstract: A high-mobility (9000 cm2/V·s) semiconducting single-walled nanotube transistor is used to construct a nonvolatile charge-storage memory element operating at room temperature. Charges are stored by application of a few volts across the silicon dioxide dielectric between nanotube and silicon substrate, and detected by threshold shift of the nanotube field-effect transistor. The high mobility of the nanotube transistor allows the observation of discrete configurations of charge corresponding to rearrangement of a single or few electrons. These states may be reversibly written, read, and erased at temperatures up to 100 K.

605 citations



Journal ArticleDOI
20 Jun 2002-Nature
TL;DR: A rapid technique for patterning nanostructures in silicon that does not require etching is devised and here demonstrated, which could open up a variety of applications and be extended to other materials and processing techniques.
Abstract: The fabrication of micrometre- and nanometre-scale devices in silicon typically involves lithography and etching. These processes are costly and tend to be either limited in their resolution or slow in their throughput1. Recent work has demonstrated the possibility of patterning substrates on the nanometre scale by ‘imprinting’2,3 or directed self-assembly4, although an etching step is still required to generate the final structures. We have devised and here demonstrate a rapid technique for patterning nanostructures in silicon that does not require etching. In our technique—which we call ‘laser-assisted direct imprint’ (LADI)—a single excimer laser pulse melts a thin surface layer of silicon, and a mould is embossed into the resulting liquid layer. A variety of structures with resolution better than 10 nm have been imprinted into silicon using LADI, and the embossing time is less than 250 ns. The high resolution and speed of LADI, which we attribute to molten silicon's low viscosity (one-third that of water), could open up a variety of applications and be extended to other materials and processing techniques.

526 citations


Journal ArticleDOI
TL;DR: In this paper, the isotope effect on the lattice thermal conductivity for group IV and group III-V semiconductors is calculated using the Debye-Callaway model modified to include both transverse and longitudinal phonon modes explicitly.
Abstract: The isotope effect on the lattice thermal conductivity for group IV and group III-V semiconductors is calculated using the Debye-Callaway model modified to include both transverse and longitudinal phonon modes explicitly. The frequency and temperature dependences of the normal and umklapp phonon-scattering rates are kept the same for all compounds. The model requires as adjustable parameters only the longitudinal and transverse phonon Gr\"uneisen constants and the effective sample diameter. The model can quantitatively account for the observed isotope effect in diamond and germanium but not in silicon. The magnitude of the isotope effect is predicted for silicon carbide, boron nitride, and gallium nitride. In the case of boron nitride the predicted increase in the room-temperature thermal conductivity with isotopic enrichment is in excess of 100%. Finally, a more general method of estimating normal phonon-scattering rate coefficients for other types of solids is presented.

513 citations


Journal ArticleDOI
TL;DR: The multiwalled silicon carbide nanotube (SiCNT) was found to transform to a beta-SiC crystalline structure by electron beam annealing under TEM.
Abstract: One-dimensional silicon−carbon nanotubes and nanowires of various shapes and structures were synthesized via the reaction of silicon (produced by disproportionation reaction of SiO) with multiwalled carbon nanotubes (as templates) at different temperatures. A new type of multiwalled silicon carbide nanotube (SiCNT), with 3.5−4.5 A interlayer spacings, was observed in addition to the previously known β-SiC (cubic zinc blende structure) nanowires and the biaxial SiC−SiOx nanowires. The SiCNT was identified by high-resolution transmission microscopy (HRTEM), elemental mapping, and electron energy loss spectroscopy (EELS). The multiwalled SiCNT was found to transform to a β-SiC crystalline structure by electron beam annealing under TEM.

Journal ArticleDOI
TL;DR: In this article, a parameterization for band-to-band Auger recombination in silicon at 300 K was proposed, which accurately fits the available experimental lifetime data for arbitrary injection level and arbitrary dopant density, for both n-type and p-type dopants.
Abstract: A parameterization for band-to-band Auger recombination in silicon at 300 K is proposed. This general parameterization accurately fits the available experimental lifetime data for arbitrary injection level and arbitrary dopant density, for both n-type and p-type dopants. We confirm that Auger recombination is enhanced above the traditional free-particle rate at both low injection and high injection conditions. Further, the rate of enhancement is shown to be less for highly injected intrinsic silicon than for lowly injected doped silicon, consistent with the theory of Coulomb-enhanced Auger recombination. Variations on the parameterization are discussed.

Journal ArticleDOI
07 Nov 2002
TL;DR: The benefits of using SiC in power electronics applications are looked at, the current state of the art of SiC is reviewed, and how SiC can be a strong and viable candidate for future power electronics and systems applications are shown.
Abstract: Silicon offers multiple advantages to power circuit designers, but at the same time suffers from limitations that are inherent to silicon material properties, such as low bandgap energy, low thermal conductivity, and switching frequency limitations. Wide bandgap semiconductors, such as silicon carbide (SiC) and gallium nitride (GaN), provide larger bandgaps, higher breakdown electric field, and higher thermal conductivity. Power semiconductor devices made with SiC and GaN are capable of higher blocking voltages, higher switching frequencies, and higher junction temperatures than silicon devices. SiC is by far the most advanced material and, hence, is the subject of attention from power electronics and systems designers. This paper looks at the benefits of using SiC in power electronics applications, reviews the current state of the art, and shows how SiC can be a strong and viable candidate for future power electronics and systems applications.

Journal ArticleDOI
TL;DR: Silicon oxide/Nafion composite membranes were studied for operation in hydrogen/oxygen proton exchange membrane fuel cells (PEMFCs) from 80 to 140°C.
Abstract: Silicon oxide/Nafion composite membranes were studied for operation in hydrogen/oxygen proton-exchange membrane fuel cells (PEMFCs) from 80 to 140°C. The composite membranes were prepared either by an impregnation of Nafion 115 via sol-gel processing of tetraethoxysilane or by preparing a recast film, using solubilized Nafion 115 and a silicon oxide polymer/gel Tetraethoxysilane, when reacted with water in an acidic medium, undergoes polymerization to form a mixture of SiO 2 and siloxane polymer with product hydroxide and ethoxide groups. This material is referred to as SiO s /-OH/-OEt. When Nafion is used as the acidic medium, the SiO 2 /siloxane polymer forms within the membrane. All composite membranes had a silicon oxide content of less than or equal to 10 wt %. The silicon oxide improved the water retention of the composite membranes, increasing proton conductivity at elevated temperatures Attenuated total reflectance-Fourier transform infrared spectroscopy and scanning electron microscopy experiments indicated an evenly distributed siloxane polymer of SiO 2 /-OH/-OEt in the composite membranes. At a potential of 0.4 V, silicon oxide/Nafion 115 composite membranes delivered four times the current density obtained with unmodified Nafion 115 in a H 2 /O 2 PEMFC at 130°C and a pressure of 3 atm. Furthermore, silicon oxide-modified membranes were more robust than the control membranes (unmodified Nafion 115 and recast Nafion), which degraded after high operation temperature and thermal cycling.

Journal ArticleDOI
TL;DR: In this paper, the authors measured the thermal conductivities along free-standing silicon layers doped with boron and phosphorus at concentrations ranging from 1×1017 to 3×1019 cm−3 at temperatures between 15 and 300 K.
Abstract: This work measures the thermal conductivities along free-standing silicon layers doped with boron and phosphorus at concentrations ranging from 1×1017 to 3×1019 cm−3 at temperatures between 15 and 300 K. The impurity concentrations are measured using secondary ion mass spectroscopy (SIMS) and the thermal conductivity data are interpreted using phonon transport theory accounting for scattering on impurities, free electrons, and the layer boundaries. Phonon-boundary scattering in the 3-μm-thick layers reduces the thermal conductivity of the layers at low temperatures regardless of the level of impurity concentration. The present data suggest that unintentional impurities may have strongly reduced the conductivities reported previously for bulk samples, for which impurity concentrations were determined from the electrical resistivity rather than from SIMS data. This work illustrates the combined effects of phonon interactions with impurities, free electrons, and material interfaces, which can be particularly...

Journal ArticleDOI
TL;DR: This Account chronicles the conceptual development, proof of principle, exploration of scope, and mechanistic investigations of a newly developed class of palladium-catalyzed cross-coupling reactions of silicon derivatives.
Abstract: This Account chronicles the conceptual development, proof of principle, exploration of scope, and mechanistic investigations of a newly developed class of palladium-catalyzed cross-coupling reactions of silicon derivatives. Under the influence of fluoride activation a myriad of oxygen-containing silicon moieties undergo mild and stereospecific cross-coupling. The diversity of methods for introduction of silicon groupings into organic molecules and the range of organic electrophiles that can be used are outlined.

Journal ArticleDOI
04 Jul 2002-Nature
TL;DR: The mechanism of hydrogen-induced crystallization of hydrogenated amorphous silicon films during post-deposition treatment with an H2 (or D2) plasma is reported, which is mediated by the insertion of H atoms into strained Si–Si bonds as the atoms diffuse through the film.
Abstract: Hydrogenated amorphous and nanocrystalline silicon films manufactured by plasma deposition techniques are used widely in electronic and optoelectronic devices1,2. The crystalline fraction and grain size of these films determines electronic and optical properties; the nanocrystal nucleation mechanism, which dictates the final film structure, is governed by the interactions between the hydrogen atoms of the plasma and the solid silicon matrix. Fundamental understanding of these interactions is important for optimizing the film structure and properties. Here we report the mechanism of hydrogen-induced crystallization of hydrogenated amorphous silicon films during post-deposition treatment with an H2 (or D2) plasma. Using molecular-dynamics simulations3,4 and infrared spectroscopy5, we show that crystallization is mediated by the insertion of H atoms into strained Si–Si bonds as the atoms diffuse through the film. This chemically driven mechanism may be operative in other covalently bonded materials, where the presence of hydrogen leads to disorder-to-order transitions.

Journal ArticleDOI
TL;DR: In this paper, theoretical and experimental results regarding the thermodynamic stability of high-k dielectrics ZrO2 and HfO2 in contact with Si and SiO2 were presented.
Abstract: We present theoretical and experimental results regarding the thermodynamic stability of the high-k dielectrics ZrO2 and HfO2 in contact with Si and SiO2 The HfO2/Si interface is found to be stable with respect to formation of silicides whereas the ZrO2/Si interface is not The metal–oxide/SiO2 interface is marginally unstable with respect to formation of silicates Cross-sectional transmission electron micrographs expose formation of nodules, identified as silicides, across the polycrystalline silicon/ZrO2/Si interfaces but not for the interfaces with HfO2 For both ZrO2 and HfO2, the x-ray photoemission spectra illustrate formation of silicate-like compounds in the MO2/SiO2 interface

Journal ArticleDOI
TL;DR: In this article, the photoluminescence of the silicon nanocrystals and their yield were measured as a function of their size, and it was found that the photophotonicity follows very closely the quantum-confinement model.
Abstract: Silicon nanocrystals with diameters between 2.5 and 8 nm were prepared by pulsed CO2 laser pyrolysis of silane in a gas flow reactor and expanded through a conical nozzle into a high vacuum. Using a fast-spinning molecular-beam chopper, they were size-selectively deposited on dedicated quartz substrates. Finally, the photoluminescence of the silicon nanocrystals and their yield were measured as a function of their size. It was found that the photoluminescence follows very closely the quantum-confinement model. The yield shows a pronounced maximum for sizes between 3 and 4 nm.

Journal ArticleDOI
TL;DR: In this article, a comprehensive model of the behavior of copper in silicon was proposed and the technical aspects of this model were discussed in detail, and the impact of the physics of copper on the development and characterization of copper diffusion barriers was discussed.
Abstract: This article reviews the progress made in the studies of copper in silicon over the last several years and puts forward a comprehensive model of the behavior of copper in silicon. Technical aspects of this model are discussed in detail. It is shown that many important aspects of the behavior of copper in silicon are not shared with the other 3d transition metals. The positive charge state of interstitial copper makes its defect reactions Fermi-level-dependent, and results in a noticeable difference in the out-diffusion and precipitation behavior of copper in n-Si and p-Si. The extremely high diffusivity of copper in silicon, which is a consequence of the small ionic radius of copper and its relatively weak interaction with the silicon lattice, makes it highly mobile at room temperature and impacts the stability of copper complexes. Large lattice strains and electrostatic effects in p-Si make the formation of copper-silicide precipitates in the hulk energetically unfavorable, unless the chemical driving force for precipitation is high enough to overcome the nucleation and precipitation harrier. Literature data on the effect of copper on minority carrier lifetime and device yield are analyzed using our improved understanding of the physics of copper in silicon. Finally, the impact of the physics of copper in silicon on the development and characterization of copper diffusion barriers is discussed.

Book
31 Dec 2002
TL;DR: In this paper, a Si bipolar transistor was used to achieve respectable Si bipolar performance down to liquid-nitrogen temperature (LNT = 77 K), but it is unlikely that conventional designed Si bipolar technology will offer performance attractive enough to make it a serious contender to CMOS, a proven technology for cryogenic applications.
Abstract: Silicon (Si) bipolar transistor technology, despite its desirable features of fast switching speed, high transconductance, and excellent current-drive capability at room temperature (RT = 300 K), is often viewed as unsuitable for the cryogenic environment because its current gain (β = Jc/JB), frequency response, and circuit speed typically degrade strongly with cooling [1,2]. Recent evidence [3–6] indicates, however, that careful profile design can be used to achieve respectable Si bipolar performance down to liquid-nitrogen temperature (LNT = 77 K). Even with these improvements, however, it is unlikely that conventionally designed Si bipolar technology will offer performance attractive enough to make it a serious contender to CMOS, a proven technology for cryogenic applications.

Journal ArticleDOI
14 Sep 2002-Langmuir
TL;DR: In this paper, the pull-off forces between flat glass or silicon surfaces and silicon AFM tips or glass microspheres of different sizes have been extensively studied as a function of relative humidity (RH) in the range 5−90%, as model systems for the behavior of cohesive powders.
Abstract: Using the atomic force microscope (AFM), the pull-off forces between flat glass or silicon surfaces and silicon AFM tips or glass microspheres of different sizes have been extensively studied as a function of relative humidity (RH) in the range 5−90%, as model systems for the behavior of cohesive powders. The glass and silicon substrates were treated to render them either hydrophobic or hydrophilic. All the hydrophilic surfaces gave simple force curves and pull-off forces increasing uniformly with RH. Small contacts (R ∼ 20 nm) gave pull-off forces close to values predicted by simple Laplace−Kelvin theory (∼20 nN), but the values with microspheres (R ∼ 20 μm) fell well below predictions for sphere−flat or sphere−sphere geometry, due to roughness and asperity contacts. The hydrophobic silicon surfaces also exhibited simple behavior, with no significant RH dependence. The pull-off force again fell well below predicted values (Johnson−Kendall−Roberts contact mechanics theory) for the larger contacts. Hydroph...

Journal ArticleDOI
TL;DR: In this article, surface-enhanced infrared absorption (SEIRA) effect was used in preparation of Au island film electrodes for in situ infrared spectroscopic studies of the electrochemical interface in attenuated total reflection mode.

Proceedings ArticleDOI
08 Dec 2002
TL;DR: In this paper, a leading edge 90 nm technology with 1.2 nm physical gate oxide, 50 nm gate length, strained silicon, NiSi, 7 layers of Cu interconnects, and low k carbon-doped oxide (CDO) for high performance dense logic is presented.
Abstract: A leading edge 90 nm technology with 1.2 nm physical gate oxide, 50 nm gate length, strained silicon, NiSi, 7 layers of Cu interconnects, and low k carbon-doped oxide (CDO) for high performance dense logic is presented. Strained silicon is used to increase saturated NMOS and PMOS drive currents by 10-20% and mobility by >50%. Aggressive design rules and unlanded contacts offer a 1.0 /spl mu/m/sup 2/ 6-T SRAM cell using 193 nm lithography.

Journal ArticleDOI
TL;DR: In this article, the photoluminescence (PL) lifetimes in nanostructured silicon are typically very long−approximately 3 orders of magnitude longer than those of direct band gap semiconductors.
Abstract: Quantum confinement in nanostructured silicon can lead to efficient light emission. However, the photoluminescence (PL) lifetimes in nanostructured silicon are typically very long−approximately 3 orders of magnitude longer than those of direct band gap semiconductors. Herein, we show that organic monolayer coated silicon nanocrystals ranging from 1 to 10 nm in diameter emit with nanosecond-scale lifetimes and high quantum yields, making it possible to measure the PL spectra of single Si quantum dots. The Si quantum dots demonstrate stochastic single-step “blinking” behavior and size-dependent PL spectra with line widths approximately only three times greater than those measured for CdSe nanocrystals at room temperature.

Journal ArticleDOI
TL;DR: In this article, the growth of crack-free GaN-based light emitting diodes (LEDs) on silicon on patterned Si(111) with areas of 100 μm×100 μm is reported.
Abstract: Cracking of GaN on Si usually occurs due to the large thermal mismatch of GaN and Si when layer thicknesses exceed approximately 1 μm in metalorganic chemical vapor deposition (MOCVD) preventing the realization of device-quality material. The thermal stress can be reduced significantly by a combination of different concepts such as the insertion of low-temperature AlN interlayers, introducing multiple AlGaN/GaN interlayers, and growing on prepatterned substrates. The growth of crack-free GaN-based light emitting diodes (LEDs) on silicon on patterned Si(111) with areas of 100 μm×100 μm is reported

Journal ArticleDOI
TL;DR: In this article, the authors proposed a mechanism of viscous flow and diffusion of silicon and oxygen in silica that involves motion of SiO molecules, which is consistent with experimental measurements of silica viscosity.
Abstract: Experimental measurements of the viscosity of silica (SiO2) are critically examined; the best measurements show an activation energy of 515 kJ/mole above 1400 °C and 720 kJ/mole below this temperature. The diffusion of silicon and oxygen in silica have temperature dependencies close to that of the high temperature viscosity. Mechanisms of viscous flow and diffusion of silicon and oxygen in silica are proposed that involve motion of SiO molecules. Viscous flow is proposed to result from the motion of line defects composed of SiO molecules At temperatures below 1400 °C the fraction of SiO molecules in line defects changes with temperature. The relaxation of this fraction to an equilibrium value depends on the time. These proposed mechanisms are consistent with experimental measurements of silica viscosity.

Journal ArticleDOI
TL;DR: In this article, the authors proposed to use anisotropic nano-sized objects to allow micron-scale colloids to link or functionalize with a four-fold valence, similar to the sp3 hybridized chemical bonds associated with, e.g., carbon, silicon and germanium.
Abstract: We propose coating spherical particles or droplets with anisotropic nano-sized objects to allow micron-scale colloids to link or functionalize with a four-fold valence, similar to the sp3 hybridized chemical bonds associated with, e.g., carbon, silicon and germanium. Candidates for such coatings include triblock copolymers, gemini lipids, metallic or semiconducting nanorods and conventional liquid crystal compounds. We estimate the size of the relevant nematic Frank constants, discuss how to obtain other valences and analyze the thermal distortions of ground state configurations of defects on the sphere.

Book
22 Apr 2002
TL;DR: In this article, the Chemical Dissolution of Silicon is described as a process of anodic Oxidation, followed by the electrochemical dissolution of silicon and the formation of pore formation.
Abstract: Preface.Introduction, Safety and Instrumentation. The Chemical Dissolution of Silicon. The Semiconductor--Electrolyte Junction. The Electrochemical Dissolution of Silicon. Anodic Oxidation. Electrochemical Pore Formation. Microporous Silicon. Mesoporous Silicon. Macroporous Silicon. Applications.AppendicesSupplier References.References.Subject Index.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a 4-fold valence for anisotropic nanosized objects, similar to the sp3 hybridized chemical bonds associated with carbon, silicon, and germanium.
Abstract: We propose coating spherical particles or droplets with anisotropic nanosized objects to allow micron-scale colloids to link or functionalize with a 4-fold valence, similar to the sp3 hybridized chemical bonds associated with, e.g., carbon, silicon, and germanium. Candidates for such coatings include triblock copolymers, gemini lipids, metallic or semiconducting nanorods, and conventional liquid crystal compounds. We estimate the size of the relevant nematic Frank constants, discuss how to obtain other valences and analyze the thermal distortions of ground-state configurations of defects on the sphere.