Theory and ab initio calculation of radiative lifetime of excitons in semiconducting carbon nanotubes

Exciton dynamics in carbon nanotubes: from the Luttinger liquid to harmonic oscillators

We show that the absorption spectrum in semiconducting nanotubes can be determined using the bosonization technique combined with mean-field theory and a harmonic approximation. In this framework, a multiple band semiconducting nanotube reduces to a system of weakly coupled harmonic oscillators. We also find that gaps of any size destroy the Luttinger liquid phase in single-walled carbon nanotubes and give rise to electron density fluctuations that resemble excitons built from quasiparticles. Interband processes, such as multiple exciton generation, become progressively weaker as the length to diameter ratio grows larger.

Prolonged spontaneous emission and dephasing of localized excitons in air-bridged carbon nanotubes

The bright exciton emission of carbon nanotubes is appealing for optoelectronic devices and fundamental studies of light-matter interaction in one-dimensional nanostructures. However, to date, the photophysics of excitons in carbon nanotubes is largely affected by extrinsic effects. Here we perform time-resolved photoluminescence measurements over 14 orders of magnitude for ultra-clean carbon nanotubes bridging an air gap over pillar posts. Our measurements demonstrate a new regime of intrinsic exciton photophysics with prolonged spontaneous emission times up to T1=18 ns, about two orders of magnitude better than prior measurements and in agreement with values hypothesized by theorists about a decade ago. Furthermore, we establish for the first time exciton decoherence times of individual nanotubes in the time domain and find fourfold prolonged values up to T2=2.1 ps compared with ensemble measurements. These first observations motivate new discussions about the magnitude of the intrinsic dephasing mechanism while the prolonged exciton dynamics is promising for applications.

Many-body effects in semiconducting single-wall silicon nanotubes

The electronic and optical properties of semiconducting silicon nanotubes (SiNTs) are studied by means of the many-body Green's function method, i.e., GW approximation and Bethe-Salpeter equation. In these studied structures, i.e., (4,4), (6,6) and (10,0) SiNTs, self-energy effects are enhanced giving rise to large quasi-particle (QP) band gaps due to the confinement effect. The strong electron-electron (e-e) correlations broaden the band gaps of the studied SiNTs from 0.65, 0.28 and 0.05 eV at DFT level to 1.9, 1.22 and 0.79 eV at GW level. The Coulomb electron-hole (e-h) interactions significantly modify optical absorption properties obtained at noninteracting-particle level with the formation of bound excitons with considerable binding energies (of the order of 1 eV) assigned: the binding energies of the armchair (4,4), (6,6) and zigzag (10,0) SiNTs are 0.92, 1.1 and 0.6 eV, respectively. Results in this work are useful for understanding the physics and applications in silicon-based nanoscale device components.

Measurement of a reaction-diffusion crossover in exciton-exciton recombination inside carbon nanotubes using femtosecond optical absorption

Exciton-exciton recombination in isolated semiconducting single-walled carbon nanotubes was studied using femtosecond transient absorption. Under sufficient excitation to saturate the optical absorption, we observed an abrupt transition between reaction- and diffusion-limited kinetics, arising from reactions between incoherent localized excitons with a finite probability of ~0.2 per encounter. This represents the first experimental observation of a crossover between classical and critical kinetics in a 1D coalescing random walk, which is a paradigm for the study of nonequilibrium systems.

Photoluminescence of single-walled carbon nanotubes: the role of Stokes shift and impurity levels

Recent experiments have indicated that dopants and defects can trigger new redshifted photoluminescence (PL) peaks below the E11 peak in single-walled carbon nanotubes (SWCNTs). To understand the origin of the new PL peaks, we study theoretically the excited-state properties of SWCNTs with some typical dopants and defects by ab initio many-body perturbation theory. Our calculations demonstrate that the Stokes shift in doped centers can be as large as 170 meV, which is much larger than that of intact SWCNTs and must be taken into account. We find dipole-allowed transitions from localized midgap and shallow impurity levels, which can give rise to pronounced PL peaks. Dark excitons, on the other hand, seem to have oscillator strengths that are too small to account for the new PL peaks.

Quantum efficiency and capture cross section of first and second excitonic transitions of single-walled carbon nanotubes measured through photoconductivity

Comparing photoconductivity measurements, using p-n diodes formed along individual single-walled carbon nanotubes (SWNT), with modeling results, allows determination of the quantum efficiency, optical capture cross section, and oscillator strength of the first (E11) and second (E22) excitonic transitions of SWNTs. This is in the infrared region of the spectrum, where little experimental work on SWNT optical absorption has been reported to date. We estimate quantum efficiency (η) ~1-5% and provide a correlation of η, capture cross section, and oscillator strength for E11 and E22 with nanotube diameter. This study uses the spectral weight of the exciton resonances as the determining parameter in optical measurements.

Bright, long-lived and coherent excitons in carbon nanotube quantum dots

Carbon nanotubes exhibit a wealth of unique physical properties. By virtue of their exceptionally low mass and extreme stiffness they provide ultrahigh-quality mechanical resonances, promise long electron spin coherence times in a nuclear-spin free lattice for quantum information processing and spintronics, and feature unprecedented tunability of optical transitions for optoelectronic applications. Excitons in semiconducting single-walled carbon nanotubes could facilitate the upconversion of spin, mechanical or hybrid spin-mechanical degrees of freedom to optical frequencies for efficient manipulation and detection. However, successful implementation of such schemes with carbon nanotubes has been impeded by rapid exciton decoherence at non-radiative quenching sites, environmental dephasing and emission intermittence. Here we demonstrate that these limitations may be overcome by exciton localization in suspended carbon nanotubes. For excitons localized in nanotube quantum dots we found narrow optical lines free of spectral wandering, radiative exciton lifetimes and effectively suppressed blinking. Our findings identify the great potential of localized excitons for efficient and spectrally precise interfacing of photons, phonons and spins in novel carbon nanotube-based quantum devices.

Intrinsic radiative lifetime derived via absorption cross section of one-dimensional excitons

Intrinsic radiative lifetime is an essential physical property of low-dimensional excitons that represents their optical transition rate and wavefunction, which directly measures the probability of finding an electron and a hole at the same position in an exciton. However, the conventional method that is used to determine this property via measuring the temperature-dependent photoluminescence (PL) decay time involves uncertainty due to various extrinsic contributions at high temperatures. Here, we propose an alternative method to derive the intrinsic radiative lifetime via temperature-independent measurement of the absorption cross section and transformation using Einstein's A-B-coefficient equations derived for low-dimensional excitons. We experimentally verified our approach for one-dimensional (1D) excitons in high-quality 14 × 6 nm² quantum wires by comparing it to the conventional approach. Both independent evaluations showed good agreement with each other and with theoretical predictions. This approach opens a promising path to studying low-dimensional exciton physics.

Multiparticle Exciton Ionization in Shallow Doped Carbon Nanotubes

Shallow hole doping in small-diameter semiconducting carbon nanotubes with a valley degeneracy is predicted to result in the resonant ionization of excitons into free electron-hole pairs. This mechanism, which relies on the chirality of the electronic states, causes excitons to decay with high efficiencies where the rate scales as the square of the dopant density. Moreover, multiparticle exciton ionization can account for delocalized fluorescence quenching when a few holes per micrometer of tube length are present.

Exciton states and optical properties of carbon nanotubes

Exciton states and related optical properties of a single-walled carbon nanotube are reviewed, primarily from a theoretical viewpoint. The energies and wavefunctions of excitons are discussed using a screened Hartree-Fock approximation with an effective-mass or k·p approximation. The close relationship between a long-range electron-hole exchange interaction and a depolarization effect is clarified. I discuss optical properties including the radiative lifetime of excitons, absorption spectra and radiation force. To describe these properties in a unified scheme, a self-consistent method is introduced for calculating the scattering light and induced current density due to excitons. I also briefly review experimental results on the Aharonov-Bohm effect in excitons and quasi-dark excitons excited by light polarized perpendicular to the tube axis.

Optoelectronic properties of single-wall carbon nanotubes

Single-wall carbon nanotubes (SWCNTs), with their uniquely simple crystal structures and chirality-dependent electronic and vibrational states, provide an ideal laboratory for the exploration of novel 1D physics, as well as quantum engineered architectures for applications in optoelectronics. This article provides an overview of recent progress in optical studies of SWCNTs. In particular, recent progress in post-growth separation methods allows different species of SWCNTs to be sorted out in bulk quantities according to their diameters, chiralities, and electronic types, enabling studies of (n,m)-dependent properties using standard macroscopic characterization measurements. Here, a review is presented of recent optical studies of samples enriched in 'armchair' (n = m) species, which are truly metallic nanotubes but show excitonic interband absorption. Furthermore, it is shown that intense ultrashort optical pulses can induce ultrafast bandgap oscillations in SWCNTs, via the generation of coherent phonons, which in turn modulate the transmission of a delayed probe pulse. Combined with pulse-shaping techniques, coherent phonon spectroscopy provides a powerful method for studying exciton-phonon coupling in SWCNTs in a chirality-selective manner. Finally, some of the basic properties of highly aligned SWCNT films are highlighted, which are particularly well-suited for optoelectronic applications including terahertz polarizers with nearly perfect extinction ratios and broadband photodetectors.

Observation of negative and positive trions in the electrochemically carrier-doped single-walled carbon nanotubes

Understanding of electronic and optical features of single-walled carbon nanotubes (SWNTs) has been a central issue in science and nanotechnology of carbon nanotubes. We describe the detection of both the positive trion (positively charged exciton) and negative trion (negatively charged exciton) as a three-particle bound state in the SWNTs at room temperature by an in situ photoluminescence spectroelectrochemistry method for an isolated SWNT film cast on an ITO electrode. The electrochemical hole and electron dopings enable us to detect such trions on the SWNTs. The large energy difference between the singlet bright exciton and the negative and positive trions showing a tube diameter dependence is determined by both the exchange splitting energy and the trion binding energy. In contrast to conventional compound semiconductors, on the SWNTs, the negative trion has almost the same binding energy to the positive trion, which is attributed to nearly identical effective masses of the holes and electrons.

Transient absorption spectroscopy and imaging of individual chirality-assigned single-walled carbon nanotubes

Femtosecond transient absorption microscopy was employed to study the excited-state dynamics of individual semiconducting single-walled carbon nanotubes (SWNTs) with simultaneously high spatial (∼200 nm) and temporal (∼300 fs) resolution. Isolated SWNTs were located using atomic force microscopy, and Raman spectroscopy was employed to determine the chiral index of select nanotubes. This unique experimental approach removes sample heterogeneity in ultrafast measurements of these complex materials. Transient absorption spectra of the individual SWNTs were obtained by recording transient absorption images at different probe wavelengths. These measurements provide new information about the origin of the photoinduced absorption features of SWNTs. Transient absorption traces were also collected for individual SWNTs. The dynamics show a fast, ∼1 ps, decay for all the semiconducting nanotubes studied, which is significantly faster than the previously reported decay times for SWNT suspensions. We attributed this fast relaxation to coupling between the excitons created by the pump laser pulse and the substrate.

Brightening of the lowest exciton in carbon nanotubes via chemical functionalization

Using time-dependent density functional theory, we found that chemical functionalization at low concentrations of single-walled carbon nanotubes (SWNTs) locally alters the π-conjugated network of the nanotube surface and leads to a spatial confinement of the electronically excited wave functions. Depending on the adsorbant positions, the chemisorption significantly modifies the optical selection rules. Our modeling suggests that photoluminescent efficiency of semiconducting SWNT materials can be controlled by selective chemical functionalization.

Luminescence properties of individual empty and water-filled single-walled carbon nanotubes

The influence of water filling on the photoluminescence (PL) properties of SWCNTs is studied by ensemble and single-molecule PL spectroscopy. Red-shifted PL and PL excitation spectra are observed upon water filling for 16 chiralities and can be used to unambiguously distinguish empty SWCNTs from filled ones. The effect of water filling on the optical transitions is well-reproduced by a continuum dielectric constant model previously developed to describe the influence of the nanotube outer environment. Empty nanotubes display narrower luminescence lines and lower inhomogeneous broadening, signatures of reduced extrinsic perturbations. The radial breathing mode phonon sideband is clearly observed in the PL spectrum of small diameter empty tubes, and a strong exciton-phonon coupling is measured for this vibration. Biexponential PL decays are observed for empty and water-filled tubes, and only the short-living component is influenced by the water filling. This may be attributed to a shortening of the radiative lifetime of the bright state by the inner dielectric environment.

Intensity-dependent exciton dynamics of (6,5) single-walled carbon nanotubes: momentum selection rules, diffusion, and nonlinear interactions

The exciton dynamics for an ensemble of individual, suspended (6,5), single-walled carbon nanotubes revealed by single color E(22) resonant pump-probe spectroscopy for a wide range of pump fluences are reported. The optically excited initial exciton population ranges from approximately 5 to 120 excitons per ∼725 nm nanotube. At the higher fluences of this range, the pump-probe signals are no longer linearly dependent on the pump intensity. A single, predictive model is described that fits all data for two decades of pump fluences and three decades of delay times. The model introduces population loss from the optically active zero momentum E(22) state to the rest of the E(22) subband, which is dark due to momentum selection rules. In the single exciton limit, the E(11) dynamics are well described by a stretched exponential, which is a direct consequence of diffusion quenching from an ensemble of nanotubes of different lengths. The observed change in population relaxation dynamics as a function of increasing pump intensity is attributed to exciton-exciton Auger de-excitation in the E(11) subband and, to a lesser extent, in the E(22) subband. From the fit to the model, an average defect density 1/ρ = 150 nm and diffusion constants D(11) = 4 cm(2)/s and D(22) = 0.2 cm(2)/s are determined.

Observation of electronic Raman scattering in metallic carbon nanotubes

We present experimental measurements of the electronic contribution to the Raman spectra of individual metallic single-walled carbon nanotubes (MSWNTs). Photoexcited carriers are inelastically scattered by a continuum of low-energy electron-hole pairs created across the graphenelike linear electronic subbands of the MSWNTs. The optical resonances in MSWNTs give rise to well-defined electronic Raman peaks. This resonant electronic Raman scattering is a unique feature of the electronic structure of these one-dimensional quasimetals.

Fluorescent single-walled carbon nanotube aerogels in surfactant-free environments

A general challenge in generating functional materials from nanoscale components is integrating them into useful composites that retain or enhance their properties of interest. Development of single walled carbon nanotube (SWNT) materials for optoelectronics and sensing has been especially challenging in that SWNT optical and electronic properties are highly sensitive to environmental interactions, which can be particularly severe in composite matrices. Percolation of SWNTs into aqueous silica gels shows promise as an important route for exploiting their properties, but retention of the aqueous and surfactant environment still impacts and limits optical response, while also limiting the range of conditions in which these materials may be applied. Here, we present for the first time an innovative approach to obtain highly fluorescent solution-free SWNT-silica aerogels, which provides access to novel photophysical properties. Strongly blue-shifted spectral features, revelation of new diameter-dependent gas-phase adsorption phenomena, and significant increase (approximately three times that at room temperature) in photoluminescence intensities at cryogenic temperatures all indicate greatly reduced SWNT-matrix interactions consistent with the SWNTs experiencing a surfactant-free environment. The results demonstrate that this solid-state nanomaterial will play an important role in further revealing the true intrinsic SWNT chemical and photophysical behaviors and represent for the first time a promising new solution- and surfactant-free material for advancing SWNT applications in sensing, photonics, and optoelectronics.

Violation of the condon approximation in semiconducting carbon nanotubes

The Condon approximation is widely applied in molecular and condensed matter spectroscopy and states that electronic transition dipoles are independent of nuclear positions. This approximation is related to the Franck-Condon principle, which in its simplest form holds that electronic transitions are instantaneous on the time scale of nuclear motion. The Condon approximation leads to a long-held assumption in Raman spectroscopy of carbon nanotubes: intensities arising from resonance with incident and scattered photons are equal. Direct testing of this assumption has not been possible due to the lack of homogeneous populations of specific carbon nanotube chiralities. Here, we present the first complete Raman excitation profiles (REPs) for the nanotube G band for 10 pure semiconducting chiralities. In contrast to expectations, a strong asymmetry is observed in the REPs for all chiralities, with the scattered resonance always appearing weaker than the incident resonance. The observed behavior results from violation of the Condon approximation and originates in changes in the electronic transition dipole due to nuclear motion (non-Condon effect), as confirmed by our quantum chemical calculations. The agreement of our calculations with the experimental REP asymmetries and observed trends in family dependence indicates the behavior is intrinsic.

The role of length and defects on optical quantum efficiency and exciton decay dynamics in single-walled carbon nanotubes

We perform Monte Carlo simulations of the time-resolved, spatially resolved, and integrated photoluminescence from a nanotube to investigate the role of the nanotube length L and defects using an exciton random-walk and defect-induced quenching model. When nonradiative decay is due solely to diffusion quenching, the quantum efficiency is approximately proportional to L2 at low quantum efficiency. With defects present, the quantum efficiency depends only weakly on the number defects but is instead tied to Leff2 where Leff is the root-mean-square separation between defects. The time-resolved photoluminescence decay of nanotubes is multiexponential for both pristine nanotubes and nanotubes with defects. The dominant time scale for a pristine nanotube is proportional to L2/D, where D is the diffusion constant. The presence of defects on the nanotube introduces additional time scales.

Observation of charged excitons in hole-doped carbon nanotubes using photoluminescence and absorption spectroscopy

We report the first observation of trions (charged excitons), three-particle bound states consisting of one electron and two holes, in hole-doped carbon nanotubes at room temperature. When p-type dopants are added to carbon nanotube solutions, the photoluminescence and absorption peaks of the trions appear far below the E11 bright exciton peak, regardless of the dopant species. The unexpectedly large energy separation between the bright excitons and the trions is attributed to the strong electron-hole exchange interaction in carbon nanotubes.

Single-walled carbon nanotubes as excitonic optical wires

Although metallic nanostructures are useful for nanoscale optics, all of their key optical properties are determined by their geometry. This makes it difficult to adjust these properties independently, and can restrict applications. Here we use the absolute intensity of Rayleigh scattering to show that single-walled carbon nanotubes can form ideal optical wires. The spatial distribution of the radiation scattered by the nanotubes is determined by their shape, but the intensity and spectrum of the scattered radiation are determined by exciton dynamics, quantum-dot-like optical resonances and other intrinsic properties. Moreover, the nanotubes display a uniform peak optical conductivity of approximately 8 e(2)/h, which we derive using an exciton model, suggesting universal behaviour similar to that observed in nanotube conductance. We further demonstrate a radiative coupling between two distant nanotubes, with potential applications in metamaterials and optical antennas.

Brightening of triplet dark excitons by atomic hydrogen adsorption in single-walled carbon nanotubes observed by photoluminescence spectroscopy

Adsorption and desorption of atomic hydrogen on single-walled carbon nanotubes were observed by photoluminescence spectroscopy. A satellite peak appeared at the lower energy side of the E11 photoluminescence emission peak after exposure to atomic hydrogen and then disappeared after annealing at 300 °C in vacuum. The energy difference between the satellite peak and E11 peak was 40-80 meV, depending on the tube diameter. The satellite peak was attributed to the triplet dark exciton that became optically active because of the effectively enhanced spin-orbit interaction induced by adsorbed hydrogen atoms.

Strong charge-transfer excitonic effects and the Bose-Einstein exciton condensate in graphane

Using first principles many-body theory methods (GW+Bethe-Salpeter equation) we demonstrate that the optical properties of graphane are dominated by localized charge-transfer excitations governed by enhanced electron correlations in a two-dimensional dielectric medium. Strong electron-hole interaction leads to the appearance of small radius bound excitons with spatially separated electron and hole, which are localized out of plane and in plane, respectively. The presence of such bound excitons opens the path towards an excitonic Bose-Einstein condensate in graphane that can be observed experimentally.

Efficient narrow-band light emission from a single carbon nanotube p-n diode

Electrically driven light emission from carbon nanotubes could be used in nanoscale lasers and single-photon sources, and has therefore been the focus of much research. However, high electric fields and currents have either been necessary for electroluminescence, or have been an undesired side effect, leading to high power requirements and low efficiencies. Furthermore, electroluminescent linewidths have been broad enough to obscure the contributions of individual optical transitions. Here, we report electrically induced light emission from individual carbon nanotube p-n diodes. A new level of control over electrical carrier injection is achieved, reducing power dissipation by a factor of up to 1,000, and resulting in zero threshold current, negligible self-heating and high carrier-to-photon conversion efficiencies. Moreover, the electroluminescent spectra are significantly narrower ( approximately 35 meV) than in previous studies, allowing the identification of emission from free and localized excitons.

Defect-induced photoluminescence from dark excitonic states in individual single-walled carbon nanotubes

We show that new low-energy photoluminescence (PL) bands can be created in the spectra of semiconducting single-walled carbon nanotubes by intense pulsed excitation. The new bands are attributed to PL from different nominally dark excitons that are "brightened" because of a defect-induced mixing of states with different parity and/or spin. Time-resolved PL studies on single nanotubes reveal a significant reduction of the bright exciton lifetime upon brightening of the dark excitons. The lowest-energy dark state has longer lifetimes and is not in thermal equilibrium with the bright state.

Electron-hole interaction in carbon nanotubes: novel screening and exciton excitation spectra

The optical response of single-walled carbon nanotubes is dominated by exciton states with unusually large binding energies. We show that screening in semiconducting tubes enhances rather than reduces the electron-hole interaction for separations larger than the tube diameter. This "antiscreening" region deepens the relative energy level of the higher exciton states yielding unconventional excitation spectra. The effect explains the discrepancy in the current experimentally extrapolated exciton binding energies (deduced using conventional model spectra) and those obtained from ab initio calculations on isolated tubes.

Evidence for dark excitons in a single carbon nanotube due to the Aharonov-Bohm effect

We studied exciton structures and the Aharonov-Bohm effect in a single carbon nanotube using micro-photoluminescence (PL) spectroscopy under a magnetic field at low temperatures. A single sharp PL peak from the bright exciton state of a single carbon nanotube was observed under zero magnetic field, and the additional PL of dark exciton state appeared below the bright exciton peak under high magnetic fields. It was found that the split between the bright and dark exciton states is several millielectron volts at zero field. The tube diameter dependence of the splitting arises from the intervalley short-range Coulomb interaction.

Direct observation of dark excitons in individual carbon nanotubes: inhomogeneity in the exchange splitting

We report the direct observation of spin-singlet dark excitons in individual single-walled carbon nanotubes through low-temperature micro-magneto-photoluminescence spectroscopy. A magnetic field (B) applied along the tube axis brightened the dark state, leading to the emergence of a new emission peak. The peak rapidly grew in intensity with increasing B at the expense of the originally dominated bright exciton peak and became dominant at B>3 T. This behavior, universally observed for more than 50 tubes of different chiralities, can be quantitatively modeled by incorporating the Aharonov-Bohm effect and intervalley Coulomb mixing. The directly measured dark-bright splitting values were 1-4 meV for tube diameters 1.0-1.3 nm. Scatter in the splitting value emphasizes the role of the local environment surrounding a nanotube in determining its excitonic fine structure.

Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes

The absorption cross section of highly luminescent individual single-walled carbon nanotubes is determined using time-resolved and cw luminescence spectroscopy. A mean value of approximately 1 x 10(-17) cm2 per carbon atom is obtained for (6,5) tubes excited at their second optical transition, and corroborated by single tube photothermal absorption measurements. Biexponential luminescence decays are systematically observed, with short and long lifetimes around 45 and 250 ps. This behavior is attributed to the band edge exciton fine structure with a dark level lying a few meV below a bright one.

Phonon and electronic nonradiative decay mechanisms of excitons in carbon nanotubes

We investigate theoretically the rates of nonradiative decay of excited semiconducting nanotubes by a variety of decay mechanisms and compare them with experimental findings. We find that the multiphonon decay (MPD) of free excitons is too slow to be responsible for the experimentally observed lifetimes. However, MPD lifetimes of localized excitons could be 2-3 orders of magnitude shorter. We also propose a new decay mechanism that relies on a finite doping of nanotubes and involves exciton decay into an optical phonon and an intraband electron-hole pair. The resulting lifetime is in the range of 5 to 100 ps, even for a moderate doping level.

Study of the tunnelling initiated leakage current through the carbon nanotube embedded gate oxide in metal oxide semiconductor structures

The tunnelling currents through the gate dielectric partly embedded with semiconducting single-wall carbon nanotubes in a silicon metal-oxide-semiconductor (MOS) structure have been investigated. The application of the gate voltage to such an MOS device results in the band bending at the interface of the partly embedded oxide dielectric and the surface of the silicon, initiating tunnelling through the gate oxide responsible for the gate leakage current whenever the thickness of the oxide is scaled. A model for silicon MOS structures, where carbon nanotubes are confined in a narrow layer embedded in the gate dielectric, is proposed to investigate the direct and the Fowler-Nordheim (FN) tunnelling currents of such systems. The idea of embedding such elements in the gate oxide is to assess the possibility for charge storage for memory device applications. Comparing the FN tunnelling onset voltage between the pure gate oxide and the gate oxide embedded with carbon nanotubes, it is found that the onset voltage decreases with the introduction of the nanotubes. The direct tunnelling current has also been studied at very low gate bias, for the thin oxide MOS structure which plays an important role in scaling down the MOS transistors. The FN tunnelling current has also been studied with varying nanotube diameter.

Photon antibunching in the photoluminescence spectra of a single carbon nanotube

We report the first observation of photon antibunching in the photoluminescence from single carbon nanotubes. The emergence of a fast luminescence decay component under strong optical excitation indicates that Auger processes are partially responsible for inhibiting two-photon generation. Additionally, the presence of exciton localization at low temperatures ensures that nanotubes emit photons predominantly one by one. The fact that multiphoton emission probability can be smaller than 5% suggests that carbon nanotubes could be used as a source of single photons for applications in quantum cryptography.