Time-resolved charge detection in graphene quantum dots

We present real-time detection measurements of electron tunneling in a graphene quantum dot. By counting single electron charging events on the dot, the tunneling process in a graphene constriction and the role of localized states are studied in detail. In the regime of low charge detector bias we see only a single time-dependent process in the tunneling rate which can be modeled using a Fermi-broadened energy distribution of the carriers in the lead. We find a non-monotonic gate dependence of the tunneling coupling attributed to the formation of localized states in the constriction. Increasing the detector bias above 2 mV results in an increase of the dot-lead transition rate related to back-action of the charge detector current on the dot.Comment: 8 pages, 6 figure

Electron-Hole Crossover in Graphene Quantum Dots

We investigate the addition spectrum of a graphene quantum dot in the vicinity of the electron-hole crossover as a function of perpendicular magnetic field. Coulomb blockade resonances of the 50 nm wide dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 50 states displays the unique complex evolution of the diamagnetic spectrum of a graphene dot from the low-field regime to the Landau regime with the n=0 Landau level situated in the center of the transport gap marking the electron-hole crossover. The average peak spacing in the energy region around the crossover decreases with increasing magnetic field. In the vicinity of the charge neutrality point we observe a well resolved and rich excited state spectrum.Comment: 4 pages, 3 figure

Charge Detection in Graphene Quantum Dots

We report measurements on a graphene quantum dot with an integrated graphene charge detector. The quantum dot device consists of a graphene island (diameter approx. 200 nm) connected to source and drain contacts via two narrow graphene constrictions. From Coulomb diamond measurements a charging energy of 4.3 meV is extracted. The charge detector is based on a 45 nm wide graphene nanoribbon placed approx. 60 nm from the island. We show that resonances in the nanoribbon can be used to detect individual charging events on the quantum dot. The charging induced potential change on the quantum dot causes a step-like change of the current in the charge detector. The relative change of the current ranges from 10% up to 60% for detecting individual charging events.Comment: 4 pages, 3 figure

Energy gaps in etched graphene nanoribbons

Transport measurements on an etched graphene nanoribbon are presented. It is shown that two distinct voltage scales can be experimentally extracted that characterize the parameter region of suppressed conductance at low charge density in the ribbon. One of them is related to the charging energy of localized states, the other to the strength of the disorder potential. The lever arms of gates vary by up to 30% for different localized states which must therefore be spread in position along the ribbon. A single-electron transistor is used to prove the addition of individual electrons to the localized states. In our sample the characteristic charging energy is of the order of 10 meV, the characteristic strength of the disorder potential of the order of 100 meV.Comment: 5 pages, 5 figure

Observation of excited states in a graphene quantum dot

We demonstrate that excited states in single-layer graphene quantum dots can be detected via direct transport experiments. Coulomb diamond measurements show distinct features of sequential tunneling through an excited state. Moreover, the onset of inelastic cotunneling in the diamond region could be detected. For low magnetic fields, the positions of the single-particle energy levels fluctuate on the scale of a flux quantum penetrating the dot area. For higher magnetic fields, the transition to the formation of Landau levels is observed. Estimates based on the linear energy-momentum relation of graphene give carrier numbers of the order of 10 for our device.Comment: 3 pages, 3 figure

Dirac electrons in graphene-based quantum wires and quantum dots

In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene.Comment: Contribution for J. Phys.: Cond. Mat. special issue on graphene physic

Variations in the work function of doped single- and few-layer graphene assessed by Kelvin probe force microscopy and density functional theory

We present Kelvin probe force microscopy measurements of single-and few-layer graphene resting on SiO2 substrates. We compare the layer thickness dependency of the measured surface potential with ab initio density functional theory calculations of the work function for substrate-doped graphene. The ab initio calculations show that the work function of single-and bilayer graphene is mainly given by a variation of the Fermi energy with respect to the Dirac point energy as a function of doping, and that electrostatic interlayer screening only becomes relevant for thicker multilayer graphene. From the Raman G-line shift and the comparison of the Kelvin probe data with the ab initio calculations, we independently find an interlayer screening length in the order of four to five layers. Furthermore, we describe in-plane variations of the work function, which can be attributed to partial screening of charge impurities in the substrate, and result in a nonuniform charge density in single-layer graphene

Modeling the concentration–response function of the herbicide dinoseb on `Daphnia magna' (survival time, reproduction) and `Pseudokirchneriella subcapitata' (growth rate)

Models describing dose–response relationships are becoming increasingly popular in ecotoxicology. They allow simple and thorough evaluations of toxicity test results, including inter- and extrapolations to concentrations or exposure times other than those tested. Simple parametric regression models are of particular interest because their parameters may be attributed mechanistic meanings and they can be applied without sophisticated mathematical and computational support. We recently proposed a four-parameter logistic regression model to fit the survival data of `Daphnia magna' under dinoseb stress. The model parameters are the maximum survival time, the minimum time required for an individual to die, effect concentration, EC50, and a curve shape parameter. This model has now been applied to compare the lethality and reproduction toxicity of `D. magna' and the growth inhibition of `Pseudokirchneriella subcapitata' under dinoseb stress. It can be fitted adequately to all the measured data and the parameters can be attributed biological meanings in any of the three endpoints. A comparison of the modeled concentration-response functions of all three endpoints for dinoseb toxicity shows that the range of ECs with respect to both `D. magna' and algae is steep (a decrease of between 0.1 and 0.6 mg/L). The survival and reproduction of `D. magna' exhibit similar characteristic concentration–response functions and toxicities. The statistical no-effect concentration (SNEC) is 0.14 (survival) and 0.11 (reproduction) mg/L, respectively. On the other hand, algae seem to be less sensitive to dinoseb than `D. magna', (SNEC: 0.48 mg/L). However, further investigations of individual algae may lead to a more suitable comparison. We speculate that the four parameters of the model function can be related to specific properties of chemicals and organisms. Characterization of these properties would allow simple and appropriate estimation of the toxic effects of these chemicals

Effects of dinoseb on the entire life-cycle of `Daphnia magna'. Part II: Modelling of survival and proposal of an alternative to No-Observed-Effect-Concentration (NOEC)

Risk assessment is in urgent need of more accurate toxic effect endpoints than those currently in use, especially for low concentrations. Often such endpoints are estimated by analysis of variance, linear interpolation, or smoothing. As these statistical methods are not always satisfactory, some authors have proposed to describe the entire dose-response curves by fully formalized parametric regression models whose parameters have toxicological meaning. These models allow a better evaluation of pollutant effects, including inter- and extrapolation to any other than the measured effect values. Following this line, a four-parameter logistic regression model (standard model) was fitted to survival data of `Daphnia magna' under pesticide (dinoseb) stress. The heterogeneity of the variance was taken into account with a both-sides logarithmic transformation. Besides the standard model, a hormesis and a threshold model were tested too. These two others models have been described in the literature and might better represent the dose-response function we are looking for. All three models showed a good fit to our data, and the statistics gave no hints as to which model is the most appropriate. As no evidence was seen for hormesis or for the existence of a threshold concentration, we used the simplest, namely, the standard model, for most of our calculations. Model calculations allow the quantification of the effects on individuals' longevity as well as on mean survival time of the population. We used them to define a no-effect value, the statistical-no-effect concentration (SNEC). The SNEC is based on the confidence bands of the modeled regression and represents the highest value for which an effect is statistically not different from the control. The SNEC is an alternative to classical endpoints, like the no-observed-effect concentration (NOEC) or the low-effect concentrations (e.g., EC10, EC5, EC1)