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We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.'s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.

We report experiment and theory on an ambipolar gate-controlled Si(111)-vacuum field effect transistor where we study electron and hole (low-temperature 2D) transport in the same device simply by changing the external gate voltage to tune the system from being a 2D electron system at positive gate voltage to a 2D hole system at negative gate voltage. The electron (hole) conductivity manifests strong (moderate) metallic temperature dependence with the conductivity decreasing by a factor of 8 (2) between 0.3 K and 4.2 K with the peak electron mobility (∼18  m2/V s) being roughly 20 times larger than the peak hole mobility (in the same sample). Our theory explains the data well using random phase approximation screening of background Coulomb disorder, establishing that the observed metallicity is a direct consequence of the strong temperature dependence of the effective screened disorder.

Cantilevered or suspended nanowires show promise for force or mass sensing applications due to their small mass, high force sensitivity and high frequency bandwidth. To use these as quantitative sensors, their bending stiffness or mass must be calibrated experimentally, often using thermally driven vibration. However, this can be difficult because nanowires are slightly asymmetric, which results in two spatially orthogonal bending eigenmodes with closely spaced frequencies. This asymmetry presents problems for traditional stiffness calibration methods, which equate the measured thermal vibration spectrum near a resonance to that of a single eigenmode. Moreover, the principal axes may be arbitrarily rotated with respect to the measurement direction. In this work, the authors propose a method for calibrating the bending stiffness and mass of such nanowires' eigenmodes using a single measurement taken at an arbitrary orientation with respect to the principal axes.

Individual metal alloy nanowires of constant diameter and high aspect ratio have previously been self-assembled at selected locations on atomic force microscope (AFM) probes by the method reported in Yazdanpanah et al (2005 J. Appl. Phys. 98 073510). This process relies on the room temperature crystallization of an ordered phase of silver-gallium. A parallel version of this method has been implemented in which a substrate, either an array of micromachined tips (similar to tips on AFM probes) or a lithographically patterned planar substrate, is brought into contact with a continuous, nearly planar film of melted gallium. In several runs, freestanding wires are fabricated with diameters of 40-400 nm, lengths of 4-80 µm, growth rates of 80-170 nm s( - 1) and, most significantly, with yields of up to 97% in an array of 422 growth sites. These results demonstrate the feasibility of developing a batch manufacturing process for the decoration of wafers of AFM tips and other structures with selectively patterned freestanding nanowires.

We have performed scanning gate microscopy (SGM) on graphene field effect transistors (GFET) using a biased metallic nanowire coated with a dielectric layer as a contact mode tip and local top gate. Electrical transport through graphene at various back gate voltages is monitored as a function of tip voltage and tip position. Near the Dirac point, the response of graphene resistance to the tip voltage shows significant variation with tip position, and SGM imaging displays mesoscopic domains of electron-doped and hole-doped regions. Our measurements reveal substantial spatial fluctuation in the carrier density in graphene due to extrinsic local doping from sources such as metal contacts, graphene edges, structural defects and resist residues. Our scanning gate measurements also demonstrate graphene's excellent capability to sense the local electric field and charges.

We investigate the mechanical properties of cantilevered silver-gallium (Ag(2)Ga) nanowires using laser Doppler vibrometry. From measurements of the resonant frequencies and associated operating deflection shapes, we demonstrate that these Ag(2)Ga nanowires behave as ideal Euler-Bernoulli beams. Furthermore, radial asymmetries in these nanowires are detected through high resolution measurements of the vibration spectra. These crystalline nanowires possess many ideal characteristics for nanoscale force and mass sensing, including small spring constants (as low as 10(-4) N m(-1)), high frequency bandwidth with resonance frequencies in the 0.02-10 MHz range, small suspended mass (picograms), and relatively high Q-factors (approximately 2-50) under ambient conditions. We evaluate the utility of Ag(2)Ga nanowires for nanocantilever applications, including ultrasmall mass and high frequency bandwidth piconewton force detection.

The micro-Wilhelmy method is a well-established method of determining surface tension by measuring the force of withdrawing a tens of microns to millimeters in diameter cylindrical wire or fiber from a liquid. A comparison of insertion force to retraction force can also be used to determine the contact angle with the fiber. Given the limited availability of atomic force microscope (AFM) probes that have long constant diameter tips, force-distance (F-D) curves using probes with standard tapered tips have been difficult to relate to surface tension. In this report, constant diameter metal alloy nanowires (referred to as "nanoneedles") between 7.2 and 67 microm in length and 108 and 1006 nm in diameter were grown on AFM probes. F-D and Q damping AFM measurements of wetting and drag forces made with the probes were compared against standard macroscopic models of these forces on slender cylinders to estimate surface tension, contact angle, meniscus height, evaporation rate, and viscosity. The surface tensions for several low molecular weight liquids that were measured with these probes were between -4.2% and +8.3% of standard reported values. Also, the F-D curves show well-defined stair-step events on insertion and retraction from partial wetting liquids, compared to the continuously growing attractive force of standard tapered AFM probe tips. In the AFM used, the stair-step feature in F-D curves was repeatably monitored for at least 0.5 h (depending on the volatility of the liquid), and this feature was then used to evaluate evaporation rates (as low as 0.30 nm/s) through changes in the surface height of the liquid. A nanoneedle with a step change in diameter at a known distance from its end produced two steps in the F-D curve from which the meniscus height was determined. The step features enable meniscus height to be determined from distance between the steps, as an alternative to calculating the height corresponding to the AFM measured values of surface tension and contact angle. All but one of the eight measurements agreed to within 13%. The constant diameter of the nanoneedle also is used to relate viscous damping of the vibrating cantilever to a macroscopic model of Stokes drag on a long cylinder. Expected increases in drag force with insertion depth and viscosity are observed for several glycerol-water solutions. However, an additional damping term (associated with drag of the meniscus on the sidewalls of the nanoneedle) limits the sensitivity of the measurement of drag force for low-viscosity solutions, while low values of Q limit the sensitivity for high-viscosity solutions. Overall, reasonable correspondence is found between the macroscopic models and the measurements with the nanoneedle-tipped probes. Tighter environmental control of the AFM and treatments of needles to give them more ideal surfaces are expected to improve repeatability and make more evident subtle features that currently appear to be present on the F-D and Q damping curves.

A calibrated method of force sensing is demonstrated in which the buckled shape of a long flexible metallic nanowire, referred to as a 'nanoneedle', is interpreted to determine the applied force. An individual needle of 157 nm diameter by 15.6 µm length is grown on an atomic force microscope (AFM) cantilever with a desired orientation (by the method of Yazdanpanah et al 2005 J. Appl. Phys. 98 073510). Using a nanomanipulator the needle is buckled in the chamber of a scanning electron microscope (SEM) and the buckled shapes are recorded in SEM images. Force is determined as a function of deflection for an assumed elastic modulus by fitting the shapes using the generalized elastica model (De Bona and Zelenika 1997 Proc. Inst. Mech. Eng. C 211 509-17). In this calibration the elastic modulus (68.3 GPa) was determined using an auxiliary AFM measurement, with the needle in the same orientation as in the SEM. Following this calibration the needle was used as a sensor in a different orientation than the AFM coordinates to deflect a suspended PLLA polymer fiber from which the elastic modulus (2.96 GPa) was determined. The practical value of the sensing method does depend on the reliability and ruggedness of the needle. In this study the same needle remained rigidly secured to the AFM cantilever throughout the entire SEM/AFM calibration procedure and the characterization of the nanofiber.

In a two-step method, carbon nanotubes, inorganic nanowires, or graphene sheets are connected between two anchor points to form nanomaterial air bridges. First, a recently developed method of forming directionally oriented polymer nanofibers by hand-application is used to form suspended composite polymer-nanomaterial fibers. Then, the polymer is sacrificed by thermally induced depolymerization and vaporization, leaving air bridges of the various materials. Composite fibers and bundles of nanotubes as thin as 10 nm that span 1 microm gaps have been formed by this method. Comparable bridges are observed by electrospinning solutions of the same nanomaterial-polymer composites onto micrometer-scale corrugated surfaces. This method for assembling nanomaterial air-bridges provides a convenient way to suspend nanomaterials for mechanical and other property determinations, and for subsequent device fabrication built up from the suspended nanosubstrates.

Loose graphene sheets, one to a few atomic layers thick, are often observed on freshly cleaved HOPG surfaces. A straightforward technique using electrostatic attraction is demonstrated to transfer these graphene sheets to a selected substrate. Sheets from one to 22 layers thick have been transferred by this method. One sheet after initial deposition is measured by atomic force microscopy to be only an atomic layer thick (∼0.35 nm). A few weeks later, this height is seen to increase to ∼0.8 nm. Raman spectroscopy of a single layer sheet shows the emergence of an intense D band which dramatically decreases as the number of layers in the sheet increase. The intense D band in monolayer graphene is attributed to the graphene conforming to the roughness of the substrate. The disruption of the C-C bonds within the single graphene layer could also contribute to this intense D band as evidenced by the emergence of a new band at 1620 cm(-1).