Size distribution of sputtered particles from Au nanoislands due to MeV self-ion bombardment

Nanoisland gold films, deposited by vacuum evaporation of gold onto Si(100) substrates, were irradiated with 1.5 MeV Au$^{2+}$ ions up to a fluence of $5\times 10^{14}$ ions cm$^{-2}$ and at incidence angles up to $60^{\circ}$ with respect to the surface normal. The sputtered particles were collected on carbon coated grids (catcher grid) during ion irradiation and were analyzed with transmission electron microscopy and Rutherford backscattering spectrometry. The average sputtered particle size and the areal coverage are determined from transmission electron microscopy measurements, whereas the amount of gold on the substrate is found by Rutherford backscattering spectrometry. The size distributions of larger particles (number of atoms/particle, $n$ $\ge$ 1,000) show an inverse power-law with an exponent of $\sim$ -1 in broad agreement with a molecular dynamics simulation of ion impact on cluster targets.Comment: 13 pages, 8 figures, Submitted for publication in JA

Analytic Coulomb matrix elements in the lowest Landau level in disk geometry

Using Darling's theorem on products of generalized hypergeometric series an analytic expression is obtained for the Coulomb matrix elements in the lowest Landau level in the representation of angular momentum. The result is important in the studies of Fractional Quantum Hall effect (FQHE) in disk geometry. Matrix elements are expressed as simple finite sums of positive terms, eliminating the need to approximate these quantities with slowly-convergent series. As a by-product, an analytic representation for certain integals of products of Laguerre polynomials is obtained.Comment: Accepted to J. Math. Phys.; 3 pages revtex, no figure

Replicating Nanostructures on Silicon by Low Energy Ion Beams

We report on a nanoscale patterning method on Si substrates using self-assembled metal islands and low-energy ion-beam irradiation. The Si nanostructures produced on the Si substrate have a one-to-one correspondence with the self-assembled metal (Ag, Au, Pt) nanoislands initially grown on the substrate. The surface morphology and the structure of the irradiated surface were studied by high-resolution transmission electron microscopy (HRTEM). TEM images of ion-beam irradiated samples show the formation of sawtooth-like structures on Si. Removing metal islands and the ion-beam induced amorphous Si by etching, we obtain a crystalline nanostructure of Si. The smallest structures emit red light when exposed to a UV light. The size of the nanostructures on Si is governed by the size of the self-assembled metal nanoparticles grown on the substrate for this replica nanopatterning. The method can easily be extended for tuning the size of the Si nanostructures by the proper choice of the metal nanoparticles and the ion energy in ion-irradiation. It is suggested that off-normal irradiation can also be used for tuning the size of the nanostructures.Comment: 12 pages, 7 figures, regular paper submitted to Nanotechnolog

Nanodot to Nanowire: A strain-driven shape transition in self-organized endotaxial CoSi2 on Si (100)

We report a phenomenon of strain-driven shape transition in the growth of nanoscale self-organized endotaxial CoSi2 islands on Si (100) substrates. Small square shaped islands as small as 15\times15 nm2 have been observed. Islands grow in the square shape following the four fold symmetry of the Si (100) substrate, up to a critical size of 67 \times 67 nm2. A shape transition takes place at this critical size. Larger islands adopt a rectangular shape with ever increasing length and the width decreasing to an asymptotic value of ~25 nm. This produces long wires of nearly constant width.We have observed nanowire islands with aspect ratios as large as ~ 20:1. The long nanowire heterostructures grow partly above (~ 3 nm) the surface, but mostly into (~17 nm) the Si substrate. These self-organized nanostructures behave as nanoscale Schottky diodes. They may be useful in Si-nanofabrication and find potential application in constructing nano devices.Comment: 9 pages, 7 figure

Gravitational lensing constraint on the cosmic equation of state

Recent redshift-distance measurements of Type Ia supernovae (SNe Ia) at cosmological distances suggest that two-third of the energy density of the universe is dominated by dark energy component with an effective negative pressure. This dark energy component is described by the equation of state $p_{x} = w \rho_{x}$ $(w \geq -1)$. We use gravitational lensing statistics to constrain the equation of state of this dark energy. We use $n(\Delta\theta)$, image separation distribution function of lensed quasars, as a tool to probe $w$. We find that for the observed range of $\Omega_m \sim 0.2 - 0.4$, $w$ should lie between $-0.8 \leq w \leq -0.4$ in order to have five lensed quasars in a sample of 867 optical quasars. This limit is highly sensitive to lens and Schechter parameters and evolution of galaxies.Comment: Modified results and inclusion of calculations with new set of parameter

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case $\mu\propto r^{-2}$ for the energy density which arises in many astrophysical applications. In the second class the singularity at the center of the star is not present in the energy density. The models presented in this paper allow for increasing and decreasing profiles in the behavior of the energy density.Comment: 9 pages, to appear in Pramana - J. Phy

The angular size - redshift relation in power-law cosmologies

A linear evolution of the cosmological scale factor is a feature in several models designed to solve the cosmological constant problem via a coupling between scalar or tensor classical fields to the space-time curvature as well as in some alternative gravity theories. In this paper, by assuming a general time dependence of the scale factor, $R \sim t^{\alpha}$, we investigate observational constraints on the dimensionless parameter $\alpha$ from measurements of the angular size for a large sample of milliarcsecond compact radio sources. In particular, we find that a strictly linear evolution, i.e., $\alpha \simeq 1$ is favoured by these data, which is also in agreement with limits obtained from other independent cosmological tests. The dependence of the critical redshift $z_m$ (at which a given angular size takes its minimal value) with the index $\alpha$ is briefly discussed.Comment: 5 pages, 4 figures, LaTe

Low current MeV Au<SUP>2+</SUP> ion-induced amorphization in silicon: rutherford backscattering spectrometry and transmission electron microscopy study

The amorphization due to MeV Au2+ ion implantation in Si(1 1 1) has been studied using Rutherford backscattering spectrometry/channeling (RBS/C) and transmission electron microscopy (TEM) methods. 1.5 MeV Au2+ ions were implanted into Si(1 1 1) substrates at various fluences at low currents (0.02-0.04&#956;A cm-2) while the samples were kept at room temperature. The RBS/C results for as-implanted specimen shows the onset fluence for amorphization to be &#8776;5&#215; 1013 ions cm-2 which is much lower than the fluence reported earlier. Selected area diffraction (TEM) for a sample implanted at a of 1&#215;1014 ions cm-2 confirms the occurrence of the amorphization. Earlier, amorphization studies by Alford and Theodore, using 2.4 MeV gold ions in silicon (1 0 0) reported a threshold fluence of 1.8&#215;1015 ions cm-2 for amorphization when the implantation was carried out at higher currents (0.2-5 &#956; A cm-2) [J. Appl. Phys. 76 (1994) 7265]. The nuclear energy loss (Sn) for 1.5 MeV gold ions in silicon is &#8776;13% greater than the value for 2.4 MeV and cannot be the sole reason for lower threshold fluence for the amorphization. The amorphization at a relatively lower fluence for the low current implantations could be possible due to reduction in the dynamical annealing effects

Composite-fermion crystallites in quantum dots

The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large. We show that the composite-fermion theory provides an excellent account of the states in both regimes. The quantum mechanical formation of composite fermions with a large number of attached vortices automatically generates omposite fermion crystallites in finite quantum dots.Comment: 5 pages, 3 figure