Directional reconstruction and anisotropy studies

The incident directions of cosmic ray particles at the highest energies are readily measured by modern detectors. Provided that there are sufficient data, the interpretation of such directions should give strong information on the origin of cosmic rays. However, the choice of statistical methods used in such an analysis can be of paramount importance in the reliability of the interpretation. This article summarizes the conclusions which may be drawn from the present data, and proposes methods needed to interpret statistically the large quantities of data which will become available in the near future. To cite this article: R.W. Clay et al., C. R. Physique 5 (2004).     

Polarization anisotropy in the optical properties of silicon ellipsoids

A new real space quantum mechanical approach with local field effects included is applied to the calculation of the optical properties of silicon nanocrystals. Silicon ellipsoids are studied and the role of surface polarization is discussed in details. In particular, surface polarization is shown to be responsible for a strong optical anisotropy in silicon ellipsoids, much more pronounced with respect to the case in which only quantum confinement effects are considered. The static dielectric constant and the absorption spectra are calculated, showing that the perpendicular and parallel components have a very different dependence on the ellipsoid aspect ratio. Then, a comparison with the classical dielectric model is performed, showing that the model only works for large and regular structures, but it fails for thin elongated ellipsoids.     

Ellipsometric study of refractive index anisotropy in porous silicon

Porous Si layers of different thicknesses were prepared by anodising p⁺-type Si substrates with a resistivity of 0.01 Ω cm. The porosity of the samples ranged from 23% to 62%. The refractive index values for the ordinary and extraordinary rays were determined by multiple angle of incidence ellipsometry, from which an optical anisotropy parameter varying from 13% to 20% was obtained. The porous Si layers were modelled as uniaxially anisotropic films on an isotropic substrate, with an optical axis perpendicular to the sample surface. The morphological anisotropy which is typical for the p⁺-type porous Si with a predominating cylindrical geometry is responsible for these optical properties. All the porous Si layers studied were found to be optically negative.     

Directional anisotropy of surface self-diffusion on Pt(110)

The rate of surface self-diffusion on a Pt(110) single crystal in the [1$\text{1}$0] and [001] directions was measured at 1200–1750 K by monitoring the decay of a sinusoidal surface profile. The surface diffusion rate in the [1$\text{1}$o] direction was much faster than in the [001] direction. The activation energy of surface self-diffusion was 1.70 and 3.16 eV for the [1$\text{1}$0] and [001] directions, respectively, in good agreement with theoretical estimates. For large amplitudes of the profile the decay rate for the [001] direction was also dependent on the amplitude. This behavior can be explained by the appearance of (111) facets on the profile, which cause a retardation of the profile decay.     

Etchant anisotropy controls the step bunching instability in KOH etching of silicon

STM investigations of vicinal Si(111) surfaces etched in KOH solutions under controlled flow conditions show that step bunching instability is due to inhomogeneities that develop in the etchant as the result of highly step-site-specific etching reactions. Other previously postulated mechanisms for step bunching, including anisotropic surface diffusion, surface strain, and impurity deposition, are conclusively ruled out. The inhomogeneities locally accelerate etching near surface steps. Kinetic Monte Carlo simulations of this process qualitatively reproduce the observed morphologies.     

Conductivity anisotropy ofn-type silicon in the range of warm and hot carriers

The electric conductivity ofn-type silicon was measured as a function of the field intensity in different crystallographic directions at temperatures between 78 and 275 °K. From the data at medium fields (range of warm carriers) the coefficientsβ ₀ andγ ₀ ofSchmidt-Tiedemann's anisotropy theory were determined. Especially at low temperatures these coefficients are different for lightly and heavily doped crystals. The differences can be explained by the influence of ionized impurity scattering in addition to lattice scattering. The repopulation of the energy valleys of the conduction band as a function of the field intensity was calculated from the ratioγ ₀/β ₀ and — in the range of hot carriers — from the conductivities measured in <001> and <111> directions. A maximum increase of population of a cool valley was found to be between 0.5 and 1.2 of the zero-field population, depending on the particular sample, the field intensity being about 0.5 kV/cm and the lattice temperature 89 °K.     

Influence of anisotropy on the dispersion of surface plasmon-phonon polaritons in silicon carbide

Surface plasmon-phonon polaritons (SPPP’s) of types 3 and 4 are investigated in doped anisotropic single crystals of hexagonal silicon carbide (6H-SiC) in the orientation corresponding to K⊥C and xy⊥C. It is shown that a dispersion dependence of the type-3 SPPP’s bounded by K appears in 6H-SiC when the plasmon frequency increases to ν _p⊥⩾350 cm⁻¹. At ν _p⊥⩾400 cm⁻¹, ν _s(K) exists for type-4 SPPP’s in the frequency range Ω _∥ ⁺ <ν< _⊥ ⁺ . When the concentration of free charge carriers is increased, the dispersion curves are displaced toward higher frequencies. The conditions for the existence of type-3 and type-4 SPPP’s in 6H-SiC are determined. Fiz. Tverd. Tela (St. Petersburg) 40, 636–639 (April 1998)     

Molecular dynamics simulation of brittle fracture in silicon

Brittle fracture in silicon is simulated with molecular dynamics utilizing a modified embedded atom method potential. The simulations produce propagating crack speeds that are in agreement with previous experimental results over a large range of fracture energy. The dynamic fracture toughness is found to be equal to the energy consumed by creating surfaces and lattice defects in agreement with theoretical predictions. The dynamic fracture toughness is approximately 1/3 of the static strain energy release rate, which results in a limiting crack speed of 2/3 of the Rayleigh wave speed.     

Modifying of etching anisotropy of silicon substrates by surface active agents

The influence of alcohol additives on etch rate anisotropy of Si(hkl) planes has been studied. The etching processes were carried out in 3 and 5 M KOH aqueous solutions saturated and non-saturated with alcohols. Isopropanol, 1-propanol and tert-butanol were examined. It has been showed that the etching process cannot be controlled only by the surface tension of the solution. Saturation of the etching solution with alcohols modifies etch rate anisotropy, lowering the ratio of the etch rate of (110) and vicinal planes to the etch rate of (100) plane. The morphology of Si(hkl) planes etched in 3 M KOH solution saturated with tert-butyl alcohol has been studied in detail. Smooth (331) and (221) planes have been achieved in this solution. The (100) plane turned out to be densely covered by hillocks, opposite to the (100) plane etched in weak-alkaline solution saturated with isopropanol. To explain this phenomenon, the mechanism of hillocks formation on Si(100) surface has been proposed.     

Strong photoluminescence anisotropy in porous silicon layers prepared by polarized-light assisted anodization

Linearly-polarized infrared (1.06 μm) laser light with intensities ranging from 5.3 to 97 mW/cm² has been used to obtain anisotropically luminescent porous silicon (PSi) layers by photoanodic etching in a hydrofluoric acid solution. Remarkably large photoluminescence (PL) anisotropy has been observed in samples prepared with the highest illumination intensity. These samples show very low degrees of linear polarization when the PL excitation light is polarized parallel to the polarization direction of the etching light. When the excitation light is polarized perpendicular to that, we obtain usual degrees of linear polarization of several percent. This result indicates that anisotropic Si nanostructures in PSi layers can be made isotropic with high orientation selectivity by the polarized-light assisted technique. A simple two-dimensional model is presented to explain the observed prominent anisotropy.     

Computer simulation of Ti3Al intermetallic cleavage fracture

The decohesion energy and the energy of unstable stacking faults for all cracking planes and dislocation slip systems observed experimentally are calculated using the molecular dynamics method with N-particle atomic potentials. A dimensionless parameter characterizing the brittle behavior of the material is calculated for basis, prism, and pyramid faces in terms of the model elaborated by Kelly et al. and extended by Rice and Thompson. Cleavage in Ti₃Al is due to low decohesion energy values, which facilitates cracking, and high energies of unstable stacking faults, which prevents the formation of a plastic zone and stress relaxation at its vertex.     

Surface plasmon enhancement of an optical anisotropy in porous silicon/metal composite

We report on the theoretical results obtained by applying the modified effective medium theory to a composite material consisting of mesoporous Si on (110)-oriented substrate with pores filled with silver through, e.g., electroplating process. The theory developed permits a self-consistent determination of the effective dielectric permittivity tensor of such materials. It is shown that the optical anisotropy of such a composite can be greatly enhanced at some wavelength ranges. While this anisotropy is generally uniaxial as in non-metal-filled mesoporous Si etched on (110) substrate, the sign of the anisotropy (i.e., positive or negative) changes in some portions of the spectrum. The optimum material parameters for an experimental observation of the theoretically predicted effects are determined. PACS 78.20.-e; 78.20.Bh; 78.20.Ci; 78.20.Fm; 78.30.Fs; 78.55.Mb     

Effect of photonic crystal structure on the nonlinear optical anisotropy of birefringent porous silicon

Anisotropic photonic crystal structures consisting of birefringent porous silicon layers with alternating porosity were fabricated. The in-plane birefringence formed as a result of anisotropic etching in Si(110) results in unique multilayered structures with two distinct photonic bandgaps for orthogonal light polarizations. Nonlinear optical studies based on the third-harmonic generation from these structures demonstrate variation in the symmetry of the nonlinear optical response.     

Role of surface reconstructions in (111) silicon fracture

The (111) cleavage in crystalline silicon was investigated by hybrid quantum/classical atomistic simulations showing that its remarkable stability is largely due to asymmetric π-bonded reconstructions of the cleavage surfaces created by the advancing crack front. Further simulations show that the same reconstructions can induce an asymmetric dynamical response to added shear stress components. This explains why [211] upward steps are much more common than [211] downward steps on (111) cleavage surfaces, while "zigzag" cleavage with alternated (111) and (111) facets will still occur in crystal samples fractured under [110] uniaxial loading.     

On the temperature independence of statistical model parameters for cleavage fracture in ferritic steels

The work relates to the effect of temperature on the model parameters in local approaches (LAs) to cleavage fracture. According to a recently developed LA model, the physical consensus of plastic deformation being a prerequisite to cleavage fracture enforces any LA model of cleavage fracture to observe initial yielding of a volume element as its threshold stress state to incur cleavage fracture in addition to the conventional practice of confining the fracture process zone within the plastic deformation zone. The physical consistency of the new LA model to the basic LA methodology and the differences between the new LA model and other existing models are interpreted. Then this new LA model is adopted to investigate the temperature dependence of LA model parameters using circumferentially notched round tensile specimens. With the published strength data as input, finite element (FE) calculation is conducted for elastic-perfectly plastic deformation and the realistic elastic-plastic hardening, respectively, to provide stress distributions for model calibration. The calibration results in temperature independent model parameters. This leads to the establishment of a ‘master curve’ characteristic to synchronise the correlation between the nominal strength and the corresponding cleavage fracture probability at different temperatures. This ‘master curve’ behaviour is verified by strength data from three different steels, providing a new path to calculate cleavage fracture probability with significantly reduced FE efforts.     

Surface self-diffusion on Pt(110): Directional dependence and influence of surface-energy anisotropy

The decay of periodic surface profiles by surface self-diffusion is simulated by numerically solving the phenomenological equations for this process. The crystalline nature of the surface is taken into account by introducing an anisotropic surface free energy,(). Depending on the degree of anisotropy of(), the decay kinetics and the shapes of the profiles are largely different. A comparison with measurements of profile decay on Pt(l10) single crystal surfaces shows that the anisotropy in() along the [1¯10] azimuth should be about 2–3%, while that along the [001] azimuth is expected near 8%. In the latter case large amplitude profiles exhibit (111) faceting and slow decay kinetics which are non-exponential. The rate of surface self-diffusion on Pt(110) is anisotropic with the [1¯10] direction being faster than the [001] direction.     

Monitoring the ordering in biomolecular films on vicinal silicon surfaces by reflectance difference/anisotropy spectroscopy

DNA base molecules, adenine, thymine, guanine, and cytosine may be employed as charge transport molecules in biomolecular electronic devices. Their electronic properties are comparable with those of inorganic wide bandgap materials, e.g. GaN with the absorption onset in the near ultra-violet (UV) range. A recent field effect transistor study based on a modified DNA base revealed that the prototype bio-transistor gives rise to a better voltage gain compared to one based on carbon nanotubes (CNTs) [G. Mauricio, P. Visconti, V. Arima, S. D’Amico, A. Biasco, E. D’Amone, R. Cingolani, R. Rinaldi, Nanoletters 3 (2003) 479]. Here, in situ reflectance difference/anisotropy spectroscopy (RDS/RAS) is employed under ultra-high vacuum (UHV) conditions for monitoring the growth of DNA base molecules on vicinal hydrogen passivated Si(1 1 1) surfaces. Such vicinal substrates consisting of steps and terraces may serves as suitable templates for molecular ordering. Indeed, RDS/RAS measurements reveal information about molecular ordering of DNA bases induced by the density of steps on silicon surfaces. All four molecules, however, behave differently on the vicinal substrates. The first transition dipole moments corresponding to adenine and thymine molecules align mainly perpendicular to the step edge direction while for guanine and cytosine they align parallel to this direction, however, only in very thin layers. The RDS/RAS signal of the guanine and cytosine layers with thicknesses above 20 nm saturates due to a loss of ordering at higher coverages. Additionally, time-resolved RDS/RAS measurements at the silicon E₂ (4.25 eV) critical point (CP) demonstrate the sensitivity to the biomolecular/inorganic interface formation.     

The electronicg-factor anisotropy determined from measurements near the magic field of anomalous muonium in silicon and germanium

The field dependences of the anomalous muoniumSR frequencies have been measured in Si and Ge around the magic field. The results show a clear electronicg-factor anisotropy exists for Ge withg _¦-g₁=0.033, while that of Si is much smaller and essentially zero within the experimental accuracy.Work supported by National Science Foundation Grant DMR-79-09223.