Simulation of anisotropic wet-chemical etching using a physical model

We present a method to describe the orientation dependence of the etch rate of silicon, or any other single crystalline material, in anisotropic etching solutions by analytical functions. The parameters in these functions have a simple physical meaning. Crystals have a small number of atomically smooth faces, which etch (and grow) slowly as a consequence of the removal (or addition) of atoms by rows and layers. However, smooth faces have a roughening transition (well known in statistical physics); at increasing temperature they become rougher, and accordingly the etch and growth rates increase. Consequently, the basic physical parameters of our functions are the roughness of the smooth faces and the velocity of steps on these faces. This small set of parameters describes the etch rate in the two-dimensional space of orientations (on the unit sphere). We have applied our method to the practical case of etch rate functions for silicon crystals in KOH solutions. The maximum deviation between experimental data and simulation using only nine physically meaningful parameters is less than 5% of the maximum etch rate. This method, which in this study is used to describe anisotropic etching of silicon, can easily be adjusted to describe the growth or etching process of any crysta

Visualizing intrinsic localized modes with a nonlinear micromechanical array

Micromechanical cantilever arrays provide the opportunity to visualize the nonlinear excitations of a discrete nonlinear system in real time. Both stationary and moving localized nonlinear excitations can be produced either by driving the system at a frequency outside the plane wave spectrum or by driving the system at a frequency within the small amplitude dispersion curve range. To see these modes the tips of the cantilevers are imaged on a 1D CCD camera. The brightness of the image depends on the oscillation amplitude of the cantilever so that a distribution of amplitudes in the array can be recorded as a function of position and time. Both the stationary and traveling excitations have been successfully simulated using a nonlinear lumped element lattice model. The former ILM can appear in any size lattice while the latter requires a low density of modes for the formation of smoothly running excitation

Counting discrete emission steps from intrinsic localized modes in a quasi-one-dimensional antiferromagnetic lattice

金沢大学理学部Intrinsic localized modes (ILMs) in a quasi-1D antiferromagnetic material (C2H5NH3)2CuCl4 are counted by using a novel nonlinear energy magnetometer. The ILMs are produced by driving the uniform spin wave mode unstable with an intense microwave pulse. Subsequently a subset of these ILMs become captured by and locked to a cw driver so that their properties can be examined at a later time with a tunable cw low power probe source. Four-wave mixing is used to enhance the emission signal from the few large amplitude ILMs over that associated with the many small amplitude plane wave modes. A discrete step structure observed in the emission signal is identified with individual ILMs becoming unlocked from the driver. At most driver power and frequency settings the resulting emission step structure appears uniformly distributed; however, sometimes, nearby in parameter space, families of emission steps are evident as the driver frequency or power is varied. Two different experimental methods give consistent results for counting individual ILMs. Because of the discreteness in the emission both the size of an ILM and its energy can be estimated from these experiments. For the uniformly distributed case each ILM extends over ~42 antiferromagnetic unit cells and has an energy value of 1.3×10−12 J while for the case with families the ILM length becomes ～54 antiferromagnetic unit cells with an energy of 1.5×10−12 J. An unresolved puzzle is that the emission step height does not depend on experimental parameters the way classical numerical simulations suggest

Analysis of ILM Logic Operations via van der Pol Phase Planes

AbstractLogic operations that have previously been numerically demonstrated using intrinsic localized modes (ILMs) in a driven nonlinear 1-D lattice are analyzed using van der Pol phase planes. The time dependent application of a vibrational impurity mode either can produce or destroy an ILM. The appearance or absence of the resulting ILM can be understood via trajectories in the phase plane controlled by the evolving attractors associated with the time dependent impurity mode. Switching between the two possible branches depends on the phase of the amplitude modulation when the impurity mode is removed

Concentration Dependence of Superconductivity and Order-Disorder Transition in the Hexagonal Rubidium Tungsten Bronze RbxWO3. Interfacial and bulk properties

We revisited the problem of the stability of the superconducting state in RbxWO3 and identified the main causes of the contradictory data previously published. We have shown that the ordering of the Rb vacancies in the nonstoichiometric compounds have a major detrimental effect on the superconducting temperature Tc.The order-disorder transition is first order only near x = 0.25, where it cannot be quenched effectively and Tc is reduced below 1K. We found that the high Tc's which were sometimes deduced from resistivity measurements, and attributed to compounds with .25 < x < .30, are to be ascribed to interfacial superconductivity which generates spectacular non-linear effects. We also clarified the effect of acid etching and set more precisely the low-rubidium-content boundary of the hexagonal phase.This work makes clear that Tc would increase continuously (from 2 K to 5.5 K) as we approach this boundary (x = 0.20), if no ordering would take place - as its is approximately the case in CsxWO3. This behaviour is reminiscent of the tetragonal tungsten bronze NaxWO3 and asks the same question : what mechanism is responsible for this large increase of Tc despite the considerable associated reduction of the electron density of state ? By reviewing the other available data on these bronzes we conclude that the theoretical models which are able to answer this question are probably those where the instability of the lattice plays a major role and, particularly, the model which call upon local structural excitations (LSE), associated with the missing alkali atoms.Comment: To be published in Physical Review

Quantum Disordered Regime and Spin Gap in the Cuprate Superconductors

We discuss the crossover from the quantum critical, $z\!=\!1$, to the quantum disordered regime in high-T$_c$ materials in relation to the experimental data on the nuclear relaxation, bulk susceptibility, and inelastic neutron scattering. In our scenario, the spin excitations develop a gap $\Delta\!\sim\!1/\xi$ well above T$_c$, which is supplemented by the quasiparticle gap below T$_c$. The above experiments yield consistent estimates for the value of the spin gap, which increases as the correlation length decreases.Comment: 14 pages, REVTeX v3.0, PostScript file for 3 figures is attached, UIUC-P-93-07-06

Efficient Selfconsistent Calculations of Multiband Superconductivity in UPd2_2Al3_3

An efficient physically motivated computational approach to multiband superconductivity is introduced and applied to the study of the gap symmetry in a heavy-fermion, UPd$_2$Al$_3$. Using realistic pairing potentials and accurate energy bands that are computed within density functional theory, self-consistent calculations demonstrate that the only accessible superconducting gap with nodes exhibits d-wave symmetry in the $A_{1g}$ representation of the $D_{6h}$ point group. Our results suggest that in a superconductor with gap nodes the prevailing gap symmetry is dictated by the constraint that nodes must be as far as possible from high-density areas

Electromagnetic nucleon-delta transition in the perturbative chiral quark model

We apply the perturbative chiral quark model to the gamma N -> Delta transition. The four momentum dependence of the respective transverse helicity amplitudes A(1/2) and A(3/2) is determined at one loop in the pseudoscalar Goldstone boson fluctuations. Inclusion of excited states in the quark propagator is shown to result in a reasonable description of the experimental values for the helicity amplitudes at the real photon point.Comment: 25 page

Nonlinear magnetic susceptibility and aging phenomena in reentrant ferromagnet: Cu0.2_{0.2}Co0.8_{0.8}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Linear and nonlinear dynamic properties of a reentrant ferromagnet Cu$_{0.2}$Co$_{0.8}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound are studied using AC and DC magnetic susceptibility. This compound undergoes successive phase transitions at the transition temperatures $T_{h}$ (= 16 K), $T_{c}$ (= 9.7 K), and $T_{RSG}$ (= 3.5 K). The static and dynamic behaviors of the reentrant spin glass phase below $T_{RSG}$ are characterized by those of normal spin glass phase with critical exponent $\beta$ = 0.57 $\pm$ 0.10, a dynamic critical exponent $x$ = 8.5 $\pm$ 1.8, and an exponent $p$ (= 1.55 $\pm$ 0.13) for the de Almeida -Thouless line. A prominent nonlinear susceptibility is observed between $T_{RSG}$ and $T_{c}$ and around $T_{h}$, suggesting a chaotic nature of the ferromagnetic phase ($T_{RSG} \leq T \leq T_{c}$) and the helical spin ordered phase ($T_{c} \leq T \leq T_{h}$). The aging phenomena are observed both in the RSG and FM phases, with the same qualitative features as in normal spin glasses. The aging of zero-field cooled magnetization indicates a drastic change of relaxation mechanism below and above $T_{RSG}$. The time dependence of the absorption $\chi^{\prime \prime}$ is described by a power law form ($\approx t^{-b^{\prime \prime}}$) in the ferromagnetic phase, where $b^{\prime \prime} \approx 0.074 \pm 0.016$ at $f$ = 0.05 Hz and $T$ = 7 K. No $\omega t$-scaling law for $\chi^{\prime \prime}$ [$\approx (\omega t)^{-b^{\prime \prime}}$] is observed.Comment: 14 pages, 16 figures, and 2 table

Possible Flavor Mixing Structures of Lepton Mass Matrices

To search for possible textures of lepton mass matrices, we systematically examine flavor mixing structures which can lead to large lepton mixing angles. We find out 37 mixing patterns are consistent with experimental data, taking into account phase factors in the mixing matrices. Only six of the patterns can explain the observed data without any tuning of parameters, while the others need particular choices for the phase values. It is found that these six mixing patterns are those predicted by the models which have been proposed to account for fermion mass hierarchies. On the other hand, the others may give new flavor mixing structures of lepton mass matrices and therefore new possibilities of model construction.Comment: 21 page