Facet Slope Research Articles

Study of ordinary facets revealed in (1 0 0) InP by etching in HCl

We studied the tilt, curvature and surface morphology of side facets of mesa ridges revealed in (1 0 0) InP by etching in 3HCl (37%):1H 3PO 4 (85%) through InGaAs mask. The ridges lay at variable angle ω ∈ [45.5°; 90°] to [0 1 1] within the sector between [0 0 1] and [ 0 1 ¯ 1 ] . For each ω, a unique ridge shape was exposed defined at each of its long sides by a single positively sloped facet. Ridges with ω = 45.5° were confined to facets tilted at α ∼ 45°, related to {1 1 0} planes. The facets were straight and very smooth with a root-mean-square roughness σ as low as 0.9 nm. The other ridges had more moderately sloped facets: as ω increased, their tilt gradually decreased to α ∼ 35° at ω = 90°. While the facets with ω < 50° were very smooth and straight, the ones with 50° ≤ ω ≤ 90° were rougher, striated and increasingly curved. The roughness of the facet surfaces was associated with the striations and was explained as follows: during the etching in 3HCl:1H 3PO 4, relative fluctuations along edges of the InGaAs mask (line-edge roughness—LER) were transferred as striations onto the ridge facets. The transfer was markedly suppressed for the facets with 45.5° ≤ ω < 50° because the LER was quickly undercut as fast etching micro- and nano-sized facets were exposed at such orientations. By contrast, slowly etching or etch-stop micro- and nano-sized facets were revealed under the fluctuations for the ridges at 50° ≤ ω ≤ 90°. The undercutting of the LER was consequently suppressed, and the ridge facets were formed striated and rougher.

Dispensed polymer waveguides and laser-fabricated couplers for optical interconnects on printed circuit boards

Optical interconnects can provide chip-to-chip data communication with much needed bandwidth as processor speed and density keep growing. Optical waveguides and couplers are essential components for implementing optical interconnections. Techniques for directly dispensing polymer waveguides in laser-ablated trenches on printed circuit boards and for fabricating optical couplers are presented for quick prototype of optical interconnects. High-quality UV curable polymer waveguides were routinely fabricated. High-efficiency couplers, blazed grating couplers on sloped waveguides, sloped facet metal film couplers, and reflective-undercut facet couplers can be fabricated by using excimer laser ablation.

Interfacial dynamics of the rhomboidal pyramid pattern on ion-eroded Cu(110)

Consecutive transitions between regular and periodic nanostructures induced by ion bombardment on the Cu(110) surface have been studied as a function of the sputtering parameters (primary ion energy, substrate temperature, and ion flux). The morphologies can vary from the well-known ripple patterns oriented along the two main symmetry directions of the fcc(110) substrate, to mounded structures, and include the far from equilibrium rhomboidal pyramid motif recently observed on the Rh(110) surface. The dependence of the nanostructure facet slope and lateral separation from ion energy allows us to identify a morphological regime accessed for low ion energy, below $500\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, corresponding to the formation of rhomboidal pyramids. The dependence from the ion flux and substrate temperature bears strong similarities with a growth experiment, and is determined by the relaxation of isolated adatom and/or vacancy clusters created in the topmost surface layer by an ion impact. The selection of preferential step orientation and slopes follows from a delicate balance between the diffusion currents along the two main diffusion channels, the $⟨1\overline{1}0⟩$ and the ⟨001⟩.

Extending the Clapper–Yule model to rough printing supports

The Clapper-Yule model is the only classical spectral reflection model for halftone prints that takes explicitly into account both the multiple internal reflections between the print-air interface and the paper substrate and the lateral propagation of light within the paper bulk. However, the Clapper-Yule model assumes a planar interface and does not take into account the roughness of the print surface. In order to extend the Clapper-Yule model to rough printing supports (e.g., matte coated papers or calendered papers), we model the print surface as a set of randomly oriented microfacets. The influence of the shadowing effect is evaluated and incorporated into the model. By integrating over all incident angles and facet orientations, we are able to express the internal reflectance of the rough interface as a function of the rms facet slope. By considering also the rough interface transmittances both for the incident light and for the emerging light, we obtain a generalization of the Clapper-Yule model for rough interfaces. The comparison between the classical Clapper-Yule model and the model extended to rough surfaces shows that the influence of the surface roughness on the predicted reflectance factor is small. For high-quality papers such as coated and calendered papers, as well as for low-quality papers such as newsprint or copy papers, the influence of surface roughness is negligible, and the classical Clapper-Yule model can be used to predict the halftone-print reflectance factors. The influence of roughness becomes significant only for very rough and thick nondiffusing coatings.

Considerations on the chronological and causal relationships between talus flatirons and palaeoclimatic changes in central and northeastern Spain

Talus flatirons are relatively common landforms in arid and semiarid areas. They are frequent in the Duero, Tajo and Ebro Tertiary Basins in Spain. The generation of a flatiron requires the alternation of periods with a prevalence of accumulation processes followed by periods with a preponderance of erosion processes. In the three Tertiary basins considered here talus flatirons have been found in numerous places and up to five stages of slope evolution have been recognised in some locations. The second youngest stage (S 2) has been dated in several places in the Ebro and Duero Basins through 14C. The age of this stage ranges from 2529 ± 52 to 3590 ± 40 14C yBP. The third youngest stage (S 3) has yielded dates of 27,862 ± 444 radiocarbon years BP in the Ebro Basin, and 28,550 ± 130 14C yBP in the Duero Basin. S 4 has been dated in the Ebro Basin to 35,570 ± 490 14C yBP. The S 2 slope facets correspond to the Iron and Bronze Age Cold Stages. The S 3 and S 4 flatirons may be correlated with the Heinrich events H 3 and H 4. These dates may indicate that the accumulation periods on the slopes correspond to cold global events. The dates obtained for the stages S 3 and S 4 in the central and northeastern sectors of Spain and their good correlation with Heinrich events suggest that flatirons could be related to climatic sequences in the Upper Pleistocene and Holocene.

Optimizing faceting for beauty

Demands for beauty of a gem are related to the level of cutting technology that has been attained. Working the stone unavoidably results in its loss of weight, so the beauty of a gem is in conflict with its potential value. The appearance of a faceted stone is produced by optical effects; therefore the problem of optimizing the faceting of a stone is reduced to determining the criteria which affect its beauty and defining the faceting parameters which best satisfy those criteria. A correctly faceted stone is a compromise between different criteria. This selection of optimum parameters is affected by the physical properties of the gem and how it will be used. A faceted gem is an optical device which transforms light sources into light specks on the surface, which is different for each position of a viewer. The stone will be set in a jewellery article which will most probably be seen from certain directions, thus its appearance should be optimized for the most likely combinations of viewer and light source positions. For example, for a viewer looking perpendicularly into the table, one can determine the directions of light sources which are visible in the stone. In optimizing the directions of light sources it is important to consider the influence of the viewer’s head and body, which are not light sources. The body of the observer can lead to asymmetrical distribution of light on the surface of the stone and incorrect facet slopes can lead to ‘dead’ regions of the gem. To optimize the arrangement of facets an artist will consider the appearance of the entire gem.

Adaptive symmetric mean filter: a new noise-reduction approach based on the slope facet model

Two new noise-reduction algorithms, namely, the adaptive symmetric mean filter (ASMF) and the hybrid filter, are presented in this paper. The idea of the ASMF is to find the largest symmetric region on a slope facet by incorporation of the gradient similarity criterion and the symmetry constraint into region growing. The gradient similarity criterion allows more pixels to be included for a statistically better estimation, whereas the symmetry constraint promises an unbiased estimate if the noise is completely removed. The hybrid filter combines the advantages of the ASMF, the double-window modified-trimmed mean filter, and the adaptive mean filter to optimize noise reduction on the step and the ramp edges. The experimental results have shown the ASMF and the hybrid filter are superior to three conventional filters for the synthetic and the natural images in terms of the root-mean-squared error, the root-mean-squared difference of gradient, and the visual presentation.

Edge-coupled InGaAs p-i-n photodiode with the pseudowindow defined by an etching process

We have fabricated an edge-coupled InGaAs p-i-n photodiode (EC-PD) with its pseudowindow defined by conventional photolithographic processes and its facet formed by etching. Through fine tuning the window thickness, the transit-time-limited bandwidth was largely increased and device bandwidth was improved from /spl sim/8 GHz toward /spl sim/20 GHz. Such a tuning process is in fact a controlled selective chemical etching process, and optimizes the window thickness through reducing the thickness of undepleted absorption region. Although after tuning, the device preserves low leakage, the anisotropic chemical etching results in a sloped and reentrant facet that degrades the optical coupling efficiency and thus the device responsivity, which drops from 0.5 to 0.4 A/W at 1.3-/spl mu/m wavelength for a device without an anti-reflection coating. For the EC-PD with the optical input facet formed by etching instead of the cleavage process, the device yield can be improved and direct die separation is feasible, which amounts to a huge cost reduction. Furthermore, an edge-coupled photodiode array, which requires several reliable diodes in series, can be realized.

Landslide hazards in eastern Himalayas

The Himalayas, with extreme variations in relief, are characterised by very steep slopes, harsh (i.e. cold and humid) climate and a dynamic geotectonic setting. These characteristics appear responsible for widespread slope failures and mass movements, which are often accentuated by various human activities. The importance and severity of landslide phenomenon was not recognised until recently because of sparse habitation, remoteness of its occurrence, and limited sphere of influence of the individual slides. During the last few decades, increasing developmental activities, such as unplanned urbanization, communication, dam construction, deforestation, and agriculture, have substantially affected the geo-environment and aggravated the landslide hazard in the eastern Himalayas.&#x0D; Three sample areas: i) along the National Highway 31 A (the East Sikkim District), ii) in the area of the Rarnmarn Hydroelectric Project Stage II (the Darjeeling District), and iii) in the Kalimpong Municipal area (the Darjeeling District), all within the inner tectonic belt of the Lesser Himalaya, were investigated for preparing LHZ maps on 1:25,000 scale. Landslide hazard evaluation factors (LHEF) were rated for each of the major causative factors, namely lithology, structure, slope morphometry, relative relief, land use, and drainage density, and summed up to obtain the total estimated hazard (TEHD) values for each slope facet. The TEHD values from 0 to 10 were classified into live zones of increasing relative hazard.

Slope distribution of a rough surface measured by transmission scattering and polarization

Transmission scattering from medium to air was used to measure the slope distribution of the rough plane surface of a transparent glass hemisphere. A facet model successfully explained the measured results of refraction, scattering, and polarization: Transmission scattering existed for incident angles greater than the critical angle, all measured curves for the normalized scattered intensity versus the facet slope angle for different detection directions overlapped, and the measured polarization of scattering was approximately constant for >99% of the facets. The slope distribution obtained by transmission scattering agrees with those of the surface profiles in the valid range of the profiler and can represent the slope distribution of the rough surface.

Backscattering on soil structure described by plane facets

In this paper, a new approach for soil roughness description is proposed. It is based on numerical three-dimensional soil surface images obtained by a stereoscopic device with a very fine resolution. The collected database contains four soils with different roughness (from smooth to ploughed). Each three-dimensional (3D) image is first approximated by juxtaposition of small plane facets. Statistics are then retrieved from sizes and slopes of facets in the segmented image. Analytical formulations are proposed for statistical laws showing a clear discrimination between the different soils of our database. In order to study numerically backscattering behaviour over soil, we generate profiles with respect to the retrieved statistics by applying Monte Carlo method. The Moment Method is used to compute the backscattered field over perfect conductor generated profiles. Finally, the results of numerical electromagnetic simulation are compared with the analytical Integral Equation Model (IEM) solution. Excellent agreement is obtained for soils belonging to the validity domain of IEM. For rougher soils, our model shows a realistic behaviour with incidence angle.

Forest gradient response in Sierran landscapes: the physical template

Vegetation pattern on landscapes is the manifestation of physical gradients, biotic response to these gradients, and disturbances. Here we focus on the physical template as it governs the distribution of mixed-conifer forests in California’s Sierra Nevada. We extended a forest simulation model to examine montane environmental gradients, emphasizing factors affecting the water balance in these summer-dry landscapes. The model simulates the soil moisture regime in terms of the interaction of water supply and demand: supply depends on precipitation and water storage, while evapotranspirational demand varies with solar radiation and temperature. The forest cover itself can affect the water balance via canopy interception and evapotranspiration. We simulated Sierran forests as slope facets, defined as gridded stands of homogeneous topographic exposure, and verified simulated gradient response against sample quadrats distributed across Sequoia National Park. We then performed a modified sensitivity analysis of abiotic factors governing the physical gradient. Importantly, the model’s sensitivity to temperature, precipitation, and soil depth varies considerably over the physical template, particularly relative to elevation. The physical drivers of the water balance have characteristic spatial scales that differ by orders of magnitude. Across large spatial extents, temperature and precipitation as defined by elevation primarily govern the location of the mixed conifer zone. If the analysis is constrained to elevations within the mixed-conifer zone, local topography comes into play as it influences drainage. Soil depth varies considerably at all measured scales, and is especially dominant at fine (within-stand) scales. Physical site variables can influence soil moisture deficit either by affecting water supply or water demand; these effects have qualitatively different implications for forest response. These results have clear implications about purely inferential approaches to gradient analysis, and bear strongly on our ability to use correlative approaches in assessing the potential responses of montane forests to anthropogenic climatic change.

Scarp retreat rates in semiarid environments from talus flatirons (Ebro Basin, NE Spain)

Triangular slope facets or talus flatirons are presented as a useful tool for the calculation of scarp retreat rates in arid regions. In the central sector of the Ebro Basin, sequences of talus flatirons have been developed around mesas capped by Miocene limestone. These talus flatirons are grouped in four stages of slope evolution (S 2, S 3, S 4, S 5). By the extrapolation of the relict talus profiles with the adjusted log-functions, the position of the scarp for each one of the stages is located. The mean values obtained indicate a scarp retreat of 23 m between stages S 3 and S 2, 8 m between S 4 and S 3 and 26 m between S 5 and S 4. The ages obtained by radiocarbon dating are 2529±52 B.P. and 2930±60 B.P. for stage S 2, 27 864±444 B.P. for S 3 and 35 570±490 B.P. for S 4. Consequently, the mean scarp retreat rates are 0.9 mm/yr for the S 2–S 3 interval and 1 mm/yr for S 3–S 4. The scarp retreat rate is related to the lithological and structural features of both the caprock and the underlying clay sediments and to the palaeoclimatic evolution of the region that controls the intensity of weathering and water erosion processes that affect the slope system.

Bedrock surface roughness and the distribution of subglacially precipitated carbonate deposits: implications for formation at Glacier de Tsanfleuron, Switzerland

Two carbonate deposits are identified on the exposed bedrock surface in the forefield of Glacier de Tsanfleuron, Switzerland: macrocrystalline sparite and microcrystalline micrite. Comparison of the distributions of these forms with lee-side slope facets identified by high-pass filtering of a flow-parallel bedrock profile at a range of frequencies reveals two significant results. First, while the distribution of sparite is consistent with formation in the lee side of subglacial bedrock hummocks, that of micrite is not. This contrasts with previous investigations in which both sparite and micrite have been considered to form by mineral concentration and precipitation during the refreezing of regelation-related basal meltwaters in the lee side of bedrock hummocks. Alternative mechanisms of micrite formation involving carbonate deposition and/or precipitation within subglacial bedrock hollows are proposed. Second, the distribution of sparite is most strongly correlated with the distribution of lee-side slope facets identified by filtering at a frequency equivalent to a hummock wavelength of c. 0·1 m. This correspondence indicates empirically that pressure-related melting and refreezing (regelation) operates most effectively around bedrock hummocks that are shorter than c. 0·1 m. © 1998 John Wiley & Sons, Ltd.

Slope stability of Tehri Dam Reservoir Area, India, using landslide hazard zonation (LHZ) mapping

Abstract A 260 m high dam is under construction across the Bhagirathi River in the Garhwal Himalaya (India) to impound 3.6 x 10 9 m 3 of water at the maximum reservoir level. The reservoir will over a distance of about 44 km in the Bhagirathi Valley and about 25 km in the Bhillangna Valley. A landslide hazard zonation map of the reservoir area has been prepared. The relative influences of six major causative factors have been calculated to identify the important controlling factors in high hazard slope facets.

High performance 660 nm InGaP/AIGaInP quantum wellmetal cladding ridge waveguide laser diode

A high performance 660 nm metal cladding ridge waveguide laser diode was fabricated from a compressively strained In/sub 0.6/Ga/sub 0.4/P/(Al/sub x/Ga/sub 1-x/)/sub 0.5/In/sub 0.5/P single quantum well laser structure. The 4 /spl mu/m wide ridge waveguide diode had a threshold current of 31 mA with a differential quantum efficiency of 45%/facet (slope efficiency of 0.85 W/A) under CW operation. The characteristic temperature was 120 K from 20 to 75/spl deg/C. The diode operated in a single transverse mode up to 22 mW/facet.

Reactive ion etching of sloped sidewalls for surface emitting structures using a shadow mask technique

A novel, very simple technique for the direct adjustment of the slope of facets in a reactive ion etching process is presented. The etching process is performed by screening the sample partially with an aluminum shadow mask, which is located inside the dark space of the plasma. The sidewall angle of etched lines, defined by a pattern mask on the sample, depends strongly on the distance between the shadow mask and the sample. The investigations are carried out with a methane-hydrogen plasma. The angle of inclination of the sidewalls can be varied in a controllable manner by more than 45°. This technique is well suited to fabricate 90° reflectors, which are necessary for three-dimensional optical interconnects with planar waveguide structures. To analyze the optical quality of the etched mirror plane, the beam transformation was investigated by reflectivity measurements using a single aluminum-evaporated mirror structure, which is illuminated by a focused laser beam at a wavelength of 633 nm.

Cervical zygapophyseal joints: geometrical parameters and relationship to cervical kinematics

The relationship was examined between the height and slope of the cervical zygapophyseal joints and the patterns of motion of the cervical vertebrae. The height and orientation of the C 3C 7 superior articular processes were measured in lateral radiographs of 40 normal subjects. The C 4-C 6 facets were oriented at approximately 40° to the vertical, while the C 3 and C 7 facets were more steeply oriented. The heights of the superior articular processes were found to increase at progressively lower vertebral levels. Contrary to published views, the slope of the superior articular facets has no bearing on the pattern of motion of the cervical vertebrae. No relationship was found between slope of the facets and the location of the instantaneous axes of rotation of the cervical vertebrae. In contrast the height of the articular processes was perfectly related to the location of the axes of rotation. Articular height, but not slope, is a major determinant of the patterns of motions of the cervical vertebrae. This study provides data necessary to confirm or deny the putative roles of the cervical zygapophyseal joints in determining motion of the cervical spine in the sagittal plane.

The partition wavenumber in acoustic backscattering from a two-scale rough surface described by a power-law spectrum

Scattering from the ocean bottom is often assumed to be controlled by two spatial scales: the larger scale associated with reflections from plane facets, and the smaller one associated with diffuse scattering from height variations. Choosing the wavenumber for this partitioning has proven to be important but troublesome. For this work, scattering data are simulated using Helmholtz-Kirchhoff or physical optics theory and selected input geomorphology. These data are inverted to provide rms slope of facets and rms heights of small-scale roughness using a simple two-scale roughness model introduced previously (J. W. Caruthers and J. C. Novarini, IEEE J. Oceanic Eng., vol. 18, pp. 100-106, 1993). Bottom relief is described by power spectra of the power law form, and the bottom is assumed to be impenetrable. The work introduces a new criterion for effecting this partition based on setting a roughness parameter equal to unity. The criterion is shown to be valid for the cases analyzed based on the ability of the inversion model to recover the input geomorphology. >

Geometric model of crystal growth between rigid walls I. Kinetical faceting by geometric constraints

A geometric model of interface controlled crystal growth between two parallel rigid walls is presented. The interface equation of motion includes the migration driving force due to a bulk term and to local curvature. The interface mobility depends only on the local orientation. The walls impose geometrical constraints on the triple phase junction and the contact angle which is fixes by mechanical equilibrium. In the absence of external fields (e.g., the condition of slow growth), we solve this equation asymptotically, and we obtain the steady state shape and velocity of the interface. It is found that the geometric constraints cause kinetic faceting of the propagating interface. The velocity of the faceted interface depends on the facet slope and the walls wetting conditions. Experimental results of the propagating interface morphology during solid phase epitaxy may fit this description.