Gaussian Height Research Articles

Fractional Brownian motion as a rough surface

In this study we consider two dimensional fractional Brownian motion (fBM) as a rough surface, tuned by the Hurst exponent H, with a focus on the scaling relations. While this system fulfills partially the requirements for self-similar Gaussian surfaces, (like Gaussian height distribution), it shows deviations for the global features. A thorough examination of the Kondev’s hyperscaling relations is presented. The global features associated with level lines which define contour loop ensemble (CLE) are studied in terms of H. We show that in the thermodynamic limit the fractal dimension of loops (Df), the critical exponent of the distribution of loop length (τl), and the gyration radius (τr) vary linearly with H. The hyperscaling relations between these quantities however challenge this hypothesis. While Df, τl and τr fulfill partially the Kondev relations, the loop correlation exponent xl depends weakly on H, i.e. shows deviations from 12 which is hypothesized by Kondev to be super-universal for the Gaussian surfaces.

Revisiting the Vertical Distribution of H i Absorbing Clouds in the Solar Neighborhood

The vertical distribution of cold neutral hydrogen (H i) clouds is a constraint on models of the structure, dynamics, and hydrostatic balance of the interstellar medium. In 1978, Crovisier pioneered a method to infer the vertical distribution of H i absorbing clouds in the solar neighborhood. Using data from the Nançay 21 cm absorption survey, Crovisier determined the mean vertical displacement of cold H i clouds, 〈∣z∣〉. We revisit that author’s analysis and explore the consequences of truncating the H i absorption sample in Galactic latitude. For any nonzero latitude limit, we find that the quantity inferred by Crovisier is not the mean vertical displacement but rather a ratio involving higher moments of the vertical distribution. The resultant distribution scale heights are thus ∼1.5 to ∼3 times smaller than previously determined. In light of this discovery, we develop a Bayesian Monte Carlo Markov Chain method to infer the vertical distribution of H i absorbing clouds. We fit our model to the original Nançay data and find a vertical distribution moment ratio 〈∣z∣3〉/〈∣z∣2〉 = 97 ± 15 pc, which corresponds to a Gaussian scale height σ z = 61 ± 9 pc, an exponential scale height λ z = 32 ± 5 pc, and a rectangular half-width W z,1/2 = 129 ± 20 pc. Consistent with recent simulations, the vertical scale height of cold H i clouds appears to remain constant between the inner Galaxy and the Galactocentric distance of the solar neighborhood. Local fluctuations might explain the large-scale height observed at the same Galactocentric distance on the far side of the Galaxy.

Machine-learning descriptor search on the density of states profile of bimetallic alloy systems and comparison with the d-band center theory.

In this study, the electronic density of states (DOSs) calculated with density functional theory (DFT) were analyzed by the machine-learning techniques. More than 400 pure metal and bimetallic alloy systems were calculated with DFT, and obtained the surface DOSs and the CH3 adsorption energy (Ead). By fitting the Gaussian functions to the DOS, multiple descriptors, such as the Gaussian peak positions, heights, and widths were extracted. Several regression methods, such as the least absolute shrinkage of selection operator (LASSO), random-forest, gradient-boosting, and extra-tree were used to find the relationship between these descriptors and the Ead. The results show that the energy position of the peaks in the d-projected DOS is the most important descriptor, in agreement with the previously known d-band center theory. It was also shown that the peak position in d-projected DOS improves the regression model in addition to the d-band center, since it reduces the regression error.

Reynolds Number Dependency of Wall-Bounded Turbulence Over a Surface Partially Covered by Barnacle Clusters

The settlement of barnacles on a ship hull is a common form of marine biofouling. In this study, the Reynolds number dependency of turbulent flow over a surface partially covered by barnacle clusters is investigated using direct numerical simulations of turbulent channel flow at friction Reynolds numbers ranging from 180 to 720. Mean flow, Reynolds and dispersive stress statistics are evaluated and compared to the corresponding results for a generic irregular rough surface with a Gaussian height distribution. For the barnacle surface, distinctive features emerge in the velocity statistics due to the interplay between the barnacle clusters and the large, connected smooth-wall sections surrounding them. This aspect is further investigated by applying a rough-smooth decomposition to the local time-averaged flow statistics for the barnacle surface. Using this decomposition, the partial recovery of smooth-wall behaviour over the smooth sections of the barnacle surface can be observed in the Reynolds stress statistics with the streamwise Reynolds stresses exhibiting a similar behaviour as previously found for boundary layers over surfaces with a rough to smooth transition.

Carrier transport across PtSe2/n-type GaN heterojunction

We fabricated PtSe2/n-type GaN heterojunction diode by transferring a large-scale grown two-dimensional (2D) PtSe2 layered film onto a 3D GaN substrate. The PtSe2 film transferred onto GaN was ∼5.84-nm thick and had 11 layers with interlayer spacing of 0.52 nm. An exploration of the temperature-dependence of the current–voltage (I–V) characteristics of the PtSe2/n-type GaN heterojunction in the range 125–400 K revealed a strong dependency of the ideality factor and barrier height on measurement temperature. This indicates a presence of low- and high-barrier-height patches resembling barrier inhomogeneities along the interface. A barrier inhomogeneity analysis with a consideration for the Gaussian barrier heights distribution demonstrated the existence of a double Gaussian barrier distribution having a mean barrier height of 0.97 and 1.41 eV in low- and high-temperature regimes, respectively. An examination of the temperature-dependency of reverse leakage current indicated the dominance of variable-range hopping conduction in lower temperature region (<225 K) and Poole–Frenkel emission mechanism in higher temperature region (>250 K). The interface state density Nss of the PtSe2/n-type GaN heterojunction determined from the capacitance method was lesser than that attained from the forward I–V characteristics that can be accredited to the inhomogeneous spreading of the Nss.

Temperature-dependent Schottky diode behavior of Ni Schottky contacts to α-Ga2O3 film epitaxially grown on sapphire substrate

We fabricated Ni Schottky contacts on α-Ga2O3 epitaxial layers grown on a c-plane sapphire substrate and explored their current–voltage (I–V) characteristics dependence on temperature spanning over a wide temperature range of 100–425K. The Ni/α-Ga2O3 Schottky diode displayed excellent rectification, exhibiting a high barrier height of 1.39 eV, a low leakage current of the order 10−12 A, and a breakdown voltage of 215 V at room temperature. The reverse leakage current was confined within an order of magnitude over the entire measured temperature range, indicating the thermal stability of the diode. A large ideality factor of 1.20 attained at room temperature clearly indicates the diode behavior deviation from the ideal thermionic emission theory. The I–V characteristics revealed that the barrier height and ideality factor shows strong temperature dependence, indicating the existence of barrier inhomogeneity at the Schottky interface. An analysis of the barrier inhomogeneity using the thermionic emission with the assumption of a Gaussian barrier height distribution implies the prevailing double Gaussian barrier height distribution in the Ni/α-Ga2O3 Schottky diode with a transition at 250 K. The Richardson constant derived from the modified Richardson plot, evaluated by assuming the barrier height Gaussian distribution, was close to the theoretical Richardson constant of α-Ga2O3.

Capabilities and limits of surface roughness measurements with monochromatic speckles.

For coherent light illumination, surface roughness leads to speckles in the scattered light image. By evaluating the speckle contrast or image auto-correlation, a measurement of the roughness parameter S q is possible. While these measurement principles have been well known for decades, a fundamental understanding of the minimal achievable measurement uncertainty is missing. Therefore, the measurement uncertainty limits for four unavoidable sources of uncertainty are derived by means of theoretical and numerical approaches. The study is focused on the case of monochromatic speckles, which provide the highest sensitivity, as well as on the case of planar surface and isotropic surface roughness with a Gaussian height distribution and Gaussian correlation function. The considered uncertainty sources are the natural randomness of surface roughness itself, speckle noise, quantum shot noise, and camera noise. As a result, for the studied experimental configuration, speckle noise is determined as the largest contribution to measurement uncertainty, which leads to a minimal achievable relative uncertainty of 1%-2% for S q =(0.03-0.15)λ. According to theoretical studies, the speckle noise limit of the relative uncertainty is inversely proportional to four times the square root of the independent number of evaluated speckles. In addition, an absolute uncertainty limit is reached for ever-smoother surfaces, which amounts to λ divided by 64 times the square root of the independent number of evaluated speckles. Furthermore, systematic errors due to cross-sensitivity with respect to other parameters of surface roughness (height distribution, correlation length) as well as the surface position and shape (axial offset, tilt, curvature) are quantified and discussed. For the considered small deviations of different influencing quantities, the quantified errors are one order of magnitude smaller than the speckle noise limit.

Bistatic Radar Scattering from Non-Gaussian Height Distributed Rough Surfaces

In modeling a rough surface, it is common to assume a Gaussian height distribution. This hypothesis cannot describe an eventual asymmetry between crests and troughs of natural surfaces. We analyzed the bistatic scattering from a rough surface with non-Gaussian height distributions using the Kirchhoff scattering theory. Two extreme cases of Gamma-distributed surfaces were compared in particular: exponential and Gaussian distributions. The bistatic angular dependence was examined under various root mean square (RMS) heights and power spectrum densities. Contribution sources to the coherent and incoherent scattering components were singled out relating to the surface height distribution. For an exponential height surface, the coherent scattering strengthens even as the surface becomes rough. The non-Gaussian effect on the incoherent scattering is connected with surface power spectrum density. The height distribution impacts differ in the different regions of the bistatic scattering plane and thus complicate the differentiation of the scattering patterns due to height distribution.

Monolithic two-color short-wavelength InGaAs infrared photodetectors using InAsP metamorphic buffers

A bias-selectable two-color heterojunction bandgap engineered InGaAs thin film infrared photodetector, monolithically grown on an InP substrate by metal–organic chemical vapor deposition, is demonstrated. The detector structure has two back-to-back diodes, with In0.53Ga0.47As and In0.83Ga0.17As absorbers separated by n+-InAsxP1-x metamorphic buffers to accommodate for the lattice mismatch between the absorbers of ∼2%. The surface of the topmost metamorphic buffer of InAs0.63P0.37, acting as a lattice-matched virtual substrate for the In0.83Ga0.17As absorber, has a Gaussian height distribution with a low surface roughness of 2.8 nm. The InAsxP1-x buffers achieve a gradual lattice constant transition from In0.53Ga0.47As to In0.83Ga0.17As, with a sufficient strain relaxation of 97%. Compared to the In0.53Ga0.47As diode, the In0.83Ga0.17As diode shows a higher reverse saturation current density by a factor of approximately 104, owing to a shorter minority carrier lifetime and a higher intrinsic carrier concentration. The bias-dependent two-color detection at the cutoff wavelengths of 1.7 μm and 2.6 μm is achieved, enabled by the In0.53Ga0.47As (blue channel) and In0.83Ga0.17As (red channel) absorption, respectively. The two-color InGaAs photodetector exhibits high specific detectivities of 4.1×1011 and 3.1×109 cm·Hz1/2/W at 300 K in both the blue and red channel regions, respectively.

Computation of Backscattered Fields in Polarimetric SAR Imaging Simulation of Complex Targets

This article presents the computation of the backscattered field in simulation of synthetic aperture radar (SAR) raw data. We develop an improved Kirchhoff approximation to estimate the surface fields induced by the incident waves. The improved Kirchhoff approximation is a second-order iterative solution of the integral equations governing the targets’ electric and magnetic current densities. In computing the second-order re-radiated fields, we applied the shoot-bouncing-ray (SBR) technique to enhance propagation path tracking efficiency. The geometrical theory of diffraction (GTD) was employed to account for the diffraction fields from the edges and wedges, which constitute the total scattered fields collected by SAR in synthetic aperture. As the SAR moves along the azimuth direction, the backscattered signal computation is repeated as the antenna beam crosses the targets. This procedure demands heavy computational resources but requires no priori assumptions of radar cross-sections (RCSs) nor speckle statistics. The raw data is generated as an output signal of the SAR system response into which the backscattered signal is input. We chose three types of the target to demonstrate our approach to confirm the effectiveness. The first set of targets are three dihedral reflectors – two of them were rotated to constitute three unique scattering matrices. The results show that the polarimetric information, both relative amplitudes and phases, are well–preserved. The second target is a rough surface with exponential power spectral density and Gaussian height probability density. We examined image speckle statistics of multi-looking image. The third target type is an electrically large cargo ship (container) sitting over a sea surface. Polarimetric analysis via the Pauli and Y4R decompositions reveals that the polarimetric features are well preserved. Simulation results demonstrate that the present approach is fully coherent in streamlining the data flow from backscattered field to complex single look images within the SAR imaging scene.

Recovery of coherent reflection from rough-surface scattered acoustic fields via the frequency-difference autoproduct.

The acoustic field reflected from a random rough surface loses coherence with the incident field in the Kirchhoff approximation as kh cos θ increases, where k is the incident field wavenumber, h is the root mean square roughness height, and θ is the incidence angle. Thus, for fixed rough-surface properties and incidence angle, a reflected field at lower wavenumber should retain more coherence. Recent results suggest that the frequency-difference autoproduct formed from complex acoustic field amplitudes at two nearby frequencies can recover acoustic information at the difference of those frequencies even when the difference frequency is below the recorded field's bandwidth. Herein analytical, computational, and experimental results are presented for the extent to which the frequency-difference autoproduct recovers coherence from randomly rough-surface-scattered constituent fields that have lost coherence. The analytical results, developed from the Kirchhoff approximation and formal ensemble averaging over randomly rough surfaces with Gaussian height distributions and Gaussian correlation functions, indicate that the coherence of the rough-surface-reflected frequency-difference autoproduct depends on the surface correlation length and Δkh cos θ, where Δk is the difference of the autoproduct's constituent field wavenumbers. These results compare favorably with Monte Carlo simulations of rough surface scattering, and with laboratory experiments involving long surface correlation lengths where 1 ≤kh cos θ≤ 3.

Temperature dependence of electrical behaviour of inhomogeneous Ni/Au/4H–SiC Schottky diodes

Temperature dependence of electrical parameters of Ni/Au/4H–SiC Schottky diodes in a small temperature interval has been studied. Current–voltage characteristics were measured between 35 and 80 °C. I–V curves have not a linear part in semi-logarithmic plot which indicates barrier height inhomogeneity. We analyzed forward part of the I–V curves assuming Gaussian barrier height distribution and parallel connection of diode patches with different barrier heights. Using the least squares method we determined mean barrier height, standard deviation of the barrier height distribution and finally series resistance of the diode as a function of temperature. The extracted barrier height and standard deviation of the distribution decrease with increasing temperature. In contrary the series resistance of the diode increases with increasing temperature. As an interesting feature and a consequence of the series resistance increase with temperature a crossing of the I–V curves in practically the one point of the I–V curve has been observed. At this cross-point the current flowing through the diode is independent of the temperature.

Spectral analysis of the topography parameters for isotropic Gaussian rough surfaces applied to gold coating

In the fabrication of microelectronic devices, sputtering of thin films leads to isotropic rough surfaces described by (i) a Gaussian height distribution and (ii) a constant power spectral density (PSD) up to a roll-off frequency of q0 from which it decays as a power law. This paper introduces a robust approach to estimate the topography parameters such as the density, the mean radius of curvature and the height distribution of summits for isotropic Gaussian rough micro-surfaces. The proposed approach consists of computing the PSD function from the atomic force microscopy measurements, approximating the value of q0 and the magnitude P0 of the plateau by curve fitting algorithms, and analytically deriving the topography parameters using the random process theory. The robustness of the proposed methodology is assessed on a sputtered gold micro-surface. The investigations show that the proposed PSD-based approach reduces the dependence of the topography parameters on the sampling length compared to the deterministic method. Moreover, the PSD-based estimated density of summits is in a good agreement with scanning electron microscopy analysis, in contrast to both deterministic and autocorrelation-based methods. The proposed approach is therefore more suitable to extract topography parameters from measurements of micro-surfaces for the development of contact asperity-based models.

Stereometric analysis of Amazon rainforest Anacardium occidentale L. leaves.

AFM, profilometry and SEM measurements on both sides of the Anacardium occidentale L. leaf reveal that ultrastructure presented some singularities due to their different morphologies and roughness. The advanced stereometry and power spectrum density of both sides of the Anacardium occidentale L. leaf were carefully studied. We use three different microscopy techniques such as scanning electron microscopy, profilometry, and atomic force microscopy for a complete description of the leaf surface morphology. The morphology of the adaxial and abaxial sides revealed a surface composed of striated cuticles and stomata cells, respectively. The height parameters obtained by profilometry revealed that the abaxial side was rougher. However, both sides presented similar Gaussian height distribution and asymmetry. The advanced stereometric parameters obtained by the topographic maps of AFM revealed that the two sides have some singularities due to their different morphologies and roughness, but with similar microtextures. However, average PSD spectra showed that adaxial and abaxial sides are dominated by relatively low and high spatial frequencies, showing that the microtextures, unlike what was shown in stereometric parameters, are different. These results revealed that leaves surface morphology under different aspects and scales and the quantitative parameters confirmed the different spatial patterns displayed, which can be of great interest for the study of the biological behavior of plants from their leaves.

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

This paper proposes a brief review of acoustic wave scattering models from rough surfaces. This review is intended to provide an up-to-date survey of the analytical approximate or semi-analytical methods that are encountered in acoustic scattering from random rough surfaces. Thus, this review focuses only on the scattering of acoustic waves and does not deal with the transmission through a rough interface of waves within a solid material. The main used approximations are classified here into two types: the two historical approximations (Kirchhoff approximation and the perturbation theory) and some sound propagation models more suitable for grazing observation angles on rough surfaces, such as the small slope approximation, the integral equation method and the parabolic equation. The use of the existing approximations in the scientific literature and their validity are highlighted. Rough surfaces with Gaussian height distribution are usually considered in the models hypotheses. Rather few comparisons between models and measurements have been found in the literature. Some new criteria have been recently determined for the validity of the Kirchhoff approximation, which is one of the most used models, owing to its implementation simplicity.

Current transport properties of (Au/Ni)/HfAlO3/n-Si metal–insulator–semiconductor junction

In this study, HfAlO3 ternary alloy thin film was grown on n-type silicon using the atomic layer deposition method. The current transport mechanisms in the (Au/Ni)/HfAlO3/n-Si junction were examined over a wide temperature range (80–360 K). The values obtained for the ideality factor (n) varied from 22.93 to 3.94 and the barrier height at zero bias (ФB0) ranged from 0.221 eV to 0.821 eV as the temperature changed from 80 to 360 K. The ΦB0–n and ΦB0–q/2 kT characteristics were investigated to explain the higher n values and non-ideal behavior of the Richardson curves. Two linear regions were found at low temperatures (LTs; 80–180 K) and high temperatures (HTs; 200–360 K), which indicated the presence of a Gaussian distribution barrier height and the average barrier heights (Φ‾B0) were identified. The values obtained for Φ‾Bo were 0.734 eV for LTs and 1.125 eV for HTs, and the values of σs were 0.085 V for LTs and 0.140 V for HTs. The values obtained for Nss decreased as the temperature increased and they varied between ~1012 and 1013 eV−1 cm−2. Finally, the dielectric behavior and conductivity of the (Au/Ni)/HfAlO3/n-Si junction were investigated at frequencies between 5 kHz and 2 MHz at room temperature. The values determined for ε′ and ε′′ at −1 V and 5 kHz were 2.1 and 3.53, respectively.

Conditions of the Presence of Bimodal Amplitude Distribution of Two-Process Surfaces

Two-process surfaces are functionally important. They contain plateau and valley parts. They are created by superimpositions of two one-process textures of Gaussian probability height distributions. It is expected that the resulting two-process surface would have bimodal height probability distribution. However, typically two-process textures have unimodal ordinate distribution. The present authors developed limiting conditions of presence of bimodal ordinate distribution. These conditions depend on the material ratio at the plateau-to-valley transition (the Smq parameter), and on the ratio of heights of the plateau and valley surface parts (Spq/Svq). Generated stratified textures and measured two-process surfaces of cylinder liners were taken into consideration.

Multilook Intensity Ratio Distribution for 3-D Layered Structures With Slightly Rough Interfaces

We derive the statistics for the multilook intensity ratio for a multilayered medium bounded by randomly rough surfaces. Calculations are carried out in the context of the first-order small perturbation method and assume slightly rough surfaces of infinite extent and centered Gaussian height distributions. We show that the probability distributions for the co- and cross-polarized intensity ratios for ${n}$ -look data are functions of three parameters and that the mean exists for $n\gt 1$ and the variance for $n\gt 2$ . The obtained theoretical expressions are verified by comparison with the Monte Carlo results.

Interdependence of Amplitude Roughness Parameters on Rough Gaussian Surfaces

According to international standards, the topography and the quality of machined surfaces can be characterized simultaneously by more than 70 roughness parameters. Despite the increased accuracy of topography measurements by modern instruments, the gained information about the 3D surface is still not well understood. The fact that machined surfaces are in general of Gaussian height distribution motivated the authors to study the interdependence of the standardized amplitude roughness parameters of computer-generated random rough (Gaussian) surfaces. In this contribution, these rough surfaces are created by solving numerically a Langevin-type stochastic differential equation for a defined random process, namely a Gaussian one. This numerical scheme provides rough surfaces of pre-defined statistical features, e.g., given standard deviation and correlation length. The numerical analysis of 17 standardized amplitude roughness parameters collected from 90000 computer-generated rough surfaces revealed so far undetected interdependencies among some of these parameters, namely the results show a strong linear relation between 12 amplitude roughness parameters.

Automated Method of Extracting Urban Roads Based on Region Growing from Mobile Laser Scanning Data.

With the rapid development of three-dimensional point cloud acquisition from mobile laser scanning systems, the extraction of urban roads has become a major research focus. Although it has great potential for digital image processing, the extraction of roads using the region growing approach is still in its infancy. We propose an automated method of urban road extraction based on region growing. First, an initial seed is chosen under constraints relating to the Gaussian curvature, height and number of neighboring points, which ensures that the initial seed is located on a road. Then, the growing condition is determined by the angle threshold of the tangent plane of the seed point. Then, new seeds are selected based on the identified road points and their curvature. The method also includes a strategy for dealing with multiple discontinuous roads in a dataset. The result shows that the method can not only achieve high accuracy in urban road extraction but is also stable and robust.