Lateral Correlation Length Research Articles

Theoretical analysis of the mobility of two-dimensional electron gas in the quaternary AlxInyGa1-x-yN/GaN heterojunctions limited by the alloy composition fluctuation

We established the model of the electron mobility limited by the alloy composition fluctuation scattering in the quaternary AlxInyGa1-x-yN/GaN heterojunctions for the first time. The alloy composition fluctuation along the AlxInyGa1-x-yN/GaN heterointerface was considered and characterized by the lateral correlation length L, and the fluctuations of aluminum and indium mole fractions (Δx and Δy) independent to each other. The situation of alloy composition fluctuation is investigated in the following cases. Only x or y fluctuates, and both x and y fluctuate with equal/unequal amplitudes in the same/opposite direction. We find that the scattering with both x and y fluctuating in the same direction is the weakest, while x and y fluctuating in the opposite directions leads to the strongest scattering. This in nature stems from the disparity of the bandgap and polarization in AlInN, AlGaN and GaN. The effects of different parameters, such as x and y, Δx and Δy, L, and the thickness of AlxInyGa1-x-yN barrier layer d on the mobility are also studied. The model will in principle give a universal explanation to the effect of alloy composition fluctuation scattering on the carrier mobility in the GaN-based heterostructures with ternary or quaternary alloy barrier layers.

Effect of thermal annealing on structural properties of GeSn thin films grown by molecular beam epitaxy

GeSn alloy with 7.68% Sn concentration grown by molecular beam epitaxy has been rapidly annealed at different temperatures from 300°C to 800°C. Surface morphology and roughness annealed below or equal to 500°C for 1 min have no obvious changes, while the strain relaxation rate increasing. When the annealing temperature is above or equal to 600°C, significant changes occur in surface morphology and roughness, and Sn precipitation is observed at 700°C. The structural properties are analyzed by reciprocal space mapping in the symmetric (004) and asymmetric (224) planes by high resolution X-ray diffraction. The lateral correlation length and the mosaic spread are extracted for the epi-layer peaks in the asymmetric (224) diffraction. The most suitable annealing temperature to improve both the GeSn lattice quality and relaxation rate is about 500°C.

Surface roughness dependence of the electrical resistivity of W(001) layers

The resistivity ρ of epitaxial W(001) layers grown on MgO(001) at 900 °C increases from 5.63 ± 0.05 to 27.6 ± 0.6 μΩ-cm with decreasing thickness d = 390 to 4.5 nm. This increase is due to electron-surface scattering but is less pronounced after in situ annealing at 1050 °C, leading to a 7%–13% lower ρ for d < 20 nm. The ρ(d) data from in situ and ex situ transport measurements at 295 and 77 K cannot be satisfactorily described using the existing Fuchs-Sondheimer (FS) model for surface scattering, as ρ for d < 9 nm is larger than the FS prediction and the annealing effects are inconsistent with a change in either the bulk mean free path or the surface scattering specularity. In contrast, introducing an additive resistivity term ρmound which accounts for surface roughness resolves both shortcomings. The new term is due to electron reflection at surface mounds and is, therefore, proportional to the ballistic resistance times the average surface roughness slope, divided by the layer thickness. This is confirmed by a measured linear relationship between ρmound and σ/(Ld), where the root-mean-square roughness σ and the lateral correlation length L of the surfaces are directly measured using atomic force microscopy and X-ray reflectivity.

Influence of the Chemical Activity of Implanted Ions on the Structure of the Damaged Si Layer in SIMOX Substrates

High‐resolution X‐ray diffraction (HRXRD), X‐ray reflectometry (XRR), X‐ray photoelectron spectroscopy (XPS), and Atomic‐force microscopy (AFM) were used to study the influence of the chemical activity of implanted ions (N+, O+, F+ or Ne+) on the structure of the damaged Si layer in SIMOX substrates. The implantation conditions were chosen so that the number of primary defects and the projected range were approximately the same for the implanted ions. HRXRD showed that the depth distribution of the residual damage depends on the chemical activity of the impurity. This may result from the quasi‐chemical interaction between the radiation‐induced point defects (VSi and Sii) and the impurity atoms. The shape of the density profiles and the thickness of the transition surface layer obtained from the XRR data are different for the implanted ions. The [100] faceted surface features of the samples prepared by SIMOX technology are preserved after implantation with the ions. AFM revealed a reduction of the lateral correlation length. The magnitude of this effect depends on the chemical activity of the implanted ions. Silicon oxidation at a depth of 10–15 nm is shown by XPS to change depending on the implanted ion.

Temperature‐dependent morphology and characteristic parameters of annealed gold nanolayers

Gold nanostructures were formed when Au nanolayers were deposited on native‐oxide‐covered Si substrates and annealed. To analyze the annealing temperature dependent surface morphology, we calculated the height–height correlation function and the power spectrum density function from the atomic force microscopy image data. When the annealing temperature for 20 nm thick Au layer increased from 500 to 700 °C, the interface width w and the lateral correlation length ξ of the surface increased obviously from 4.8 to 44.0 nm and from 70.5 to 180.9 nm, respectively. On the other hand, the roughness exponent α was a relatively universal parameter (∼0.87). While the morphology of the surfaces was mainly self‐affine, suggesting that the random surface diffusion plays a dominant role in the kinetic roughening process of such an annealed system, the results of the morphological analysis also imply that the self‐affine surface begins to become mounded for higher annealing temperatures.

Morphological characterisation and microstructure of silver films prepared by electrodeposition method

The electrodeposition method is used to prepare silver films at different thickness. In order to characterise the films, scaling law analysis was done using concept of fractal. We obtained a growth exponent, β = 0.61 and average roughness exponent, α = 0.62 using root mean square roughness and height–height correlation function. The results indicate that the films with higher thickness have higher surface roughness. However the fractal analysis using height–height correlation shows that the value of fractal dimension decreases from 2.45 to 2.33 depending on the thickness of films. On the other hand the increase of thickness influenced the lateral correlation length strongly. Thus, these features may be controlled by choosing an optimum film thickness.

Structural properties of GeSn thin films grown by molecular beam epitaxy

GeSn thin films on Ge (001) with various Sn concentrations from 3.36 to 7.62% were grown by molecular beam epitaxy and characterized. The structural properties were analyzed by reciprocal space mapping in the symmetric (004) and asymmetric (224) planes by high resolution X-ray diffraction (XRD). The lateral correlation length (LCL) and the mosaic spread (MS) were extracted for the epi-layer peaks in the asymmetric (224) diffraction. With the increase of Sn concentration, the LCL reduces while the MS increases, indicating degrading crystalline quality. Dislocations were observed in the sample with 7.62% Sn concentration by transmission electron microscope, consistent with the strain relaxation found in XRD mapping. Besides, the surface morphologies were investigated.

Influence of hydrophobic and superhydrophobic surfaces on reducing aerodynamic insect residues

Insect fouling during takeoff, climb and landing can result in increased drag and fuel consumption for aircrafts with laminar-flow surfaces. This study investigates the effectiveness of various hydrophobic and superhydrophobic surfaces in reducing residue of insects on an aerodynamic surface at relatively high impact speeds (about 45m/s). An experimental setup consisting of a wind tunnel and a method to inject live flightless fruit flies was used to test the effectiveness of various surfaces against insect fouling. Insect fouling was analyzed based on residue area and height from multiple impacts. In general most of the residue area was due to the hemolymph spreading while most of the residue height was due to adhesion of exoskeleton parts. Hydrophobic and especially superhydrophobic surfaces performed better than a hydrophilic aluminum surface in terms of minimizing the residue area of various insect components (exoskeleton, hemolymph, and red fluid). Surfaces with reduced wettability and short lateral length scales tended to have the smallest residue area. Residue height was not as strongly influenced by surface wettability since even a single exoskeleton adhered to the surface upon impact was enough to produce a residue height of the order of one mm. In general, the results indicate that hemolymph spread needs to be avoided (e.g. by having reduced wettability and short lateral correlation lengths) in order to minimize the residue area, while exoskeleton adherence needs to be avoided (e.g. by having oleophobic properties and micro/nano roughness) in order to minimize the residue height. In particular, two of the superhydrophobic coatings produced substantial reduction in residue height and area, relative to the baseline surface of aluminum. However, the surfaces also showed poor mechanical durability on the high-speed insect impact location. This suggests that although low wettability materials show great insect anti-fouling behavior, their durability needs to be substantially improved in order to withstand harsh aerospace conditions.

Analysis of surface roughness correlation function by X‐ray reflectivity

X‐ray reflectivity (XRR) is a powerful tool for the analysis on surface and interface roughness. In the conventional XRR analysis, the reflectivity was calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot–Croce. We have developed an improved XRR formalism which derives more accurate surface and interface roughness. In this study, we introduced the effective roughness depending on the incidence angle of X‐rays. The newly developed XRR formalism, which derives more accurate surface and interface roughness, is found to be dependent on the size of coherent X‐rays probing area, and further derives the roughness correlation function as well as the lateral correlation length. Copyright © 2016 John Wiley & Sons, Ltd.

Zinc Oxide Thin Films Characterization, AFM, XRD and X-ray Reflectivity

In this study, surface structures of two zinc oxide (ZnO) thin films, prepared by sol–gel spin and dip-coating methods, were investigated. Ex situ Atomic Force Microscopy (AFM), X-ray diffraction (XRD), and X-ray reflectivity measurements were carried out in order to study the surface structure. XRD measurements showed nanostructured ZnO thin films with well-defined orientations. Fractal analysis was applied on the AFM data to illustrate the surface morphology of thin films. Fractal analysis provided a precious depiction of irregularities found in ZnO thin films and revealed that both interface width W and lateral correlation length ξ are strongly affected by coating method. Calculations showed that the film that was prepared by dip-coating had correlation length, interface width and fractal dimension of 56.2, 2.3, and 2.2 nm, respectively. These parameters for spin-coated sample were 354.8, 8.5, and 2.64 nm, respectively. Optimization of X-ray reflectivity by Genetic Algorithm optimization revealed structural parameters of thin films such as surface and interface roughness and thickness of the films. These calculations showed that dip-coated thin film has a smooth surface, whereas spin-coated thin film has a rough surface.

Evaluating the impacts of fine-scale capillary heterogeneity and wettability on the behavior of buoyancy-driven CO2 migration and trapping mechanisms

One of the primary concerns in CO2 sequestration is long-term immobilization of CO2. There are several storage mechanisms to immobilize CO2 in a porous medium: structural, dissolution, residual, and mineral trapping. Storage analysis with fine-scale heterogeneity requires the investigation of a newly suggested mechanism: capillary barrier trapping. This study covers a quantitative assessment of the CO2 trapping capacity with residual, dissolution, and capillary barrier trapping mechanisms in heterogeneous formations. The effects of heterogeneity on CO2 trapping capacity are studied under different wettability scenarios. The Leverett J-function is applied so that every grid block has a different drainage capillary pressure curve, which is physically consistent with its heterogeneous properties and wettability. Based on contact angle, residual saturation and relative permeability curves are modeled. Different heterogeneity and wettability causes considerable variations in leakage of CO2, ranging from 6 to 38 %. The lateral correlation length of permeability affects the spatial distribution of CO2. As the permeability variation increases, the total amount of trapped CO2 increases significantly indicating a reduced potential risk of leakage. Although the residual and dissolution trappings decreases as the wetting condition changes from strongly water-wet to intermediate gas-wet, the amount of CO2 trapped by the capillary barriers increases considerably, and the mobile phase saturation of the CO2 is reduced. The results of this study have emphasized the importance of capillary barrier trapping, which takes a large portion of the immobilized CO2 phase, for stable underground storage.

Nanostructured surfaces investigated by quantitative morphological studies

The morphology of different surfaces has been investigated by atomic force microscopy and quantitatively analyzed in this paper. Two different tools have been employed to this scope: the analysis of the height–height correlation function and the determination of the mean grain size, which have been combined to obtain a complete characterization of the surfaces. Different materials have been analyzed: SiOxNy, InGaN/GaN quantum wells and Si nanowires, grown with different techniques. Notwithstanding the presence of grain-like structures on all the samples analyzed, they present very diverse surface design, underlying that this procedure can be of general use. Our results show that the quantitative analysis of nanostructured surfaces allows us to obtain interesting information, such as grain clustering, from the comparison of the lateral correlation length and the grain size.

Insight Mechanisms of Surface Structuring and Wettability of Ion-Treated Ag Thin Films

Insight mechanisms involved in the evolution of surface morphology and wettability of 100 MeV Ag-ion-treated Ag thin films have been studied using thermal spike and fractal analysis. The results of nanostructuring and wettability are correlated on the basis of atomic force microscopy (AFM), scanning electron microscopy (SEM), and contact angle (CA) measurements. The SEM images show ion-induced evolution of Ag nanostructures and reduction in the surface coverage area of Ag. The AFM images reveal the formation of nanostructures. The autocorrelation and power spectral density (PSD) functions are used to characterize the surface profile, and these confirm the formation of nanostructures. Fractal analysis is performed on pristine and ion beam tailored surfaces to explore the mechanism involved in nanostructuring. It is observed that interface width, lateral correlation length, and roughness exponent depend on ion doses. The variation in the wettability of surfaces is well correlated with interface width and co...

Model for small-scale crustal heterogeneity in Los Angeles basin based on inversion of sonic log data

SUMMARY High-frequencyseismicgroundmotion(10+Hz),asneededforearthquakeengineeringdesign purposes, is largely controlled by the metre-scale structure of the earth’s crust. However, the state-of-the-art velocity models poorly resolve small-scale features of the subsurface velocity and density variation. We invert 35 sonic logs (up to 3000 m in depth) in and near Los Angeles basin, CA, to obtain a statistical description of the small-scale heterogeneities of the basin. Assuming a von Karman autocorrelation function, our analysis finds that Hurst numbers, ν, between 0.0 and 0.2, vertical correlation lengths, az, of 15–150 m and standard deviations of about 5 per cent characterize the variability in the borehole data. We report average parameters for Los Angeles basin of ν = 0.064(0.058, 0.069) ± 0.01(0.006, 0.012) and az = 54(51.1, 57.6) ± 5.9(1.79, 9.53)m with 95 per cent confidence intervals listed in the parentheses. Despite the large depth range of the logs, there is no significant variation of the statistical parameters with depth. Our analysis of 371 depth-averaged shear wave velocities in the upper 30 m, Vs30, provides only an upper bound of basin scale-length estimates due to the coarse sampling distance, with a Hurst number of about 0.3 and lateral correlation lengths, ax ,o f 5–10 km.

Lateral Casimir force between self-affine rough surfaces

The effect of self-affine roughness on the lateral Casimir force between two plates is studied using a perturbative expansion method. The PWS (pairwise summation) method is applicable only at lateral correlation lengths much larger than the separation between two plates. The effect of the roughness parameters on the lateral Casimir force is investigated, and it is seen that this effect is significant, enabling one to tailor roughness parameters so that to obtain the desirable Casimir force and increase the yield of micro- or nano-electromechanical devices based on the vacuum fluctuations.

Recent Developments in the X-ray Reflectivity Analysis

X-ray reflectivity (XRR) is a powerfull tool for investigations on surface and interface structures of multilayered thin film materials. In the conventional XRR analysis, the X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. However, the calculated results have shown often strange behaviour where interference effects would increase at a rough surface. The strange result had its origin in a serious mistake that the diffuse scattering at the rough interface was not taken into account in the equation. Then we developed new improved formalism to correct this mistake. However, the estimated surface and interface roughnesses from the x-ray reflectivity measurements did not correspond to the TEM image observation results. For deriving more accurate formalism of XRR, we tried to compare the measurements of the surface roughness of the same sample by atomic force microscopy (AFM), high-resolution Rutherford backscattering spectroscopy (HRBS) and XRR. The results of analysis showed that the effective roughness measured by XRR might depend on the angle of incidence. Then we introduced the effective roughness with depending on the incidence angle of X-ray. The new improved XRR formalism derived more accurate surface and interface roughness with depending on the size of coherent X-rays probing area, and derived the roughness correlation function and the lateral correlation length. In this review, an improved XRR formalism, considering the diffuse scattering and the effective roughness, is presented. The formalism derives an accurate analysis of the x-ray reflectivity from a multilayer surface of thin film materials.

Organic-acid texturing of transparent electrodes toward broadband light trapping in thin-film solar cells

Regardless of the great importance of light trapping towards the breakthrough in the saturated photoconversion efficiencies of Si thin-film solar cells, much research on the surface texturing of transparent conducting oxides (TCOs) has been focused more on the nanostructural control during thin film growth. Herein, an organic acid for the surface texturing of ZnO:Al is introduced as an alternative to the conventional HCl etchant, making more efficient light scattering by TCO. The texturing behavior by oxalic acid is investigated in terms of vertical roughness and lateral correlation length, and a mass-transport model is developed to explain the etching evolution mechanisms. Texturing with oxalic acid results in superior light-scattering performance (by ~8% more haze at λ=1000nm) with maintaining the transparency and resistance, compared to the etching with HCl. This fascinating behavior is explained by utilizing the light-scattering haze model with the extracted two surface parameters. Significantly, this straightforward and reproducible texturing tactic extends tunability for the desirable TCO morphology, enabling efficient light trapping, and therefore appears potentially applicable for the large-scale photovoltaic devices in industry.

Early stages of growth of Si nanowires by metal assisted chemical etching: A scaling study

We have studied the kinetic roughening in the growth of Si nanowires (NWs) by metal assisted chemical etching (MACE) process as a function of the etching time using atomic force microscopy imaging. In the early stage of growth of Si NWs by Ag assisted MACE process, we have determined the scaling exponents α, β, and 1/z. In the formation of Si NWs, nascent Ag+ ions play an important role in diffusing through the Si surface by means of excess holes that control the size of the NWs. In this system, kinetic roughening of the growth front within the detectable range of lengths of Si NWs was observed. We have observed an α = 0.74 ± 0.01 at the early stage of growth of Si NWs. Interface width w increases as a power law of etching time (t), w∼tβ, with growth exponent β = 0.30 ± 0.05 and lateral correlation length ξ grows as ξ∼t1/z with 1/z = 0.32 ± 0.05. These exponents α, β, and 1/z determine the universality class in which the system belongs to. The growth mechanism is explained by conventional shadowing instability model, which is common for columnar type of surface growth.

Fractal and multifractal characteristics of swift heavy ion induced self-affine nanostructured BaF2 thin film surfaces.

Fractal and multifractal characteristics of self-affine surfaces of BaF2 thin films, deposited on crystalline Si ⟨1 1 1⟩ substrate at room temperature, were studied. Self-affine surfaces were prepared by irradiation of 120 MeV Ag(9+) ions which modified the surface morphology at nanometer scale. The surface morphology of virgin thin film and those irradiated with different ion fluences are characterized by atomic force microscopy technique. The surface roughness (interface width) shows monotonic decrease with ion fluences, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension, did not show either monotonic decrease or increase in nature. The self-affine nature of the films is further confirmed by autocorrelation function. The power spectral density of thin films surfaces exhibits inverse power law variation with spatial frequency, suggesting the existence of fractal component in surface morphology. The multifractal detrended fluctuation analysis based on the partition function approach is also performed on virgin and irradiated thin films. It is found that the partition function exhibits the power law behavior with the segment size. Moreover, it is also seen that the scaling exponents vary nonlinearly with the moment, thereby exhibiting the multifractal nature.

Fresnel diffraction by a square aperture with rough edge

In this paper, we study Fresnel diffraction of a square aperture with rough edge with Gaussian random process. The diffraction intensity formula depending on the random parameters is deduced by use of the scalar diffraction theory. The simulation calculations of the diffraction of the square aperture with different statistic parameters are performed. The diffraction intensity distributions exhibit elaborately the influence of the random parameters of rough edge on the diffraction of a square aperture. The results show that the larger the lateral correlation length and the larger roughness of the rough edge are, the more severe the modulation of the random spots is and the more unsymmetrical the diffraction distribution is. For the same random parameters, the modulation degree of the random spots changes with the propagation distance. Moreover, we also manufacture practically the random apertures with the help of the laser direct writing technology, and measure the diffraction distribution of the square aperture with random edge. The experimental results are consistent with the theoretic ones. These results will be instructively meaningful for the applications of the diffraction of the practical aperture.