Rms Roughness Amplitude Research Articles

Fluid Leakage in Static Rubber Seals

Interfacial surface roughness can result in fluid leakage of seals, and in the design of seals it is standard to give an upper limit for the surface root-mean-square (rms) roughness amplitude h_text{rms}. However, h_text{rms} is determined mainly by the long-wavelength roughness, which is (nearly) irrelevant for the sealing. I discuss the parameters which determine the leakage of seals, and present results for static rubber seals with circular cross-section (like rubber O-rings). I also study the influence of the fluid pressure on the interfacial surface separation and the leakrate.Graphical

Analysis of interface roughness in strained InGaAs/AlInAs quantum cascade laser structures (λ ∼ 4.6 μm) by atom probe tomography

In this study, in-plane interface roughness (IFR) values are extracted via atomic probe tomography (APT) for a few key interfaces within a quantum cascade laser (QCL) active region composed of compressively-strained InGaAs quantum wells (QWs) and tensilely-strained AlInAs barriers. The structure was grown by organometallic vapor phase epitaxy (OMVPE) at 605 °C, 100 rpm, 100 torr, with a 5 s interruption time between layers. The full-stage thickness measured via high-resolution x-ray diffraction (HR-XRD) is used to calibrate the reconstruction to within 5%. From the APT results, it is found that interfaces to two barriers of different tensile-strain value (i.e., of different Al concentration) have different RMS-roughness amplitude. Specifically, barriers of higher Al concentration have ~50% larger RMS-roughness amplitude, as the strain differential increases by a factor of 2.2. To the best of our knowledge, this is the first experimental data showing that roughness parameters within a QCL active region are different for different interfaces within the same grown structure.

Rate-dependent adhesion of viscoelastic contacts. Part II: Numerical model and hysteresis dissipation

In this paper, we propose a numerical model to describe the adhesive normal contact between a glass spherical indenter and a viscoelastic model rough substrate of PDMS material. The model accounts for dissipative process under the assumption that viscoelastic losses are localized at the (micro)-contact lines. Numerical predictions are then compared with experimental measurements, which show a strong adhesion hysteresis mostly due to viscous dissipation occurring during pull-off. This hysteresis is satisfactorily described by the contact model which allows to distinguish the energy loss due to material dissipation from the adhesion hysteresis due to elastic instability.Our analysis shows that the pull-off force required to detach the surfaces is strongly influenced by the detachment rate and the root mean square (rms) roughness amplitude, but it is almost unaffected by the maximum load from which unloading starts. Moreover, the increase in the length of the boundary line separating contact and non-contact regions, which is observed when moving from smooth to rough contacts, negligibly affects the viscous dissipation. Such increase is much less significant than the reduction in contact area, which therefore is the main parameter governing the strong decrease in the effective surface energy for the specific rough geometry considered in the present work.

Roughness dependent wettability of sputtered copper thin films: The effect of the local surface slope

Here, we investigated the static and the dynamic wetting behaviors of copper (Cu) thin films deposited by DC magnetron sputtering. The deposited films have random rough surfaces for which the rms roughness amplitude σ, the lateral correlation length ξ, and the roughness exponent α were obtained from the analysis of height topography images acquired by atomic force microscopy. The time-dependent height-height correlation functions indicated anomalous kinetic roughening with roughness exponents α ≈ 0.9 and evolving roughness parameters σ and ξ with deposition time. The latter yields a nonstationary local surface slope σ/ξ that has a crucial impact on the surface wettability. Indeed, static and dynamic contact angles’ (CAs) measurements revealed two wetting regimes associated with different growth stages leading to a transition from a metastable Cassie-Baxter to a Wenzel-like state for the roughest films. Moreover, the increasing roughness with well distributed peaks and valleys leads to increasing CAs due to trapped air in surface cavities, while after some point the larger surface features lead to a decrement of the CAs that vary only slightly with further roughening. Although the apparent wetting transition with increasing surface roughness is not favored by the local Laplace pressure estimation, the energy of the system decreases with surface roughening, or equivalently increasing local surface slope, favoring energetically a Wenzel state. Under these conditions, the water droplet can spontaneously fill the surface cavities once the impregnation is initiated by the hydrophilic nature of the surface, in agreement with our experiments for significantly large local surface slopes ρ (>0.1) and large roughness exponents α ∼ 1.

Spin Hall effect originated from fractal surface

The spin Hall effect (SHE) has shown promising impact in the field of spintronics and magnonics from fundamental and practical points of view. This effect originates from several mechanisms of spin scatterers based on spin–orbit coupling (SOC) and also can be manipulated through the surface roughness. Here, the effect of correlated surface roughness on the SHE in metallic thin films with small SOC is investigated theoretically. Toward this, the self-affine fractal surface in the framework of the Born approximation is exploited. The surface roughness is described by the k-correlation model and is characterized by the roughness exponent H , the in-plane correlation length ξ and the rms roughness amplitude δ. It is found that the spin Hall angle in metallic thin film increases by two orders of magnitude when H decreases from H = 1 to H = 0. In addition, the source of SHE for surface roughness with Gaussian profile distribution function is found to be mainly the side jump scattering while that with a non-Gaussian profile suggests both of the side jump and skew scatterings are present. Our achievements address how details of the surface roughness profile can adjust the SHE in non-heavy metals.

The effect of substrate temperature on structural and morphological properties of Au/Si(1 1 1) thin films

We report here the effects of substrate temperature on the orientation and surface morphology of 100nm thick gold films, using scanning tunneling microscopy and X-ray diffraction. The gold films were deposited using molecular beam epitaxy technique onto Si(111) 7×7 substrates. Ex situ characterizations are performed using scanning tunneling microscope at room temperature. X-ray diffraction measurements reveal the (111) orientation of the film deposited at 580°C. We present data showing the evolution of the RMS roughness amplitude of the gold films as a function of substrate temperature during deposition. For our purposes, the best compromise between roughness and grain size is found to occur for a substrate temperature maintained at 580°C.

Resistivity of thin gold films on mica induced by electron–surface scattering: Application of quantitative scanning tunneling microscopy

We report a comparison between the resistivity measured on thin gold films deposited on mica, with predictions based upon classical theories of size effects (Drude's, Sondheimer's and Calecki's), as well as predictions based upon quantum theories of electron–surface scattering (the modified theory of Sheng, Xing and Wang, the theory of Tesanovic, Jaric and Maekawa, and that of Trivedi and Aschroft). From topographic images of the surface recorded with a Scanning Tunneling Microscope, we determined the rms roughness amplitude, δ and the lateral correlation length, ξ corresponding to a Gaussian representation of the average height–height autocorrelation function, describing the roughness of each sample in the scale of length set by the Fermi wave length. Using (δ, ξ) as input data, we present a rigorous comparison between resistivity data and predictions based upon the theory of Calecki as well as quantum theoretical predictions without adjustable parameters. The resistivity was measured on gold films of different thickness evaporated onto mica substrates, between 4K and 300K. The resistivity data covers the range 0.1<x(T)<6.8, for 4K<T<300K, where x(T) is the ratio between film thickness and electron mean free path in the bulk at temperature T. We experimentally identify electron–surface and electron–phonon scattering as the microscopic electron scattering mechanisms giving rise to the macroscopic resistivity. The different theories are all capable of estimating the thin film resistivity to an accuracy better than 10%; however the mean free path and the resistivity characterizing the bulk turn out to depend on film thickness. Surprisingly, only the Sondheimer theory and its quantum version, the modified theory of Sheng, Xing and Wang, predict and increase in resistivity induced by size effects that seems consistent with published galvanomagnetic phenomena also arising from electron–surface scattering measured at low temperatures.

Characterizing the effect of uniaxial strain on the surface roughness of Si nanowire MEMS-based microstructures

ABSTRACTThis work addresses the paucity of roughness measurements by reporting on roughness parameters in uniaxial strained Si beams relevant for state of the art MOSFETs, nanowire and MEMS devices, with varying degrees of strain. Roughness is characterized by high resolution AFM and strain is characterized by Raman spectroscopy. Microstructures comprising a silicon nitride actuator are used to induce a wide range of stress levels in Si beams. The microstructures also allow the comparison of surface evolution in the strain direction (along the Si beam) compared with the unstrained direction (across the Si beam). A gradual reduction in rms roughness amplitude and increase in roughness correlation length in the direction of the applied stress are found for increasing values of strain. In contrast, surface roughness in the direction perpendicular to the applied stress remained largely unchanged from the unstrained initial state.

Surface roughness influence on the quality factor of high frequency nanoresonators

Surface roughness influences significantly the quality factor of high frequency nanoresonators for large frequency–relaxation times (ωτ&amp;gt;1) within the non-Newtonian regime, where a purely elastic dynamics develops. It is shown that the influence of short wavelength roughness, which is expressed by the roughness exponent H for the case of self-affine roughness, plays a significant role in comparison with the effect of the long wavelength roughness parameters such as the rms roughness amplitude and the lateral roughness correlation length. Therefore, the surface morphology can play an important role in designing high frequency resonators operating within the non-Newtonian regime.

Contact angle influence on the pull-in voltage of microswitches in the presence of capillary and quantum vacuum effects

Capillary condensation between the electrodes of microswitches influences the effective pull-in voltage in a manner that depends on the contact angle of the capillary meniscus and the presence of plate surface roughness. Indeed, surface roughening is shown to have a stronger influence on the pull-in potential for relatively small contact angles with respect to that of a flat surface when capillary condensation takes place. For long wavelength roughness ratios w∕ξ⪡1 with w the rms roughness amplitude and ξ the in-plane correlation length, the pull-in voltage increases with increasing theoretical contact angle θ0 for flat surfaces. With decreasing correlation length ξ (increasing roughness), the pull-in potential decreases faster for smaller contact angles θ0 In addition, with decreasing roughness exponent H (0&amp;lt;H&amp;lt;1), which characterizes short wavelength roughness fluctuation at short length scales (&amp;lt;ξ), the pull-in potential shows a steeper decrease with decreasing correlation length ξ. Finally, with increasing relative humidity, the sensitivity of the pull-in voltage at small correlation lengths attenuates significantly with increasing contact angle θ0.

Surface roughening of metal–polymer systems during plastic deformation

This paper concentrates on the evolution of roughness at the surface of a glassy polymeric coating that co-deforms with a metal under uniaxial strain. In experiments and simulations the roughness is described by three parameters: the rms roughness amplitude w, a correlation length ξ, and a Hurst exponent H. In the plane strain simulations, the three stages (elastic, softening and hardening) in the stress–strain behavior of the polymer can be distinguished in their effect on the rms roughness amplitude w( ε). w( ε) decreases as a function of the thickness d of the coating for strains in the elastic and hardening regime. In the softening regime, shear bands originating at the interface intersect at a distance above the interface. In simulations, this leads to a distinct non-monotonous behavior of w( ε) as a function of thickness, with w( ε) reaching values above that at the interface at some thicknesses. In both experiments and simulations, it is found that the Hurst exponent H increases with increasing d. The correlation length ξ at the polymer surface increases with increasing d in the simulations, whereas in the experiment an increase is observed only above a certain value of d.

Adhesion along metal-polymer interfaces during plastic deformation.

In this paper a numerical study is presented that concentrates on the influence of the interface roughness that develops during plastic deformation of a metal, on the work of adhesion and on the change of interface energy upon contact with a glassy polymer. The polymer coating is described with a constitutive law that mimics the behavior of Poly-Ethylene Terephthalate. It includes an elastic part, a yield stress, softening and hardening with increasing strains. For the interface between the metal and the polymer a mixed-mode (mode I and II) stress-separation law is applied that defines the interface energy and an interaction length scale. At the onset of deformation the surface of the substrate has a self-affine roughness characterized by the so-called Hurst exponent, a correlation length and an rms roughness amplitude, that evolves as a function of increasing strain. The findings are the following: the interface energy decreases until the strain at yield of the polymer coating. Interestingly, after yielding as the polymer starts to soften macroscopically, the decreasing average stress levels result in partial recovery of the interface energy at the interface. At higher strains, when macroscopic hardening develops the recovery of the interface stops and the interface energy decreases. The effect of coating thickness is discussed as well as the physical relevance of various model parameters.

Capillary condensation and quantum vacuum effects on the pull-in voltage of electrostatic switches with self-affine rough plates

In this work, we study the influence of capillary forces in combination with electrostatic and quantum vacuum generated forces on the pull-in voltage of microswitches having self-affine rough surfaces. This type of roughness is described by the rms roughness amplitude w, the in-plane correlation length ξ, and the roughness exponent H that quantifies the degree of surface irregularity at short length scales (&amp;lt;ξ). It is shown that an attractive capillary force decreases more the effective pull-in voltage when the plate surfaces are rougher. The latter corresponds to smaller roughness exponents H and/or larger long wavelength roughness ratios w∕ξ. Notably, the capillary contribution increases the sensitivity of the effective pull-in voltage on the roughness exponent H. This behavior takes place for values of H close to its experimental accuracy.

Adhesion stability of rough elastic films in presence of quantum vacuum fluctuations

In this work the influence of vacuum fluctuations through the Casimir effect on the stability of an elastic film conformal onto to a self-affine rough substrate that is brought in close proximity with another parallel plate is studied. By considering the energy balance among adhesion, elastic and Casimir energies, it is shown that beyond certain parameter values (low roughness exponent H and/or high ω/ξ ratio with ω the rms roughness amplitude and ξ the lateral correlation length) the adhesion energy is counter-balanced by the elastic energy, allowing significant contributions in this regime by the Casimir energy. With increasing lateral correlation length ξ and/or decreasing roughness amplitude ω, leading to long wavelength smoothing, the regime of roughness exponents H where the contribution of vacuum fluctuations is significant shifts drastically to a lower value. This occurs so that the short wavelength roughening compensates for the effect of long wavelength smoothing that decreases predominantly the elastic and Casimir energies.

Self-affine roughness influence on the Casimir effect

In this work we investigate the influence of self-affine roughness on the Casimir energy for plate-plate geometry. The plate roughness is characterized by the rms roughness amplitude w, the lateral correlation length ξ, and the roughness exponent H. It is shown that the latter has a prominent effect on the Casimir energy with respect to the long-wavelength roughness ratio w∕ξ. Analytic results are shown for three characteristic roughness exponents, namely, H=0, 0.5, and 1. Moreover, the dynamic evolution of the surface roughness (e.g., by metal deposition) leads to significant contributions of the roughness influence on the Casimir energy.

Self-affine roughness influence on redox reaction charge admittance

In this work we investigate the influence of self-affine electrode roughness on the admittance of redox reactions during facile charge transfer kinetics. The self-affine roughness is characterized by the rms roughness amplitude w, the correlation length ξ, and the roughness exponent H (0 < H < 1). Our calculations allow analytic expressions to be derived for the admittance as a function of the characteristic self-affine roughness parameters. Furthermore, it is shown that the magnitude of the reaction admittance is strongly influenced by the local roughness exponent H or the fine roughness details at short roughness wavelengths, while the influence of the lateral correlation length ξ or the long wavelength roughness ratio w/ ξ is of secondary importance. In addition, the dynamic roughness evolution can strongly influence the reaction admittance and it should taken carefully into consideration.

Influence of self-affine interface roughness on the charge capacitance between two dielectric media

In this paper we investigate the influence of the interface roughness on the charge capacitance between two different dielectric media. Assuming the roughness fluctuations to be self-affine, it is shown that the roughness exponent $H$, which characterizes short wavelength roughness fluctuations, plays the dominant role with respect to the rms roughness amplitude $w$ and the lateral correlation length $\ensuremath{\xi}$. Furthermore, it is shown that any evolution of the interface roughness under conditions leading to time variant local interface slope will have significant influence on charge capacitance properties.

Influence of self-affine roughness on the adhesive friction coefficient of a rubber body sliding on a solid substrate

In this work we investigate characteristics of the adhesive friction during sliding of a rubber body on a rough self-affined surface. The latter is characterized by the rms roughness amplitude w, the in-plane correlation length, and the roughness exponent H (0 <H <1). The friction coefficient is shown to be proportional to the roughness amplitude w. Moreover, the friction coefficient is shown to depend strongly on the roughness exponent H. The influence of the latter is more prominent at intermediate slidding velocities, where the friction coefficient is independent of the slidding velocity. Similar, but weaker in magnitude, is the influence of correlation length on Pad. In any case, our work shows that understanding of the adhesive friction should take properly into account of the precise roughness nature both at all lateral roughness wavelengths. (C) 2004 Elsevier B.V. All rights reserved.

Influence of self-affine and mound roughness on the surface impedance and skin depth of conductive materials

In this work, we explore the influence of self-affine and mound surface roughness on the surface impedance and skin depth. For self-affine roughness, the surface impedance and skin depth increases with decreasing the roughness exponent H (for k F ξ≫1 with k F the Fermi wave-vector), and/or increasing roughness ratio w/ ξ, where w is the rms roughness amplitude and ξ the in-plane roughness correlation length. For mound roughness, the surface impedance and skin depth decrease monotonically with increasing average mound separation λ when λ> ζ with ζ the correlation length (assuming k F ζ≫1), while for λ< ζ they are both decreased with increasing λ.

Wetting of van der Waals solid films on self-affine rough surfaces

In this work we investigate the influence of random self-affine substrate roughness on the solid layer thickness under conditions of triple-point wetting of adsorbed van der Waals films. Our calculations show that a significant solid film thickness ${\ensuremath{\lambda}}_{s}$ can be reached (in the nanometer range) for substrate roughness parameters $w/\ensuremath{\xi}l~0.05$ and/or $H\ensuremath{\approx}1$ with w the rms roughness amplitude, \ensuremath{\xi} the lateral roughness correlation length, and H the roughness exponent $(0l~Hl~1).$ Independent of substrate-particle and particle-particle interactions, with increasing roughness exponent H and/or decreasing ratio $w/\ensuremath{\xi}$ the solid film thickness ${\ensuremath{\lambda}}_{s}$ increases since the substrate surface becomes smoother. Finally, the solid layer thickness is shown to be sensitive to growth details of the substrate roughness as described in many cases in terms of dynamic scaling theory.