Surface Height Profile Research Articles

Controlling aggregate thin film surface morphology for improved light trapping using a patterned deposition rate profile

This work focuses on modeling and control of aggregate thin film surface morphology for improved light trapping using a patterned deposition rate profile. The dynamics of the evolution of the thin film surface height profile are modeled by an Edwards–Wilkinson-type equation (a second-order stochastic partial differential equation) in two spatial dimensions. The thin film surface morphology is characterized in terms of aggregate surface roughness and surface slope. These variables are computed with respect to appropriate visible light-relevant characteristic length scales and defined as the root-mean-squares of height deviation and slope of aggregate surface height profiles, respectively. Analytical solutions of the expected aggregate surface roughness and surface slope are obtained by solving the Edwards–Wilkinson equation and are used in the controller design. The model parameters of the Edwards–Wilkinson equation are estimated from kinetic Monte-Carlo simulations using a novel parameter estimation procedure. This parameter dependence on the deposition rate is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope at the end of the growth process. The cost function of the controller involves penalties on both aggregate surface roughness and mean slope from set-point values as well as constraints on the magnitude and rate of change of the control action. The controller is applied to the two-dimensional Edwards–Wilkinson equation. Simulation results show that the proposed controller successfully regulates aggregate surface roughness and slope to set-point values at the end of the deposition that yield desired levels of thin film reflectance and transmittance.

Evolution of Aggregate Surface Characteristics in Polishing Process

This paper aims to investigate the evolution of aggregate-surface characteristics due to tyre polishing action. Three kinds of aggregates were polished by the Wehner/Schluze polishing machine. The evolution of dynamic friction coefficient, surface height profiles and their power spectral density in polishing process were characterized. Spectrum analysis is conducted to characterization the polishing effects on surface texture. The results reveal that the polishing action of rubber tyre plays an important role in the changes of micro-texture, and the evolution of friction of aggregate is governed by micro-texture changes due to differential removal of mineral components.

Impact of substrate deformation on demolding force for thermal imprint process

The impact of deformation on the demolding force is investigated both experimentally and by simulation for the thermal imprint process. The effects of substrate thickness are the focus of this article. In experiments, one mold is used throughout all experiments in order to exclude any effects of the mold fabrication process. The mold pattern is transferred to a polymethylmethacrylate (PMMA) film by the thermal imprint. The PMMA surface height is measured by a commercial height profiler after the imprint, and it agrees with lateral variations in residual layer thickness. Demolding force increases as substrate thickness increases. Substrate deformation is simulated by simplifying a model to assume the presence of large cavities. Substrate deformation in the simulation agrees with the PMMA surface height profile in the experiment. The normal force to the PMMA side wall by the mold pattern is important for estimating the demolding force. Since the normal force during the pressing process is simulated, the normal force is induced by both the lateral expansion of PMMA resin and substrate deformation. The normal force from substrate deformation is selected based on a detailed analysis of the simulated normal force. The obtained normal force agrees with the demolding force in the experiment.

Dependence of film surface roughness and slope on surface migration and lattice size in thin film deposition processes

This work focuses on the study of the dependence of film surface roughness and slope on lattice size in thin film deposition processes. Two different models of thin film deposition processes, in both 1D and 2D, are considered: random deposition with surface relaxation model and deposition/migration model. Surface roughness and surface slope are defined as the root-mean-squares of the surface height profile and of the surface slope profile, respectively. Both surface roughness and slope evolve to steady-state values at large times but are subject to different dynamics and scaling properties. A linear and a logarithmic dependence of surface roughness square on lattice size are observed in the 1D and 2D lattice models, respectively, in both the random deposition with surface relaxation model and the deposition/migration model with zero activation energy contribution from each neighboring particle. Furthermore, a stronger lattice-size dependence is found in the deposition/migration model when the migration activation energy contribution from each neighboring particle becomes significant. On the other hand, a weak lattice-size dependence is found for the surface mean slope in all growth models considered, especially at large lattice sizes. Finally, the dynamics of surface roughness and surface slope is studied with respect to different characteristic length scales.

Predictive control of surface mean slope and roughness in a thin film deposition process

This work focuses on the development of a model predictive control algorithm to simultaneously regulate the surface slope and roughness of a thin film growth process to optimize thin film light reflectance and transmittance. Specifically, a thin film deposition process modeled on a one-dimensional triangular lattice that involves two microscopic processes: an adsorption process and a migration process, is considered. Kinetic Monte Carlo (kMC) methods are used to simulate the thin film deposition process. To characterize the surface morphology and to evaluate the light trapping efficiency of the thin film, surface roughness and surface slope are introduced as the root mean squares of the surface height profile and surface slope profile. An Edwards–Wilkinson (EW)-type equation is used to describe the dynamics of the surface height profile and predict the evolution of the root-mean-square (RMS) roughness and RMS slope. A model predictive control algorithm is then developed on the basis of the EW equation model to regulate the RMS slope and the RMS roughness at desired levels by optimizing the substrate temperature at each sampling time. The model parameters of the EW equation are estimated from simulation data through least-square methods. Closed-loop simulation results demonstrate the effectiveness of the proposed model predictive control algorithm in successfully regulating the RMS slope and the RMS roughness at desired levels that optimize thin film light reflectance and transmittance.

Multivariable Model Predictive Control of Thin Film Surface Roughness and Slope for Light Trapping Optimization

This work focuses on the development of a multivariable model predictive controller that simultaneously regulates thin film surface roughness and mean slope to optimize light reflectance and transmittance during thin film manufacturing by manipulating substrate temperature and deposition rate. Surface roughness and surface slope are defined as the root-mean-squares of the surface height profile and the surface slope profile, respectively. The dynamics of the evolution of the thin film surface height profile are assumed to be described by an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) in two spatial dimensions. Analytical solutions of the expected surface roughness and surface slope are obtained on the basis of the Edwards-Wilkinson equation and are used in the controller design. The model parameters of the Edwards-Wilkinson equation depend on the substrate temperature and deposition rate. This dependence is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope at the end of the growth process. The model predictive controller involves constraints on the magnitude and rate of change of the control action and optimizes a cost that involves penalty on both surface roughness and mean slope from the set-point values. The controller is applied to the two-dimensional Edwards-Wilkinson equation and is shown to successfully regulate surface roughness and mean slope to set-point values at the end of the deposition that yield desired film reflectance and transmittance.

Size-effects in time-dependent mechanics in metallic MEMS

Reliability of microelectromechanical systems (MEMS) depends a.o. on time-dependent deformation such as creep and fatigue [1]. It is known from literature that this behavior is affected by size-effects: the interaction between microstructural length scales and dimensional length scales [2,3]. Not much research has focused on characterizing size-effects in time-dependent material behavior, specifically for free-standing thin films [3]. This study investigates size-effects caused by grain statistics in timedependent deformation in µm-sized free-standing aluminum cantilever beams. A numeric-experimental method is used to determine material parameters. The experiment entails applying a constant deflection to the micro-beams for a prolonged period. The deflection is achieved with 50 nm resolution via a micro-clamp. The beams are then released. Immediately the deformation evolution is recorded by acquiring surface height profiles with a confocal optical profiler. Image correlation of the full-field beam profiles is applied to correct for specimen drift and tilt. The experiment yields the tip deflection as function of time with ~3 nm precision. In the numerical part, this data is combined with a finite element model based on a standard-solid material model. In this way material parameters describing time-dependent behavior are extracted. The time constant for the deflection evolution is determined within 20%, as verified by predicting a different experiment. Figure 1 shows the model and the numeric prediction of an experiment.

Lattice-size Dependence and Dynamics of Surface Mean Slope in a Thin Film Deposition Process

This work focuses on the study of the dynamic behavior and lattice size dependence of the surface root-mean-square slope in a porous thin film deposition process taking place on a triangular lattice. The simulation results indicate that the expected mean slope square reaches quickly a steady-state value and exhibits a very weak dependence with respect to lattice size variation. The simulation findings are corroborated by an analysis of appropriate finite-difference discretizations of surface height profiles computed by an Edwards-Wilkinson-type partial differential equation that can be used to describe the dynamics of surface height profile in the thin film deposition process under consideration.

Stochastic Modeling and Simultaneous Regulation of Surface Roughness and Porosity in Thin Film Deposition

This work focuses on stochastic modeling and simultaneous regulation of surface roughness and porosity for a porous thin film deposition process modeled via kinetic Monte Carlo (kMC) simulation on a triangular lattice. The microscopic model of the thin film growth process includes adsorption and migration processes. Vacancies and overhangs are allowed inside the film for the purpose of modeling thin film porosity. The definition of the surface height profile is first introduced for a porous thin film deposition taking place in a triangular lattice. The dynamics of surface height of the thin film are described by an Edwards-Wilkinson (EW) type equation, which is a second-order linear stochastic partial differential equation (PDE). The root-mean-square (RMS) surface roughness is chosen as one of the controlled variables. Subsequently, an appropriate definition of film site occupancy ratio (SOR) is introduced to represent the extent of porosity inside the film and is chosen as the second to-be-controlled variable. A deterministic ordinary differential equation (ODE) model is postulated to describe the time evolution of the film SOR. The coefficients of the EW equation of surface height and of the deterministic ODE model of the film SOR are estimated on the basis of data obtained from the kMC simulator of the deposition process using least-squares methods, and their dependence on substrate temperature is determined. The developed dynamic models are used as the basis for the design of a model predictive control algorithm that includes a penalty on the deviation of the surface roughness square and film SOR from their respective set-point values. Simulation results demonstrate the applicability and effectiveness of the proposed modeling and control approach in the context of the deposition process under consideration. When simultaneous control of surface roughness and porosity is carried out, a balanced trade-off is obtained in the closed-loop system between the two control objectives of surface roughness and porosity regulation.

A Numerical Study of the Retrieval of Sea Surface Height Profiles From Low Grazing Angle Radar Data

A numerical study of the retrieval of sea surface height profiles from low grazing angle radar observations is described. The study is based on a numerical method for electromagnetic scattering from 1-D rough sea profiles, combined with the ldquoimproved linear representationrdquo of Creamer for simulating weakly nonlinear sea surface hydrodynamics. Numerical computations are performed for frequencies from 2975 to 3025 MHz so that simulated radar pulse returns are achieved. The geometry utilized models a radar with an antenna height of 14 m, observing the sea surface at ranges from 520 to 1720 m. The low grazing angles of this configuration produce significant shadowing of the sea surface, and standard analytical theories of sea scattering are not directly applicable. Three approaches for retrieving sea height profile information are compared. The first method uses a statistical relationship between the surface height and the computed radar cross sections versus range (an incoherent measurement). A second method uses the phase difference between scattering measurements in two vertically separated antennas (ldquovertical interferometry) in the retrieval. The final technique retrieves height profiles from variations in the apparent Doppler frequency (coherent measurements) versus range and requires that time-stepped simulations be performed. The relative advantages and disadvantages of each of the three approaches are examined and discussed.

Regulation of film thickness, surface roughness and porosity in thin film growth using deposition rate

This work focuses on distributed control of film thickness, surface roughness and porosity in a porous thin film deposition process using the deposition rate as the manipulated input. The deposition process includes adsorption and migration processes and it is modeled via kinetic Monte Carlo simulation on a triangular lattice with vacancies and overhangs allowed to develop inside the film. A distributed parameter (partial differential equation) dynamic model is derived to describe the evolution of the surface height profile of the thin film accounting for the effect of deposition rate. The dynamics of film porosity, evaluated as film site occupancy ratio, are described by an ordinary differential equation. The developed dynamic models are then used as the basis for the design of a model predictive control algorithm that includes penalty on the deviation of film thickness, surface roughness and film porosity from their respective set-point values. Simulation results demonstrate the applicability and effectiveness of the proposed modeling and control approach in the context of the deposition process under consideration.

Macroscopic view of crystal-step transparency

We study macroscopic aspects of crystal surface relaxation in 2+1 dimensions by accounting for near-equilibrium kinetics of transparent steps at the nanoscale. For slowly varying step geometries, we show that step permeability can simply renormalize a parameter in a known relation between the large-scale surface flux and the step chemical potential. This leads to a nonlinear fourth-order partial differential equation for the surface height profile.

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman–Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto–Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.

Anisotropic diffusion in continuum relaxation of stepped crystal surfaces

We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the surface flux in terms of a new continuum-scale tensor mobility. The starting point is the Burton, Cabrera and Frank (BCF) theory, which offers a discrete scheme for atomic steps whose motion drives surface evolution. Our derivation is based on the separation of local space variables into fast and slow. The model includes: (i) anisotropic diffusion of adsorbed atoms (adatoms) on terraces separating steps; (ii) diffusion of atoms along step edges; and (iii) attachment–detachment of atoms at step edges. We derive a parabolic fourth-order nonlinear partial differential equation (PDE) for the continuum surface height profile. An ingredient of this PDE is the surface mobility for the adatom flux, which is a nontrivial extension of the tensor mobility for isotropic terrace diffusion derived previously by Margetis and Kohn (2006 Multisci. Model. Simul. 5 729–58). Approximate, separable solutions of the PDE are discussed.

Triangulation methods for height profile measurements on instationary water surfaces

The precise measurement of water surface models or profiles plays an important role in experimental hydromechanics. Conventional gauge-based techniques often come with a large instrumental effort and a limited spatial resolution. The paper shows an e‰cient non-contact photogrammetric technique for the measurement of water-surface profiles, which is based on an extension of the well-known laser light sheet projection technique. While the original laser lightsheet triangulation technique is limited to surfaces with di¤use reflection properties, the developed technique is capable of measuring on reflecting instationary surfaces. This article presents the basic principle, potential and limitations of the method. Several evolution steps of the system with di¤erent applicability and di¤erent complexity are shown. A double projection plane system capable of simultaneously measuring water surface height and tilt profiles marks the ceiling of the development. Besides the geometrical models of different levels of complexity, system calibration procedures are described. The applicability of the techniques and their accuracy potential are shown in several practical tests.

Study of the growth process of in situ polyaniline deposited films

Polyaniline (PAni) thin films were deposited onto BK7 glass substrates using the in situ deposition technique. The control of the time and the aniline concentration in the PAni polymerization reaction on the film deposition allowed us to prepare films with different thickness, down to ∼25 nm. The film growth process was monitored by measuring the UV–vis spectra and the AFM height profiles of the film surface. The curves of adsorption kinetics were analyzed with the Avrami's model, yielding an exponent n = 3 , thus indicating nucleation of spheroids at the initial stages of polymerization that grow through a diffusion process. AFM images of the surface height profiles corroborate this hypothesis, with spheroids growing with no preferred orientation during the in situ deposition.

Rocking curve FWHM maps of a chemically etched (0 0 1) oriented HPHT type Ib diamond crystal plate

Synchrotron radiation and a CCD detector were employed to map the full width at half maximum (FWHM) of rocking curves for a synthetic (0 0 1) oriented type Ib diamond plate. The plate was sawed from a diamond grown in the high-pressure–high-temperature (HPHT) process. Maps for broadening relative to a reference point on the diamond for the (2 2 4) reflection at 12 keV are reported before and after chemical etching. Significant rocking curve narrowing over most of the diamond was found, and we conclude that the diffraction performance of (0 0 1) oriented type Ib diamonds can be significantly improved over a large area by chemical etching. Stripes in the map before etching corresponded to grooves formed in the process of sawing the plate out of the as-grown stone. The FWHM map did not correlate with the surface height profile measured after ∼10 µm were removed from the surface by etching.

Adaptive interferometry of protein on a BioCD

Adaptive spinning-disk interferometry is capable of measuring surface profiles of a thin biolayer with subnanometer longitudinal resolution. High-speed phase modulation in the signal beam arises from the moving surface height profile on the spinning disk and is detected as a homodyne signal via dynamic two-wave mixing. A photorefractive quantum-well device performs as an adaptive mixer that compensates disk wobble and vibration while it phase-locks the signal and reference waves in the phase quadrature condition (pi/2 relative phase between the signal and local oscillator). We performed biosensing of immobilized monolayers of antibodies on the disk in both transmission and reflection detection modes. Single- and dual-analyte adaptive spinning-disk immunoassays were demonstrated with good specificity and without observable cross-reactivity. Reflection-mode detection enhances the biosensing sensitivity to one-twentieth of a protein monolayer, creates a topographic map of the protein layer, and can differentiate monolayers of different species by their effective optical thicknesses.

Nanopattern Formation by Periodic Array of Interfacial Misfit Dislocations in Bi(111)/Si(001) Heteroepitaxy

ABSTRACTDespite their large lattice mismatch of 18 %, the lattices of Bi(111) and Si(001) fit surprisingly well. A remaining compressive strain in the Bi film of 2.3 % along the direction is accommodated by the formation of a periodic array of edge-type misfit dislocations confined to the interface. The strain fields surrounding each dislocation interact with each other, producing a quasi-periodic nanopattern of grating-like periodic height undulations on the surface. The separation and the amplitude of the height undulations have been derived by spot profile analyzing LEED and STM surface height profiles. The observed undulations agree well with elasticity theory.

The 2004 Indian Ocean tsunami: Tsunami source model from satellite altimetry

AbstractSatellite altimetry measurements of sea surface heights for the first-time captured the Indian Ocean tsunami generated from the December 2004 great Sumatra earthquake. Analysis of the sea surface height profile suggests that the tsunami source, or the seafloor deformation, of the great earthquake propagated to the north at an extremely slow speed of less than 1 km/sec on average for the entire 1300-km-long segment along the northern Sumatra-Nicobar-Andaman Trench. The extremely slow propagation speed produces a very long duration of tens minutes, longer than earthquake source duration estimated (480–500 sec) from short-periodP-wave radiation. The satellite altimetry data requires a total seismic moment of 9.86 × 1022Nm (Mw=9.3). This estimate is approximately 2.5 times larger than the value from long-period surface wave analysis but nearly the same as that from the ultra-long-period normal mode study. The maximum amount of slip (∼30 m) is identified in an offshore region closest to the northern most part of Sumatra where the largest tsunami run-up heights were observed.