Activation Energy For Surface Diffusion Research Articles

Investigating the Trade‐off between Optical and Mechanical Properties during Constrained Sintering of Mesomorphic Ceramic Films

AbstractRobust, transparent, and birefringent inorganic films are demanded for polarization control of high‐power lasers. While single crystals or films obtained via glancing angle deposition exhibit desirable optical properties and laser damage resistance, these methods are limited by cost and scalability. Mesomorphic ceramics as inorganic solids with liquid crystalline superstructure offer appealing transparency and birefringence but lack mechanical robustness due to their high porosity. Here, the effect of sintering on optical and mechanical properties of mesomorphic ceramics is evaluated. Films prepared by blade coating are sintered under varying conditions. Constrained sintering accomplished crystallite growth, densification, and morphological changes including necking as well as cracking while preserving the crystallographic orientation. The extent of sintering as a function of thermal treatment is quantified by morphology, surface area loss, and crystallite growth. Moreover, activation energies for surface diffusion and grain growth are estimated by surface area analysis and X‐ray diffraction peak narrowing, respectively. After sintering, birefringence decreases while Young's modulus and hardness improve as the film densifies. Upon partial sintering, mesomorphic ceramics retain transparency, high birefringence, and enhanced modulus. Laser‐induced damage threshold is measured as well. The reported results represent an important step toward the assembly and sintering of robust waveplates with high laser damage resistance.

Surface stability and H adsorption and diffusion near surfaces of W borides: a first-principles study

Understanding the behavior of tungsten boride (W x B y ) surfaces in a fusion reactor environment is an important topic since boronization is a common wall conditioning method used in fusion Tokamaks. We report the results of density functional theory calculations that investigate the surface stability of W x B y (tetragonal I41/amd-WB, hexagonal P63/mmc-WB2 and tetragonal I4/m-W2B) with low-index orientations, as well as hydrogen (H) energetics near W x B y surfaces. For single element terminated W x B y surfaces, B terminated surfaces are more energetically stable than W terminated as a result of significant reconstruction of B. The H surface adsorption energy and activation energy of H diffusion penetration below W x B y surfaces are mainly related to the outer termination. Specifically, the WB(001) surface terminated with two B layers, referred to as WB(001)-TBB, has higher H adsorption affinity and lower H diffusivity on this surface than other terminations, which is controlled by the significant charge transfer from B to H. However, B atoms on the WB2(0001)-TBB surface decrease both H adsorption and diffusivity on the surface, but enhance H diffusion below the surface in comparison to W terminated WB2(0001) surface. H would be trapped and diffuse within atomic surface gaps on the WB2() surface, while H below the surface layer would jump along the [0001] direction rather than diffuse into bulk. The surface diffusion activation energy of H on the W2B(001) surface slightly varies with terminations. Once H crosses the surface layer of W2B(001) with either termination, it prefers to diffuse into the bulk, or back towards the surface, rather than move parallel to the surface. Interestingly, WB2(0001) and WB2() surfaces will have relatively higher H retention than the other W x B y surfaces evaluated in this work.

Modeling of Masked Droplet Deposition for Site-Controlled Ga Droplets.

Site-controlled Ga droplets on AlGaAs substrates are fabricated using area-selective deposition of Ga through apertures in a mask during molecular beam epitaxy (MBE). The Ga droplets can be crystallized into GaAs quantum dots using a crystallization step under As flux. In order to model the complex process, including the masked deposition of the droplets and a reduction of their number during a thermal annealing step, a multiscale kinetic Monte Carlo (mkMC) simulation of self-assembled Ga droplet formation on AlGaAs is expanded for area-selective deposition. The simulation has only two free model parameters: the activation energy for surface diffusion and the activation energy for thermal escape of adatoms from a droplet. Simulated droplet numbers within the opening of the aperture agree quantitatively with the experimental results down to the perfect site-control, with one droplet per aperture. However, the model parameters are different compared to those of the self-assembled droplet growth. We attribute this to the presence of the mask in close proximity to the surface, which modifies the local process temperature and the As background. This approach also explains the dependence of the model parameters on the size of the aperture.

Direct Determination of the Activation Energy for Diffusion of OH Radicals on Water Ice

Using a combination of photostimulated desorption and resonance-enhanced multiphoton ionization methods, the behaviors of OH radicals on the surface of an interstellar ice analog were monitored at temperatures between 54 and 80 K. The OH number density on the surface of ultraviolet-irradiated compact amorphous solid water gradually decreased at temperatures above 60 K. Analyzing the temperature dependence of OH intensities with the Arrhenius equation, the decrease can be explained by the recombination of two OH radicals, which is rate-limited by thermal diffusion of OH. The activation energy for surface diffusion was experimentally determined for the first time to be 0.14 ± 0.01 eV, which is larger than or equivalent to those assumed in theoretical models. This value implies that the diffusive reaction of OH radicals starts to be activated at approximately 36 K on interstellar ice.

Unraveling the Mechanism of Maskless Nanopatterning of Black Silicon by CF4/H2 Plasma Reactive-Ion Etching.

The process of deep texturization of the crystalline silicon surface is intimately related to its promising diverse applications, such as bactericidal surfaces for integrated lab-on-chip devices and absorptive optical layers (black silicon—BSi). Surface structuring by a maskless texturization appeals as a cost-effective approach, which is up-scalable for large-area production. In the case of silicon, it occurs by means of reactive plasma processes (RIE—reactive-ion etching) using fluorocarbon CF4 and H2 as reaction gases, leading to self-assembled cylindrical and pyramidal nanopillars. The mechanism of silicon erosion has been widely studied and described as it is for the masked RIE process. However, the onset of the erosion and the reaction kinetics leading to defined maskless patterning have not been unraveled to date. In this work, we specifically tackle this issue by analyzing the results of three different RIE recipes, specifically designed for the purpose. The mechanism of surface self-nanopatterning is revealed by deeply investigating the physical chemistry of the etching process at the nanoscale and the evolution of surface morphology. We monitored the progress in surface patterning and the composition of the etching plasma at different times during the RIE process. We confirm that nanopattering issues from a net erosion, as contributed by chemical etching, physical sputtering, and by the synergistic plasma effect. We propose a qualitative model to explain the onset, the evolution, and the stopping of the process. As the RIE process is started, a high density of surface defects is initially created at the free silicon surface by energetic ion sputtering. Contextually, a polymeric overlayer is synthesized on the Si surface, as thick as 5 nm on average, and self-aggregates into nanoclusters. The latter phenomenon can be explained by considering that the initial creation of surface defects increases the activation energy for surface diffusion of deposited CF and CF2 species and prevents them from aggregating into a continuous Volmer–Weber polymeric film. The clusterization of the polymer provides the self-masking effect since the beginning, which eventually triggers surface patterning. Once started, the maskless texturing proceeds in analogy with the masked case, that is, by combined chemical etching and ion sputtering, and ceases because of the loss of ion energy. In the case of CF4/H2 RIE processes at 10% of H2 and by supplying 200 W of RF power for 20 min, nanopillars of 200 nm in height and 100 nm in width were formed. We therefore propose that a precise assessment of surface defect formation and density in dependence on the initial RIE process parameters can be the key to open a full control of outcomes of maskless patterning.

Determination of Activation Energy of Surface Diffusion Based on Thermal Oscillations of Atoms

This paper covers calculations of the activation energy of surface diffusion of ad-atoms on the substrate surface from the point of view of thermal oscillations of substrate atoms and ad-atoms. The main characteristic of oscillations of atoms and geometric mean frequency was calculated based on statistical approximation of the Debye model using the reference values of entropy and heat capacity of metals. The basic principle of the model of activation energy calculation presented in the paper is the formation of potential wells and barriers during oscillations of atoms localized in the sites of the lattice. Oscillations of atoms were considered in the framework of quasiclassical quantum approximation as the oscillations of harmonic oscillators in the potential parabolic wells. Dimensions of the negative part of values of the potential well energy were determined by the amplitude of thermal oscillations of atoms. Positive values constituted a significant part of the potential well energy values. Barriers were formed owing to interaction of positive values of the energy of parabolic wells of adjacent atoms. Therefore, in order to make the ad-atom jump, it is necessary to get out of the potential well having the negative values, and to overcome the potential barrier. The energy required for the ad-atom jump on the substrate surface was the activation energy of surface diffusion. The results obtained in this paper agree satisfactorily with the results of another method, which is based on determining the energy of ad-atom binding with the substrate atoms.

Mechanisms of bulk and surface diffusion in metallic glasses determined from molecular dynamics simulations

The bulk and surface dynamics of Cu50Zr50 metallic glass were studied using classical molecular dynamics (MD) simulations. As the alloy undergoes cooling, it passes through liquid, supercooled, and glassy states. While bulk dynamics showed a marked slowing down prior to glass formation, with increasing activation energy, the slowdown in surface dynamics was relatively subtle. The surface exhibited a lower glass transition temperature than the bulk, and the dynamics preceding the transition were accurately described by a temperature-independent activation energy. Surface dynamics were much faster than bulk at a given temperature in the supercooled state, but surface and bulk dynamics were found to be very similar when compared at their respective glass transition temperatures. The manifestation of dynamical heterogeneity, as characterized by the non-Gaussian parameter and breakdown of the Stokes-Einstein equation, was also similar between bulk and surface for temperatures scaled by their respective glass transition temperatures. Individual atom motion was dominated by a cage and jump mechanism in the glassy state for both the bulk and surface. We utilize this cage and jump mechanisms to separate the activation energy for diffusion into two parts: (i) cage-breaking barrier (Q1), associated with the rearrangement of neighboring atoms to free up space and (ii) the subsequent jump barrier (Q2). It was observed that Q1 dominates Q2 for both bulk and surface diffusion, and the difference in activation energies for bulk and surface diffusion mainly arose from the differences in cage-breaking barrier Q1.

Quantum Mechanical Approach for Determining the Activation Energy of Surface Diffusion

A quantum mechanical approach was proposed to determine the activation energy of surface diffusion for copper, nickel, zinc and iron atoms adsorbed on a copper substrate during electrocrystallization for various overvoltages of the substrate. The activation energy of surface diffusion was calculated from the crystal total energy. An increase in the activation energy of surface diffusion with increasing surface potential is associated with an increase in the binding energy between the ad-atom and the substrate.

Kinetically Limited Phase Formation of Pt-Ir Based Compositionally Complex Thin Films.

The phase formation of PtIrCuAuX (X = Ag, Pd) compositionally complex thin films is investigated to critically appraise the criteria employed to predict the formation of high entropy alloys. The formation of a single-phase high entropy alloy is predicted if the following requirements are fulfilled: 12 J∙K−1 mol−1 ≤ configurational entropy ≤ 17.5 J∙K−1 mol−1, −10 kJ∙mol−1 ≤ enthalpy of mixing ≤ 5 kJ∙mol−1 and atomic size difference ≤ 5%. Equiatomic PtIrCuAuX (X = Ag, Pd) fulfill all of these requirements. Based on X-ray diffraction and energy-dispersive X-ray spectroscopy data, near-equiatomic Pt22Ir23Cu18Au18Pd19 thin films form a single-phase solid solution while near-equiatomic Pt22Ir23Cu20Au17Ag18 thin films exhibit the formation of two phases. The latter observation is clearly in conflict with the design rules for high entropy alloys. However, the observed phase formation can be rationalized by considering bond strengths and differences in activation energy barriers for surface diffusion. Integrated crystal orbital Hamilton population values per bond imply a decrease in bond strength for all the interactions when Pd is substituted by Ag in PtIrCuAuX which lowers the surface diffusion activation energy barrier by 35% on average for each constituent. This enables the surface diffusion-mediated formation of two phases, one rich in Au and Ag and a second phase enriched in Pt and Cu. Hence, phase formation in these systems appears to be governed by the complex interplay between energetics and kinetic limitations rather than by configurational entropy.

(Invited) Manufacturable Deposition of Two-Dimensional Tungsten Disulfide for Logic Applications

The two-dimensional (2D) semiconducting molybdenum and tungsten disulfide (MoS2 and WS2) hold promise as ultra-scaled metal-oxide-semiconductor (MOS) channel material for low power and/or high-performance logic applications. Manufacturable approaches that develop highly crystalline MX2 layers, tailor the layer number down to the atomic level and remain compatible with temperature sensitive structures, are essential to unlock the desired material functionality. However, fundamental understanding is lacking on how to design chemical deposition processes for 2D MX2, such as chemical vapor deposition (CVD).Therefore, our current research efforts focus on how to control the crystallinity, structure and morphology of WS2 crystals in the first, single layer through understanding the growth behaviour during a metal-organic (MO-)CVD process. WS2 is grown from tungsten hexacarbonyl (W(CO)6) and dihydrogen sulfide (H2S) precursors on 300 mm Si substrates covered with amorphous SiO2 and on single crystalline sapphire templates. A commercial 300 mm state-of-the-art Si and SiGe epitaxial reactor has been modified to deposit MX2 materials.In order to construct a qualitative model for relevant growth processes during WS2 MOCVD, the reaction kinetics are studied. Insight in the growth mechanisms is captured from the evolution in morphology of the WS2 crystals at different stages during the MOCVD process. Based on a statistical and morphological analysis of crystals in the first, single WS2 layer, two figures of merit describing the MOCVD process are extracted: the areal density of WS2 crystals and median lateral growth rate (lateral GR in nm2/(min∙cm2)).The WS2 MOCVD process is a profoundly thermally activated deposition process, with both nucleation rate and lateral GR dependent on deposition temperature. From an Arrhenius graph of WS2 inter-nucleus distance, the activation energy of surface diffusion is 10 kcal/mole. The areal density of WS2 crystals decreases over two orders of magnitude with deposition temperature, from 2x1010 /cm2 at 550 °C to 1x108 /cm2 at 1000 °C. However, it does not vary significantly with W(CO)6 partial pressure nor ratio between chalcogen and metal precursor partial pressure. Hence, the type and areal density of active surface sites of the starting surface determines the areal density of WS2 crystals, rather than the dose of metal precursor supplied to the starting surface. This opens opportunities to further control the areal density of WS2 crystals, for example through surface pretreatment. In contrast, the lateral growth rate of WS2 crystals in first, single layer increases most profoundly with deposition temperature and metal precursor partial pressure, with an activation energy of lateral growth approaching 31 kcal/mole. From the experimentally determined activation energies, the MOCVD process is likely governed by diffusion of reagents and reaction products (e.g., CO) across the boundary layer, and the dissociative physi-sorption of W(CO)6 precursor on starting surface.Based on these insights, the MOCVD process has been optimized and WS2 crystals with a median crystal size of 500 nm have been grown on amorphous SiO2. That learning is also applied to single crystalline sapphire substrates for their epitaxial seeding capability, considered to date the preferred approach to obtain state-of-the-art intrinsic material quality. In contrast to WS2 layers on SiO2, the WS2 crystals on the pretreated sapphire substrate develop a preferential in-plane crystalline orientation. The combination of the epitaxial seeding capability with the control over the areal density of WS2 crystals down to 1.7 x109 /cm2, implies that neighboring crystals can merge without forming a defective grain boundary yielding in principle micrometer-size crystals in the first, single layer.

New Insights into Dewetting of Cu Thin Films Deposited on Si.

Very thin metallic films are susceptible to dewetting upon thermal excursions, resulting in fragmentation and hence loss of structural integrity. Herein, 15 to 55 nm thick Cu films deposited on a Si substrate were isothermally annealed at 400 to 700 °C inside a scanning electron microscope operating in high-vacuum mode and the ensuing dewetting behavior was studied. The in situ observations revealed that the induction time before the void nucleation varied with film thickness as per a power-law with an exponent of 4, and the activation energy for both the void nucleation and the growth was close to the activation energy for surface diffusion. Hillock formation was observed to be a prerequisite for void nucleation in relatively thicker films. To complement the experimental observations, phase-field simulations incorporating a grain boundary grooving model were performed, which showed excellent agreement with the experimental observations. This validates the surface diffusion-controlled, grain boundary grooving-driven mechanism for void nucleation and dewetting of Cu films deposited on Si.

Effect of synthesis temperature on the phase formation of NiTiAlFeCr compositionally complex alloy thin films

The synthesis temperature dependent phase formation of Ni10Ti10Al25Fe35Cr20 thin films is compared to a bulk processed sample of identical composition. The as-cast alloy exhibits a dual-phase microstructure which is composed of a disordered BCC phase and AlNiTi-based B2- and/or L21-ordered phase(s). Formation of the BCC phase as well as an ordered AlNi-based B2 phase is observed for a thin film synthesised at 500 °C (ratio of synthesis temperature of thin film to melting temperature of bulk alloy: T/Tm = 0.49), which is attributed to both surface and bulk diffusion mediated growth. Post deposition annealing at 900 °C (T/Tm = 0.75) of a thin film deposited without intentional heating results in the formation of NiAlTi-based B2 and/or L21-phase(s) similar to the bulk sample, which is attributed to bulk diffusion. Depositions conducted at room temperature without intentional substrate heating (T/Tm = 0.20) resulted in the formation of an X-ray amorphous phase, while a substrate temperature increase to 175 °C (T/Tm = 0.28) causes the formation of a BCC phase. Atom probe tomography of the thin films deposited without intentional substrate heating and at 175 °C indicates the formation of ∼5 nm and ∼10 nm FeAl-rich domains, respectively. This can be rationalized based on the activation energy for surface diffusion, as Ti and Ni exhibt 2.5 to 4 times larger activation energy barriers than Al, Fe and Cr. It is evident from the homologous temperature that the phase formation observed at 500 °C (T/Tm = 0.49) is a result of both surface and bulk diffusion. As the temperature is reduced, the formation of FeAl-rich domains can be understood based on the differences in activation energy for surface diffusion and is consistent with kinetically limited thin film growth.

Direct Measurements of Activation Energies for Surface Diffusion of CO and CO2 on Amorphous Solid Water Using In Situ Transmission Electron Microscopy

Abstract The importance of the activation energy of surface diffusion (E sd) of adsorbed molecules on amorphous solid water (ASW) has been widely discussed in terms of chemical reactions on ASW at low temperatures. However, in previous work, E sd has not been measured directly but estimated from indirect experiments. It has been assumed in chemical network calculations that E sd is between 0.3 and 0.8 of the desorption energies of a molecule. It remains important to obtain direct measurements of E sd. We performed in situ observations of the deposition process of CO and CO2 on ASW using transmission electron microscopy (TEM) and deduced the E sd of CO and CO2 on ASW to be 350 ± 50 and 1500 ± 100 K, respectively. The value of E sd of CO is approximately 0.3 of the total adsorption energy of CO on ASW, i.e., much smaller than assumed in chemical network calculations, where the corresponding figure is 575 K, assuming approximately 0.5 of the desorption energy. We demonstrated that TEM is very useful not only for the observation of ices but also for the measurement of some physical properties that are relevant in astrochemistry and astrophysics. Using the E sd of CO measured in the present study (350 K), we have updated the chemical network model of Furuya et al., confirming that CO2 could be efficiently formed by the reaction CO + OH → CO2 + H in the initial stages of the evolution of molecular clouds.

Квантово-механический подход к определению энергии активации поверхностной диффузии

A quantum-mechanical approach is proposed for determining the activation energy of surface diffusion for adsorbed atoms of copper, nickel, zinc and iron on a copper substrate during electrocrystallization for various substrate overpotential. The calculation of the activation energy of surface diffusion is performed through the total energy of the crystal. An increase in the activation energy of surface diffusion with an increase in the surface potential is associated with an increase in the binding energy of the ad-atom with the substrate

Tackling the Stability Issues of Silver Nanowire Transparent Conductive Films through FeCl3 Dilute Solution Treatment

Silver nanowires (AgNWs) have been investigated as alternatives to indium tin oxide in transparent conductive films (TCFs) for electronics. However, AgNW TCFs still pose stability issues when exposed to thermal, chemical, and mechanical stimuli. Herein, we demonstrate a facile and effective route to improve stability by treating the films with dilute ferric chloride solution. Our results indicate that after treatment the films exhibit a dramatically enhanced stability against aging, high temperature oxidation, chemical etching, sulfurization, and mechanical straining. Size-dependent instability is fully explored and explained regarding surface atomic diffusion, which could be blocked by enhancing the activation energy of surface diffusion through forming a AgCl cap under ferric chloride solution treatment. Chemisorption-related Fermi level shift of silver nanowires is applied to tune their chemical reactivity to ferric chloride solution for balancing between size-dependent stability improvement and maintaining optoelectrical properties. Owing to the dilute treatment solution, the treated films exhibit a negligible change in light transmittance, whereas sheet resistance decreases by 30% and flexibility increases because of capillary-force-induced welding of contacting AgNWs and AgCl layer mediated tightening. These findings are significant for real-world applications of AgNW TCFs.

Modeling of metastable phase formation for sputtered Ti1-xAlxN thin films

Metastable titanium aluminum nitride coatings are widely applied in cutting and forming applications. Although it is generally accepted that the phase formation of metastable TiAlN is governed by kinetic factors, modeling attempts today are based solely on energetics. In this work, the metastable phase formation of TiAlN is predicted based on one combinatorial magnetron sputtering experiment, the activation energy for surface diffusion, the critical diffusion distance, as well as thermodynamic calculations. The phase formation data obtained from further combinatorial growth experiments varying chemical composition, deposition temperature, and deposition rate are in good agreement with the model. Furthermore, it is demonstrated that a significant extension of the predicted critical solubility range is enabled by taking kinetic factors into account. Explicit consideration of kinetics extends the Al solubility limit to lower values, previously unobtainable by energetics, but accessible experimentally.

Nanoporous tungsten with tailorable microstructure and high thermal stability

Nanoporous tungsten was prepared by a strategy combining mechanical alloying and chemical dealloying at room temperature. The feature size of the nanoporous structure is adjustable by modifying dealloying medium and duration. The formation of nanoporous tungsten is dependent on the surface diffusion of W atoms and their diffusivity in the dealloying medium is in a magnitude order of 10−20 m2 s−1. The structure of nanoporous tungsten has a high activation energy for surface diffusion, which contributes to its extremely high thermal stability. The nanoporous tungsten may be promising for applications at high temperatures.

THE KINETICS OF CaO ASSISTED PATTUKKU CHARCOAL STEAM GASIFICATION

Abstract Coal is a solid fuel that can be converted into syngas through gasification process. To obtain optimum gasification process design and operation, in-depth understanding of the influential parameters is required. This study aims to investigate the effect of temperature on the gasification process and to obtain its kinetics parameters. The study was carried out in a tubular reactor equipped with a heater and a condenser. Steam was used as gasifying agent, while CaO was employed as a CO2 adsorbent. The charcoal from coal was subjected to gasification at temperatures of 600°C, 700°C, and 800°C. The ratio of charcoal and CaO was 1:1. The gasification process lasted for 60 minutes with gas sample was taken every 15 minutes for composition analysis. The results showed that a temperature increase of 100°C caused a proportional increase of conversion of about 75% higher. The value of activation energy (Ea) and exponential factor (ko) were 46.645kJ/mole and 328.3894/min, respectively. For mass transfer parameters, values of activation energy for surface diffusion (Es) and surface diffusivity factor (as) were 81.126 kJ/mole and 0.138/min, respectively. Keywords: gasification; mathematical model; Pattukku coal char; steam; Thin Reaction Zone Model

Energy Landscape of Negatively Charged BSA Adsorbed on a Negatively Charged Silica Surface.

We study the energy landscape of the negatively charged protein bovine serum albumin adsorbed on a negatively charged silica surface at pH 7. We use fully atomistic molecular dynamics (MD) and steered MD (SMD) to probe the energy of adsorption and the pathway for the surface diffusion of the protein and its associated activation energy. We find an adsorption energy ∼1.2 eV, which implies that adsorption is irreversible even on experimental time scales of hours. In contrast, the activation energy for surface diffusion is ∼0.4 eV so that it is observable on the MD simulation time scale of 100 ns. This analysis paves the way for a more detailed understanding of how a protein layer forms on biomaterial surfaces, even when the protein and surface share the same electrical polarity.

Crossover from compact to branched films in electrodeposition with surface diffusion.

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G≫1), a detachment probability ε<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_{c} of that layer increases with G but is weakly affected by ε. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_{c}∼G^{γ}, with γ=1/[2(1-ν)]≈0.43, where ν≈0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_{c} can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter ε are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.