Monte carlo simulation of charging effects in linewidth metrology (II): On insulator substrate

Charging effects have been investigated quantitatively using Monte Carlo (MC) simulation when the linewidth of polymethylmethacrylate (PMMA) insulator patterns on SiO₂ insulator substrate are measured by scanning electron microscope (SEM). We established reference operating and shape conditions for array patterns and we have calculated the offset on linewidth metrology according to the change in each condition. We have used a 50% threshold algorithm for the edge determination, calculated the offsets in those conditions, and compared them with the results in the case of Si substrate. Finally, the question of which factor is the most sensitive in linewidth metrology is discussed.     

Topographic intensity profiles in the scanning electron microscope—cubes

Two-dimensional Monte Carlo computations have been used to predict the backscattered and secondary electron intensity profiles when a plane surface has a square of side d standing out from it. This was taken as a model for a gold cube of dimensions d situated on a thick gold substrate. This latter situation has been approximately reproduced experimentally and the predicted intensity profiles show quite good agreement with the observed intensity profiles for a range of values of the dimension d.     

Monte Carlo simulation of the formation of A<Superscript>III</Superscript>B<Superscript>V</Superscript> nanostructures with the use of droplet epitaxy

A Monte Carlo lattice model is proposed to describe the formation of semiconductor nanostructures by the vapor–liquid–solid growth mechanism. This model is used to simulate the growth of GaAs nanostructures by the droplet epitaxy technique in the temperature range from 500 to 600 K in As₂ fluxes with intensity of 0.005–0.04 ML/s. The morphology of the formed structures is demonstrated to depend on the growth parameters. Etching of the GaAs substrate by a gallium droplet is studied. The ranges of temperature and As flux rates necessary for the formation of GaAs nanorings are determined. The conditions of the formation of single and double concentric rings are analyzed.     

Wavelength- and energy-dispersive Electron Probe Microanalysis (EPMA) measurements with non-perpendicular incidence of the electron beam

A database of 416 wavelength‐ and energy‐dispersive EPMA measurements on tilted specimens of NiAl, TiO₂ and Ti₃Al is presented. The analyses were performed between 10 and 30 kV and the tilt angles were varied between 0° and 60° in seven steps. The necessary hardware modifications for the specimen holder are discussed, as well as the various focusing techniques used in the measurements. A comparison between the experimental data, the calculations of our proza 96t program and the results of Monte Carlo simulations shows that up to 50° tilt the predictions of our software are more than satisfactory. At larger tilt angles some deviations become noticeable. The Monte Carlo simulations appear to produce deviations at a somewhat earlier stage already, for reasons as yet unknown.     

Monte Carlo Simulation of Sudden Death Bearing Testing

Monte Carlo simulations combined with sudden death testing were used to compare resultant bearing lives to the calculated bearing life and the cumulative test time and calendar time relative to sequential and censored sequential testing. A total of 30,960 virtual 50-mm bore deep-groove ball bearings were evaluated in 33 different sudden death test configurations comprising 36, 72, and 144 bearings each. Variations in both life and Weibull slope were a function of the number of bearings failed independent of the test method used and not the total number of bearings tested. Variations in L ₁₀ life as a function of number of bearings failed were similar to variations in life obtained from sequentially failed real bearings and from Monte Carlo (virtual) testing of entire populations. Reductions up to 40% in bearing test time and calendar time can be achieved by testing to failure or the L ₅₀ life and terminating all testing when the last of the predetermined bearing failures has occurred. Sudden death testing is not a more efficient method to reduce bearing test time or calendar time when compared to censored sequential testing.     

The elusive ettringite under the high‐vacuum SEM – a reflection based on natural samples,the use of Monte Carlo modelling of EDS analyses and an extension to the ettringite group minerals

Ettringite, Ca₆Al₂(SO₄)₃(OH)₁₂.26H₂O, or C₆A₃H₃₂ as it is known in cement chemistry notation, is a major phase of interest in cement science as an hydration product and in polluted soil treatment since its structure can accommodate with many hazardous cations. Beyond those anthropogenic features, ettringite is first of all a naturally occurring mineral (although rare). An example of its behaviour under the scanning electron microscope and during energy dispersive spectroscopy (EDS) qualitative analysis is presented, based on the study of natural ettringite crystals from the N'Chwaning mine in South Africa. Monte Carlo modelling of the electron‐matter interaction zone at various voltages is presented and confronted with actual, observed beam damage on crystals, which burst at the analysis spot. Finally, theoretical energy dispersive spectroscopy spectra for all the ettringite group minerals have been computed as well as Monte Carlo modelling of the electron‐matter interaction zone. The knowledge of the estimation of the size of this zone may thus be helpful for the understanding of energy dispersive spectroscopy analysis in cement pastes or ettringite‐remediated soils.     

Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration

This article presents the calibration of a compact prover using the weighing method. An evaluation of measurement uncertainty of the prover calibration has been developed using the GUM and Monte Carlo methodologies. A water draw kit was utilized to direct the liquid flow from the compact prover to a water container in order to weigh the transferred water mass on a balance. This amount of mass was used as reference for the calculation of the prover base volume. A modeling of the flow rate into the water draw kit as a function of time was conceived. This modeling was applied for calculating the error in the liquid volume of the water container due to the switching of two solenoid valves of the water draw kit. A mathematical model of the prover base volume has been developed. This model is non-linear and the two largest sources of uncertainty are related to the balance calibration certificate that together account for 31.84% of the uncertainty budget. This work showed that the GUM approach was validated by Monte Carlo method in the calculation of the measurement uncertainty of the calibration of a compact prover. The absolute differences of the respective endpoints of the coverage intervals of these two methods are less than 0.00023% of estimate of the prover base volume whose value is 151.427 dm³. This result was obtained for a coverage probability of 95% and ${10}^6$ Monte Carlo iterations. The density of the calibration water and its uncertainty have been calculated through an innovative approach.     

Modeling the formation of silicon nanoclusters during annealing SiO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> layers

The mechanism of formation of silicon nanoclusters in layers of nonstoichiometric composition is studied by Monte Carlo simulation. Interest in silicon nanoclusters (Si-nc) coated with an oxide layer is due to their applications in modern optoelectronics and nanoelectronics. A lattice Monte Carlo model is proposed to study atomic processes in the Si-SiO₂ system. The formation of silicon nanoclusters during annealing of single SiO layers and SiO₂-SiO-SiO₂ layered structures is studied. Along with the diffusive motion of particles, the model takes into account the formation and collapse of mobile molecules of silicon monoxide. It is shown that accounting for transport of silicon under high-temperature annealing due to the motion of SiO accelerates the formation of Si-nc. Dependences of the size of nanoclusters on temperature, annealing time, and the composition of the SiO _x layer are obtained. It is found that annealing of silica films containing layers of nonstoichiometric composition can lead to the formation of silicon nanoclusters or cavities.     

A comparative study on the structure and hardness enhancement of a-BON/nc-TiN films prepared by low and high RF frequency PAMOCVD

Amorphous (a)-BON/nanocrystal (nc)-TiN bilayer coatings were deposited on a p-type silicon(1 0 0) substrate by low and high RF frequency plasma-assisted metal–organic chemical vapor deposition(PAMOCVD) system, using tetrakisdimethylaminotitanium(TDMAT, [(CH₃)₂N]₄Ti) and trimethylborate(TMB, (CH₃O)₃B) as TiN and BON precursors, respectively. We used Ar gas as a plasma source and N₂ gas as a reactive and additional nitrogen source. In this study, we have mainly investigated the relationship between the hardness and the structure of the coating layers by the effects of deposition parameters such as frequency, deposition time and substrate temperature. The results show that the surface structure of the top layer and the interface structure of layer-by-layer affect the hardness enhancement in bilayered a-BON/nc-TiN thin films. The as-grown films were characterized using X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), atomic force microscope (AFM), scanning electron microscope (SEM) and nano indenter.     

Evaluation of measurement uncertainty using mixed distribution for conducted emission measurements

For evaluation of measurement uncertainty for conducted emission measurements, we propose a new model which uses mixed distribution. Namely, evaluation of probability density function (PDF) for the measurand has been done using a Monte Carlo method and a modified least-squares method. As the Monte Carlo method required numerical calculation of approximate PDF values, pseudorandom number generator (PRNG) was developed for these requirements. For illustration, this work presents mixed distributions of two normal distributions, normal and rectangular distributions, and normal and also triangular distributions in case of conducted emission measurements. The results obtained by the Monte Carlo method and the modified least-squares method are compared to the corresponding results when applying the standard Guide to the Expression of Uncertainty in Measurement (GUM) procedure.     

Performance of brazed diamond wheels fabricated in hydrogen/methane plasmas or a vacuum

The ambience in which brazed diamond wheels are fabricated has an important effect on the sharpness of the brazed diamond grits and on the hold of the filler alloy on these grits. In this work, brazed diamond wheels were fabricated using NiCr alloy either in a 0.05-Pa vacuum or in H₂/CH₄ plasmas at a temperature of 1,020°C for 5 min. The surface of the diamond grits brazed in H₂/CH₄ plasmas and protruding out of the filler alloy is not graphitized. The layer of carbide formed on the interface between the filler alloy and diamond brazed in H₂/CH₄ plasmas allows the liquid filler alloy to soak the diamond grits better. This is good for the filler alloy gaining a firm hold on the diamond grits. Diamond grits brazed in H₂/CH₄ plasmas undergo compressing stress due to the penetration of carbon into the filler alloy. There is a white band, which denotes firm metallurgical bond, between the filler alloy and the substrate of a brazed diamond wheel fabricated in H₂/CH₄ plasmas or in the 0.05-Pa vacuum, but the bandwidth in the brazed diamond wheel fabricated in H₂/CH₄ plasmas is almost twice that in the brazed diamond wheel fabricated in the 0.05-Pa vacuum. Grinding tests showed that the percentages of both whole grain fractures and pullouts from the matrix of diamond grits brazed in H₂/CH₄ plasmas are lower than those of diamond grits brazed in the 0.05-Pa vacuum.     

Temporal characteristics of light collection in the liquid scintillation counter with a volume of 1.5 m<Superscript>3</Superscript> and quasi-mirror reflection

The temporal behavior of light collection in the 1.5-m³-volume mirror-reflecting counter filled with a highly transmitting liquid scintillator has been investigated. Using the Monte Carlo method and assuming that the luminescence decay time of the liquid scintillator is zero (τ_LS = 0), it has been ascertained that, in the case of a short flash in a counter, the exponential phase of light collection is characterized by time τ_col = 15.0 ± 1.7 ns, which is does not depend on scattering of light in the medium. The measured exponent index τ_act = 37 ± 3 ns of an actual pulse due to a muon is determined both by light collection time τ_col ≈ 15 ns and luminescence decay time τ_LS ≈ 20 ns of the scintillator in the large-volume counter.     

Activation of the SiC surface for vapor phase lubrication by Fe chemical vapor deposition from Fe(CO)5

The feasibility is demonstrated of a new approach to the vapor phase lubrication of ceramics using organophosphorus compounds. The surface of SiC is shown to be unreactive for the decomposition of trimethylphosphite, (CH₃O)₃P, a simple model for organophosphorus vapor phase lubricants such as tricresylphosphate. In order to activate the surface of SiC it has been exposed to Fe(CO)₅ at a temperature of 600 K. Chemical vapor deposition serves as a means of depositing Fe on the SiC surface. The Fe-modified SiC surface is then shown to induce the decomposition of adsorbed (CH₃O)₃P. The mechanism of (CH₃O)₃P decomposition is similar to that observed on Fe(110) surfaces modified by the presence of oxygen. It is initiated by P–O bond cleavage to produce adsorbed methoxy groups, CH₃O_(ad), which then decompose by -hydride elimination resulting in H₂, CO, H₂CO, and CH₃OH desorption. It is suggested that chemical vapor deposition of metals using high vapor pressure metal-containing compounds such as Fe(CO)₅ can serve as a mechanism for continuous, in situ activation of ceramic surfaces for vapor phase lubrication in high temperature engines.     

Estimating the uncertainty of discharge coefficient predicted for oblique side weir using Monte Carlo method

Side weir is a hydraulic structure, which is used in irrigation systems to divert some water from main to side channel. It is installed at the entrance of the side channel to control and measure passing water into the side channel. Many studies provided side weir water surface profile and coefficient of discharge to measure water discharge diverted into the side channel. These studies dealt with different side weir shapes (rectangular, trapezoidal, triangular and circular), which were installed perpendicular to the flow direction. Recently, some studies dealt with skew side weir, but these studies still need to more investigation. Here we report to investigate oblique side weir theoretically using statistical method to supported other studies in this case. Measurement uncertainty discharge coefficient C_d was obtained by two methods: analytical according to the ‘Guide to the expression of uncertainty in measurement’ and the Monte Carlo method. The results indicate that all experimental results are consistent with the analytical results. The relative expanded uncertainty of the discharge coefficient C_d does not exceed 2%.     

Tribochemical Reactions and Lubricating Effects of Fluorinated Methanes for Al2O3 Ceramic

It has been found that CF₃CH₂F (HFC-134a) gas is an effective lubricant for several ceramics because of the formation of fluorine-containing tribochemical products. To understand the influence of the molecular structure of fluorine-containing gases on the lubricating characteristics, the lubricating effects and tribochemical reactions of some fluorinated methanes for Al₂O₃ ceramic were studied. X-ray Photoelectron Spectroscopy (XPS) and Time-of-Flight Secondary Ion Mass Spectroscopy (TOF-SIMS) were used to identify the chemical structure of tribochemical products. It was found that the friction and wear of Al₂O₃ ceramic were dependent on the molecular structure of the reacting fluorocarbon gases. The lowest friction was obtained in CH₂F₂. CHF₃ showed the best anti-wear effect. The results of surface analyses indicate that greater amounts of tribochemical products are produced when Al₂O₃ rubs in CH₂F₂ than in CF₄ and CHF₃ gases. C–C/C–H/carbon and AlF₃, which are mainly formed on the sliding surface in CH₂F₂, are responsible for the low friction. The mechanism of tribochemical reactions of the different environmental molecules on the nascent surface of Al₂O₃ was also discussed.     

Effects of End Groups on the Tribochemical Reactions of Lubricants at Head-Disk Interface

Mass spectrometry was used to monitor in-situ gaseous species that were generated at the head-disk interface (HDI) in a high vacuum. It was found that the end groups of the lubricants significantly affected the wear durability at the HDI; piperonyl (–CH₂-phe = (O)₂ = CH₂) terminated Fomblin AM3001 lubricant exhibited longer life than hydroxyl (–OH) terminated Fomblin ZDOL lubricant. The continuous removal of the lubricants resulted in a continuously increasing friction coefficient. Further, the characteristics of tribochemical reactions of the lubricants (Fomblin Z series) with different end groups was investigated in details using Time-of-Flight Secondary Ion Mass Spectroscopy (TOF-SIMS) just after the sliding tests. It was found that the decomposition of the end groups was more significant than that of the backbone. The lubricants terminated with the following groups showed the following order of increasing decomposition: –CH₂O-CH₂-phe = (O)₂ = CH₂ (AM3001), –CH₂OH (ZDOL) < –CH₂OCH₂CH(OH)CH₂OH (Z Tetraol) < –CH₂(OCH₂CH₂)_nOH (ZDOL-TX), –COOH (Z Diac). The decomposition of the lubricants appeared to start from the end groups.     

Initial steps in the surface chemistry of vapor phase lubrication by organophosphorus compounds

The surface chemistry of trimethylphosphite (CH₃O)₃P has been studied on Cu(111) and Ni(111) surfaces in order to model the initial steps in the reactions of vapor phase lubrication by organophosphorus compounds. The initial reactions involve scission of the P–O bonds to deposit methoxy groups (CH₃O_(ad)) on the surfaces. On the Cu(111) surface the formation of CH₃O_(ad) species occurs only after oxidation of the surface. The CH₃O_(ad) groups on Cu(111) decompose by β‐hydride elimination to produce formaldehyde (O=CH₂) and adsorbed hydrogen. CH₃O_(ad) groups are formed from (CH₃O)₃P on the clean Ni(111) surface and decompose by complete dehydrogenation to CO and adsorbed hydrogen atoms. This chemistry is very similar to that observed for CH₃OH on these surfaces. These results suggest that alkoxides are important intermediates in the decomposition of vapor phase lubricants on metal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of eccentricity on roughness distributions in side milling

In this paper, a numerical model was used based on the tool-piece geometric intersection, which enables the determination of a roughness profile as a function of feed, tool radii and tool eccentricity in side milling processes. Average roughness R_a and peak-to-valley roughness R_t were obtained for a group or family of tools, defined by an average radius value and a standard deviation value of all tool radii. The Monte Carlo method was used to generate N random combinations of radius values for each family, according to a normal distribution. The model was validated by means of experimental tests. For each family of tools, roughness distributions were obtained at different feed values and for different eccentricity values. It was found that the higher eccentricity, the more asymmetrical roughness distributions become.