Surface Field Research Articles

DC electric field generation and distribution in magnetized plasmas

Very large DC and AC electric fields cannot be sustained between conducting electrodes because of volume gas breakdown and/or surface field emission. However, very large potential fields are now routinely generated in plasma structures, such as laser generated wake in unmagnetized plasmas. In magnetized plasmas, large DC fields can also be sustained and controlled perpendicular to the magnetic field, but the metallic end plates limiting the plasma, terminating the magnetic field lines, and usually providing the voltage drop feed between the field lines impose severe restrictions on the maximum field. However, it is shown that very large radial DC voltage drops can be sustained by injecting waves of predetermined frequencies and wave vectors, traveling along the azimuthal direction of an axially magnetized plasma cylinder, or by injecting fast neutral particles beams along this azimuthal direction. The large conductivity along the magnetic field lines and the small conductivity between the field lines then distribute this voltage drop. The global power balance and control parameters of wave and beam generated large DC electric fields in magnetized plasmas are identified, described, and analyzed.

Effects of Full-sphere Convection on M-dwarf Dynamo Action, Flux Emergence, and Spin-down

We present an analysis of 21 global MHD simulations of the dynamo action taking place in the interiors of fully convective M4 stars. We leverage our past work involving 45 simulations of shell-convecting-type M2 stars in a very similar parameter space to identify properties that their dynamos share and ways in which they differ. We find that the parameter scalings of many fundamental dynamo measures including the ratio of magnetic to kinetic energy and the cycle period are shared not only between the two sets of M-dwarf models but also with the broader literature on K and G dwarfs, suggesting that their convective dynamos are similar in nature. We find that the surface fields of the fully convective stars are stronger and more organized than those in the shell-convecting models and indicate faster spin-down than is observed, for which we suggest possible remediations. We note an abundance of dynamo states that are localized within one hemisphere at a time and find that such states are well described by a quasi-linear superposition of even- and odd-parity eigenmodes with similar amplitudes. We observe that the turbulent stirring of the deep fields of the fully convective models allows them to attain far higher peak amplitudes than those in the tachoclines of the partially convective models. We employ our AI-enabled pipeline, LoopNet, to search for buoyant, fibril magnetic fields in the simulated stars and find nearly twice as many such structures forming in the M4 models, in good agreement with observed differences in their flaring rates.

1 kV GaN-on-Si Quasi-Vertical Schottky Rectifier

This work demonstrates quasi-vertical GaN Schottky barrier diodes (SBDs) on 6-inch Si substrate with a breakdown voltage (BV) over 1 kV, the highest BV reported in vertical GaN-on-Si SBDs to date. The deep mesa inherently in quasi-vertical devices is leveraged to form a self-aligned edge termination, and the mesa sidewall is covered by the p-type nickel oxide (NiO) as a reduced surface field (RESURF) structure. This novel termination enables a parallel-plate junction electric field of 2.8 MV/cm, being close to the material limit for GaN. The device also shows a high on/off ratio of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> , low turn-on voltage of 0.5 V, and low specific on-resistance of 1.1 mΩ∙cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Moreover, the device exhibits excellent overvoltage robustness under the continuous 800 V stress in the unclamped inductive switching test. These results show the good promise of the low-cost vertical GaN-on-Si power diodes.

Results of modelling the effect of temperature on the thickness of the surfactants layer

Problem. Earthmoving machines operate under high loads, so their tribo-joints periodically operate under unsteady load conditions, which leads to their increased wear and, as a result, a rapid decrease in the residual service life of the units and the reliability of the machines in general. Under unsteady load conditions, friction in the joints of hydraulic drive elements occurs under the boundary lubrication regime. This lubrication mode occurs at high contact loads, high temperatures in the contact zone, and relatively low sliding speeds of the mating surfaces. The combination of boundary lubrication and high dynamic loads often leads to partial destruction of the boundary layer. This leads to direct contact of individual micro-irregularities of the friction surfaces, which is accompanied by a wear process. Hence the importance of the quality of both the parameters of the surface layer of friction surfaces and the parameters of the applied lubricant (oils, working fluids) on the strength and wear resistance of hydraulic drive elements. Goal. The aim of this work is to determine the effect of temperature and radius of curvature of a microroughness on the thickness of the layer of surface-active substances adsorbed on it. Methodology. The solution of the tasks involved the formation of a model of adsorption-desorption equilibrium in the system "working fluid - micron-surface", taking into account the ambient temperature, and its application to determine the dependence of the thickness of the adsorbed surfactant layer under conditions of temperature change. Results. The thickness of the adsorption layer depends mainly on the size of the adsorbing surface field and the energy of thermal vibrations of molecules. It decreases with increasing PP and increases with increasing radius of curvature of the micron roughness. The change in the thickness of the adsorption layer of surfactant molecules on the surface of the micron roughness with a change in the temperature of the RS is not uniform. With an increase in the PP temperature within 300...400 K, the thickness of the adsorption layer of surfactant molecules on the surface of the micron roughness decreases by ~24 %. With an increase in the temperature of the PP in the range of 400...450 K, the thickness of the adsorption layer of surfactant molecules on the surface of the microroughness decreases by ~76 %. The formation of a surfactant adsorption layer on the surface of the microroughness at a temperature above 443 K stops. Originality. A model of the formation of a surfactant adsorption layer on the surface of a separate microroughness on the basis of adsorption-desorption equilibrium in the system "working fluid - microroughness surface" was proposed, taking into account the ambient temperature, which allows us to analyse the nature of the temperature effect on the thickness of the adsorbed surfactant layer. Practical value. The use of the proposed mathematical model makes it possible to estimate the parameter of the surfactant adsorption layer on the surfaces of microroughnesses and rough friction surfaces based on the ambient temperature and the geometry of individual microroughnesses.

A novel substrate Voltage-assisted RESURF technique in SOI LDMOS with a heavily doped drift region

A novel substrate voltage-assisted (SVA) reduced surface field (RESURF) technique in SOI lateral double-diffused Metal-Oxide-Semiconductor (LDMOS) with a heavily doped drift region is proposed. Without any additional masks and processes, an external control circuit is designed to adaptively control the substrate voltage in the technique. The co-simulation based on TCAD and the circuit is implemented to explore the mechanism of the SVA RESURF technique. In the off-state, a negative bias is applied to the substrate, which induces positive charges to compensate for the heavily doped ionizing acceptors in the drift region. The breakdown voltage is improved and remains at the same level as the conventional RESURF device. In the on-state, a zero bias is applied to the substrate, and heavy doping in the drift region can achieve low specific on-resistance compared to the RESURF device with a lightly doped drift region. As a result, the proposed technique reconstructs the charge balance and the conventional RESURF condition. The simulation results show reduced specific on-resistance, low drain leakage current, large saturation current, high transconductance and cut-off frequency, decreased turn-on/off characteristics and improved FOM and BFOM compared with the conventional RESURF technique. Furthermore, an analytical model is developed to optimize the substrate voltage for the maximum breakdown voltage in the external control circuit design of the proposed technique.

Comparison of subcritical crack growth and dynamic fracture propagation in rocks under double-torsion tests

Relaxation and rapid displacement loading tests were performed on five types of rocks to gain a deeper understanding of the differences between subcritical crack growth (SCG) and dynamic fractures. The critical surface energy was obtained by fitting a hyperbolic sine function to the SCG velocities and mechanical energy release rates of the five rocks. The specific SCG range and the dimensions of the fracture process zone (FPZ) were determined via the displacement field of the sample bottom surface provided by digital image correlation. The FPZ lengths of the double-torsion rock samples range from 21.03 mm to 34.10 mm, and the lengths increase with the increasing maximum grain size of the rock type. The FPZ width is between 1.63 mm and 3.46 mm and exhibits a similar variation to that of the FPZ length. A three-dimensional optical scanner was used to obtain the morphologies of the subcritical crack surfaces and the dynamic fracture surfaces. The results show that the roughness of the subcritical crack surface is larger than that of the dynamic fracture surface, and both are positively correlated with the maximum grain size of the rock. The scanning electron microscope images demonstrate the change in the roughness of the crack surface; the subcritical cracks preferentially propagate along the grain boundaries while the dynamic fractures directly cut across crystals with some intergranular fractures.

Sensitivity of seasonal circulation response to snow reduction in the Northern Hemisphere and Eurasia and its impact on Eurasian climate

In this study, we analyze the impact of reduced snow cover in the Northern Hemisphere on the atmosphere and if the atmospheric response depends on the model resolution. We use the atmospheric component of the global climate model EC-Earth and perform three experiments: in the first experiment, we reduce the snow cover in the entire Northern Hemisphere by reducing the snow albedo to a constant value of 0.3, in the second experiment, we reduce the snow albedo only over Eurasia, and the third experiment is the control run using normal snow conditions. All experiments are integrated over the period 1980–2015 at standard resolution (~ 80 km) and high resolution (~ 40 km). Experiments comprise 11 and 5 ensemble members at standard resolution and high resolution, respectively. Reducing the snow albedo in the Northern Hemisphere leads to 5–10% snow cover reduction in winter and spring. Significant warm responses are found over northern Eurasia in spring and summer with a warm response reaching 3 °C. Similar but weaker warm temperature responses are found in the middle and upper troposphere (up to 2 °C) and reversed temperature responses in the stratosphere (up to – 2 °C), particularly over eastern Eurasia. This is closely associated with westerly jet flow response which is enhanced at high-latitude and weakened at low-latitude in winter and spring over eastern Eurasia. Reduced snow cover leads to warmer surface temperatures that accelerate snow-melting and further lead to different snow-hydrological responses in western and eastern Eurasia and more precipitation occurs over eastern Eurasia (increasing 10–20%), particularly in the Siberian region. When the snow albedo is reduced only in the Eurasian sector, the surface response pattern resembles the results of the Northern Hemisphere experiment. The warm response is slightly weakened about 0.25–0.5 °C over Eurasia and significantly weakened outside of Eurasia. However, the upper air circulation response is much less pronounced over Eurasia. The impact of resolution on the mean surface field response is small yet it is more pronounced on the large-scale circulation response, particularly in spring and winter.

Improving Robotic Tactile Localization Super-resolution via Spatiotemporal Continuity Learning and Overlapping Air Chambers

Human hand has amazing super-resolution ability in sensing the force and position of contact and this ability can be strengthened by practice. Inspired by this, we propose a method for robotic tactile super-resolution enhancement by learning spatiotemporal continuity of contact position and a tactile sensor composed of overlapping air chambers. Each overlapping air chamber is constructed of soft material and seals the barometer inside to mimic adapting receptors of human skin. Each barometer obtains the global receptive field of the contact surface with the pressure propagation in the hyperelastic seal overlapping air chambers. Neural networks with causal convolution are employed to resolve the pressure data sampled by barometers and to predict the contact position. The temporal consistency of spatial position contributes to the accuracy and stability of positioning. We obtain an average super-resolution (SR) factor of over 2500 with only four physical sensing nodes on the rubber surface (0.1 mm in the best case on 38 × 26 mm²), which outperforms the state-of-the-art. The effect of time series length on the location prediction accuracy of causal convolution is quantitatively analyzed in this article. We show that robots can accomplish challenging tasks such as haptic trajectory following, adaptive grasping, and human-robot interaction with the tactile sensor. This research provides new insight into tactile super-resolution sensing and could be beneficial to various applications in the robotics field.

Optimising standard solar cell designs for maximum efficiency using genetic algorithms

ABSTRACT Solar energy is an alternative to conventional fossil fuels, and maximising the energy collected through solar cell design improvements is worthwhile. Genetic algorithms (GAs) have been historically useful in pursuing design improvements in solar cell architecture and manufacturing, particularly in combination with cell modelling software. This study demonstrates solar cell structural optimisation using PC3D software in combination with a genetic algorithm (GA) to maximise solar cell power conversion efficiency. PC3D is an Excel-based tool for modelling solar cells. The cell models examined here are: Passivated-Emitter Rear Contact (PERC), Interdigitated Back Contact (IBC), Aluminium-Back Surface Field (Al-BSF), and Passivated-Emitter Rear Locally Diffused (PERL). These are all silicon PV cells with varying structural features that significantly alter the performance of each cell. Absolute efficiency improvements of 2% for PERC, 1.6% for Al-BSF, 0.9% for IBC, and 0.5% for PERL cells are achieved. The main parameters impacting cell efficiency in this model are cell thickness and minority charge carrier lifetime, which feature a necessary trade-off between the higher absorption resulting from a thicker cell and the increased likelihood of charge collection arising from longer carrier lifetimes. These parameters are managed through other related values such as cell doping.

Signs of binary evolution in seven magnetic DA white dwarfs

ABSTRACT We present our findings on the spectral analysis of seven magnetic white dwarfs that were presumed to be double degenerates. We obtained time-resolved spectroscopy at the Gemini Observatory to look for evidence of binarity or fast rotation. We find three of our targets have rotation periods of less than an hour based on the shifting positions of the Zeeman-split H α components: 13, 35, and 39 min, and we find one more target with a approximately an hour long period that is currently unconstrained. We use offset dipole models to determine the inclination, magnetic field strength, and dipole offset of each target. The average surface field strengths of our fast rotators vary by 1–2 MG between different spectra. In all cases, the observed absorption features are too shallow compared to our models. This could be due to extra flux from a companion for our three low-mass targets, but the majority of our sample likely requires an inhomogeneous surface composition. Including an additional magnetic white dwarf with similar properties presented in the literature, we find that five of the eight targets in this sample show field variations on minute/hour time-scales. A crystallization driven dynamo can potentially explain the magnetic fields in three of our targets with masses above 0.7 M⊙, but another mechanism is still needed to explain their rapid rotation. We suggest that rapid rotation or low-masses point to binary evolution as the likely source of magnetism in seven of these eight targets.

A hybrid analytical-FEM 3D approach including wear effects to simulate fretting fatigue endurance: Application to steel wires in crossed contact

Fretting fatigue causes failures in steel wire ropes. A crossed wires set-up was used to investigate the influence of displacement amplitude on fretting fatigue damage. The analysis confirms previous literature results, showing a beneficial effect of wear in gross slip regime, which extends the contact area and thus decreases the contact stresses. The computation of such combined cracking and wear processes is very expensive using a classical FEM strategy, particularly for 3D contact geometries. To palliate such limitations, a hybrid analytical-numerical strategy was developped. It consists in estimating pressure and shear stress surface fields using analytical formulations, then to transpose these fields to an FEM model. This allows to simulate contact geometry modifications in a fast and efficient way.

Dynamics of passive admixture in surface and subsurface external deformation field above an ocean guyot

Within the framework of a three-layer quasi-geostrophic model in the f-plane approximation, a numerical study of the effect of an isolated submarine obstacle on the movement of surface and subsurface patches of a neutral admixture transfered by a vertically homogeneous zonal current was carried out. The possibility of partial capture of impurities by quasi-stationary topographic eddy in the vicinity of the submarine obstacle is shown. The role of the initial location (both horizontally and vertically) on the resulting pollution distribution pattern is revealed.

Design and Performance Enhancement of a GaAs-Based Homojunction Solar Cell Using Ga0.5In0.5P as a Back Surface Field (BSF): A Simulation Approach

The GaAs semiconductor is a solar energy promising material for photovoltaic applications due to its good optical and electronic properties. In this work, a homojunction GaAs solar cell with AlxGa1-xAs and GayIn1-yP solar energy materials as window and back surface field (BSF) layers, respectively, was simulated and investigated using SCAPS-1D software. The performance of the GaAs-based solar cell is evaluated for different proportions ofxandy, which allowed us to obtain the values of 0.8 and 0.5 forxandy, respectively, as the best values for high performance. We then continued the optimization by taking into account some parameters of the solar cell, such as thickness, doping, and bulk defect density of the p-GaAs base, n-GaAs emitter, and Ga0.5In0.5P BSF layer. Solar cell efficiency increases with emitter thickness, but the recombination phenomenon is more pronounced than that of electron-hole pair generation in the case of a thicker base. The effect of variation in the work function of the back contact has also been studied, and the best performance is for a platinum (Pt) electrode. The optimized GaAs-based solar cell achieves a power conversion efficiency of 35.44% (JSC=31.52 mA/cm2,VOC=1.26 V,FF=89.14%) and a temperature coefficient of -0.036%/°C. These simulation results provide insight into the various ways to improve the efficiency of GaAs-based solar cells.

High-conductivity nickel shells encapsulated wood-derived porous carbon for improved electromagnetic interference shielding

Biomass-derived carbon materials, especially from wood, have attracted great interests in electromagnetic interference (EMI) shielding ascribed to their sustainability and unique porous structures. However, it still lacks an effective approach to optimize its shielding performance through the microstructure design. Here, core@shell structure nickel encapsulated wood-derived porous carbon (PC) is prepared to improve the EMI shielding performance of porous carbon, in which the high-conductivity nickel shells is obtained through a chemical plating approach. The shielding effectiveness (SE) can reach 83 dB at 9.5 GHz, which is much higher than other reported shielding materials. Experimental results coupled with numerical simulations indicate that the surface and interface electric field distributions could result in a rapid transportation of EM energy and thus enhance the EMI shielding performance. Moreover, the shielding thin films prepared by such microparticles could demonstrate a superior SE of 104.5 dB with a normalized SE of 139.4 dB/mm. Our study opens a new pathway for designing EMI shielding materials based on biomass-derived core@shell structural carbon materials.

Relevance of the Microbiota on Ocular Diseases: A Bibliometric and Citation Network Analysis

Background: This study aimed to analyze the relevance of different publications about microbiota on ocular diseases and their authors through a citation network analysis. In addition, the different research areas and the most cited publications have been identified. Methods: The bibliographic search was carried out through the Web of Science (WOS) database, using the following search term: “microbiota AND (vision OR eye OR visual)” for the period between 1995 and December 2022. The Citation Network Explorer and the CiteSpace software have been used to analyze the different publications. Results: 705 publications were found in the field of microbiota on ocular diseases, together with 1014 citation networks. The year 2022 was the year with more publications. The first authors with the highest number of publications in the microbiota on the ocular surface field were Chisari G, Chisari CG, and Li Y. This field is multidisciplinary, highlighting “microbiology” and “ophthalmology” as the main research areas. Publications were clustered into three main groups allowing the identification of the main research topics in this field. The principal was the composition and diversity of the bacterial community on the ocular surface of patients with several pathologies. Conclusion: It could be useful for researchers to choose suitable collaborators or projects to promote their research on the role of microbiota on ocular diseases, as well as to know the main research topics that are of major interest today.

Imaging microwave field of chip surfaces based on scanning microwave microscopy

With the rapid development of semiconductor chip circuit integration and miniaturization, especially the high integration of microwave chips, it has become critical to realize the surface microwave field imaging for such chips. In this paper, a new method of microwave field imaging for chip surface is proposed based on scanning probe microscopy. We analyse the echo signal and extract the peak-to-peak values to characterize the microwave field intensity on the chip surface by building a theoretical model of the microwave signal coupling. Using a high-precision scanning stage based on a piezoelectric ceramic tube, we realize the imaging of microwave field. The experimental results show that the imaging method can complete the chip surface microwave field imaging, which is important to support the optimization of semiconductor chip manufacturing process, fault analysis and new material research, and promote the development and progress of the semiconductor industry.

Plasmon Tunability and Field Enhancement of Gold Nanostar

Objective: The localized surface plasmon resonance (LSPR) and field enhancement of Gold nanosphere and nanostar were evaluated. Method: FDTD solutions, a product of Lumerical solutions Inc., Vancouver, Canada [17], was used to perform the electromagnetic simulations in this work. The impact of particle size and spike number on peak wavelength was studied quantitatively. Result: By altering the particle size and amount of spikes, we were able to detect a hot zone around nanostar. For Au nanostar, the peak wavelength for nanostar varies from visible to near-infrared. When compared to a nanosphere of the same dimension, the shift seen in nanostar is substantially higher, making it more suitable for biosensing applications. When the refractive index of the surrounding medium is increased, a red shift in peak wavelength is noticed, forming the basis for a plasmonic refractive index sensor. Aside from having a higher sensitivity, nanostar has a twofold hot spot system due to their unique surfaces. There is no evidence of spike aggregation in the near field pattern. As a result, it is thought to be a better nanostructure for biosensing applications. Conclusion: The LSPR and field enhancement for Au nanosphere and Nanostar were investigated using the FDTD method. The nanosphere's peak wavelength is in visible region, whereas the nanostar's range extends from visible to near-infrared, depending on the size and number of spikes. At 517 nm, the enhancement factor for a nanosphere was 102, but at 1282 nm, the enhancement factor for a nanostar with six spikes was 108.

Design of a highly efficient n-CdS/p-AgGaTe2/p+-SnS double-heterojunction thin film solar cell

In this article, AgGaTe2-based n-CdS/p-AgGaTe2/p + -SnS double-heterojunction solar cells have been designed and explored utilizing a solar cell capacitance simulator (SCAPS-1D). This design manifested n-type CdS and p + -type SnS as window and back surface field (BSF) layer, respectively with the AgGaTe2 absorber. The major contributing parameters of these layers such as thickness, doping concentration level, and bulk flaws have been adjusted to reach the optimum computation. This introduced n-CdS/p-AgGaTe2/p + -SnS double-heterostructure solar cell demonstrates the significant power conversion efficiency (PCE) of 32.48% with the open circuit voltage, VOC of 0.96 V, short circuit current, JSC of 38.64 mA cm−2, and the Fill factor, FF of 87.31%. This remarkable efficiency is originated by the formation of a higher built-in potential at the p-AgGaTe2/p + -SnS heterostructure and a decrease in the surface recombination velocity brought on by the SnS BSF layer. This computational study demonstrates the potential of AgGaTe2 as an absorber and SnS as a BSF layer, and pave the way for the AgGaTe2-based experimental research in the era of solar cells.

A Machine Learning Correction Model of the Winter Clear-Sky Temperature Bias over the Arctic Sea Ice in Atmospheric Reanalyses

Abstract Atmospheric reanalyses are widely used to estimate the past atmospheric near-surface state over sea ice. They provide boundary conditions for sea ice and ocean numerical simulations and relevant information for studying polar variability and anthropogenic climate change. Previous research revealed the existence of large near-surface temperature biases (mostly warm) over the Arctic sea ice in the current generation of atmospheric reanalyses, which is linked to a poor representation of the snow over the sea ice and the stably stratified boundary layer in the forecast models used to produce the reanalyses. These errors can compromise the employment of reanalysis products in support of polar research. Here, we train a fully connected neural network that learns from remote sensing infrared temperature observations to correct the existing generation of uncoupled atmospheric reanalyses (ERA5, JRA-55) based on a set of sea ice and atmospheric predictors, which are themselves reanalysis products. The advantages of the proposed correction scheme over previous calibration attempts are the consideration of the synoptic weather and cloud state, compatibility of the predictors with the mechanism responsible for the bias, and a self-emerging seasonality and multidecadal trend consistent with the declining sea ice state in the Arctic. The correction leads on average to a 27% temperature bias reduction for ERA5 and 7% for JRA-55 if compared to independent in situ observations from the MOSAiC campaign (respectively, 32% and 10% under clear-sky conditions). These improvements can be beneficial for forced sea ice and ocean simulations, which rely on reanalyses surface fields as boundary conditions. Significance Statement This study illustrates a novel method based on machine learning for reducing the systematic surface temperature errors that characterize multiple atmospheric reanalyses in sea ice–covered regions of the Arctic under clear-sky conditions. The correction applied to the temperature field is consistent with the local weather and the sea ice and snow conditions, meaning that it responds to seasonal changes in sea ice cover as well as to its long-term decline due to global warming. The corrected reanalysis temperature can be employed to support polar research activities, and in particular to better simulate the evolution of the interacting sea ice and ocean system within numerical models.

Effect of Eddy Current for Photovoltaic Module on Lightning-Induced Overvoltage Caused by Electromagnetic Coupling

Lightning electromagnetic field will induce a high voltage on the photovoltaic (PV) farm and also generate the eddy current. To study the effect of eddy current inside a PV module, the mechanism of the eddy current is elucidated. The density of eddy current is derived and it is solved by the method of moments. The eddy current produces a magnetic field to weaken the original field, which can reduce the lightning-induced voltage. The eddy current is mainly distributed on the outside surface of both aluminum-back surface field solar cells and aluminum foil. Moreover, the lightning transient of a PV array is computed. It is concluded that the PV backsheet cored with aluminum foil can greatly reduce the differential-mode-induced voltage of PV module. Several crucial factors, including foil material, foil thickness, and the distance to solar cells, are discussed. In order to minimize the induced voltages of PV modules, the PV module with aluminum foil on backsheet is proposed and the suitable range of the foil thickness is determined.