Molecular Flow Region Research Articles

Controlling electrothermal behavior of Metal–Carbon hybrid wire in free molecular flow region

We investigated the heat loss of the metal wire to the gases in the free molecular region, whose pressure is below 10−3 Pa. The heat transfer characteristics at the interface between the metal surface and the gases are only accessible when the conductional heat loss along the wire is comparable to or less than 100 nW/K. Unfortunately, such an infinitesimal heat flow is not controllable from typical metal wire. For this reason, we have synthesized a new material, metal-carbon hybrid wire (MCHW). In the free molecular flow region, the resistance of MCHW is inversely proportional to the pressure (P), R∼1/P, regardless of gas species, which contradicts the gas-dependent heat loss theory. At a pressure <1 × 10−4 Pa, we observe a deviation from reciprocal linearity attributed to a growing radiational heat loss. Our results realize the thermal conductive sensing of the pressure below 10−5 Pa, which has been unprecedented.

Error factors in precise thermal conductivity measurement using 3ω method for wire samples

In designing thermoelectric and heat transfer devices on the micrometer scale, the accurate thermal conductivity measurement is very important, and a variety of measurement methods have been developed so far. Among them, the 3ω method is one of the best for conductive wires because it can directly measure thermal conductivity without measuring density or specific heat, and also in the same direction as electrical or thermoelectric property. However, previous studies have not sufficiently considered the effects of ambient pressure and the conductive adhesive used to attach the sample to the electrode, which may hinder accurate measurement. In this study, using a thin gold wire as a test sample, the influence of ambient pressure and the length of conductive adhesive along the sample has been investigated quantitatively as major factors of systematic errors in the 3ω method. When the pressure was increased in the transition flow region, the measured apparent thermal conductivity increased. An analytical model for the low-pressure gas heat conduction is proposed to quantitatively explain the pressure dependence. The measured value also increased when the length of the conductive adhesive exceeded 20% of the sample length. This work has revealed that the ambient should be evacuated to the molecular flow region and the length of conductive adhesive be less than 20% of the sample length. The guidelines proposed here will help researchers in various fields to more accurately determine the thermal conductivity of micrometer-scale wires.

Численный анализ динамики молекулярного газа при импульсной лазерной абляции

The evaporation of a molecular gas with rotational degrees of freedom caused by the action of a pulsed nanosecond laser (pulsed laser ablation) of moderate intensity is considered. Model kinetic equations that account for the exchange of translational and rotational energies using a two-temperature model are used to account for the influence of internal energy on the vapor-gas cloud dynamics. Rykov equations (R-model) are integrated when modeling the flow of a diatomic gas, and a generalization of the Bhatnagar-Gross-Krook (BGK) equation for a molecular gas is used to calculate the flow of nonlinear molecules with a number of rotational degrees of freedom equal to three. Taking into account the influence of internal energy on the gas flow is realized by relaxation terms approximating the collision integral as a sum of elastic and inelastic collisions. Since in the model kinetic equations the collision frequency does not depend on the velocities, and the influence of internal energy is taken into account only due to temperature changes, it is necessary to compare with more realistic approaches, which include, for example, the method of direct simulation Monte Carlo (DSMC). The comparison shows that the change in the average temperature over time and the vapor-gas cloud parameters (density and temperature), obtained by the solution of the kinetic equations and the DSMC method, are close. Calculations of the problem of pulsed laser ablation by direct integration of kinetic equations are carried out by the method of discrete ordinates and are a difficult computational problem, which is associated with discontinuous boundary conditions, the presence of both continuum regions and free molecular flow regions in the solution, as well as the need to calculate the vapor-gas cloud dynamics for a large time interval. To reduce computational costs, grid adaptation in physical and velocity spaces is used.

Development of a calculation method of the main parameters of the multistage turbomolecular pump

We developed a calculation method of the pumping parameters of the molecular stage of the turbomolecular vacuum pump (TMP) operating in the molecular flow region. Also, the authors developed the calculation method of the main parameters of the multistage TMP for the providing the main pumping parameters including ultimate pressure, pumping speed, compression ratio. As a result of calculation, the we got the performance curve of the multistage TMP.

Coupled Model of Heat and Mass Balance for Droplet Growth in Wet Steam Non-Equilibrium Homogeneous Condensation Flow

Because of the complexity of wet steam two-phase condensation flow, many problems remain to be solved. The important part of condensation theory—the calculation of the water droplet growth model in the transition zone—is not ideal; thus, it is necessary to develop a water droplet growth model with full-scale range. On the basis of the heat and mass transfer equilibrium in droplet growth, a coupled model of heat and mass balance for droplet growth is proposed. To verify the accuracy of this model, the differences and applicable ranges of various models were analysed using the experimental data of Peters and Meyer and two widely used models. In the free molecular flow region, the heat and mass balance model coincides with the Young low-pressure correction model. In the transition region, the heat and mass balance model agrees well with the experimental values of Peters and Meyer. In the continuous flow region, the heat and mass balance model coincides with the Gyarmathy model. Therefore, the heat and mass balance model can be used to accurately describe the growth process of water droplets in the arbitrary range of Knudsen numbers.

Simulation of microscale gas flow in heterogeneous porous media based on the lattice Boltzmann method

A microscale multi-relaxation-time lattice Boltzmann model with the regularization procedure is adopted to simulate gas flow in different porous media. The diffuse reflection boundary condition is used to deal with the random solid boundaries. Because of the complex geometry of the pores, the characteristic length is no longer a constant but a function of the pore locations for the porous media. A rational method is proposed to obtain the local characteristic lengths of the porous media for the microscale gas flow simulations. The simulation results show that gas flow characteristics in different flow regions are notably different. In the continuum flow region and slip flow region, the gas flow abilities in different pores are quite different. The effect of heterogeneity of the porous media on gas velocity distribution is very obvious. As the Knudsen number increases, the differences of gas flow abilities in different pores decrease. For gas flow in the strong transition flow region and free molecular flow region, the gas flow abilities in small pores are similar to those in large pores and the effect of heterogeneity becomes small. Such phenomena are mainly caused by the different gas flow mechanisms in different flow regions. In addition, two commonly used apparent permeability calculation models are evaluated by the simulation results and a better coefficient for the Klinkenberg model is proposed according to the simulation results.

Determination of Optimum Non-Slender Bodies of Revolution having Minimum Drag in Free Molecular Flow

The problem of determining the body of revolution having minimum drag has been considered in the free molecular flow region under given integral constraints and in combination with the calculus of variations. It has been shown that for a given surface area or volume, the optimum shape is sharp nosed if diameter is prescribed and it is flat nosed if the length is prescribed. When the volume and thickness are known the optimum shape has cusp at the origin whereas if surface area and diameter are given the optimum body shape is independent of the value of k, a parameter dependent upon the temperature ratio and the speed ratio.

Conductance Characteristics of Hydrogen Isotopes between Viscous and Molecular Flow Regions in Spherical Pellet Packed-Beds at 77.4 K

We have been studying the dynamic behavior of hydrogen isotopes flowing between viscous and molecular regions in an adsorbent packed-bed column, for the purpose of developing a pressure swing adsorption (PSA) process system for hydrogen isotope separation. This PSA system consists of adsorption, evacuating desorption and hydrogen replenishing processes. The kinetics in the adsorption process has been becoming to be predictable in theoretical simulation based on experimental results, but it is difficult as yet to simulate the dynamic behaviors in evaluating and replenishing processes because of the complicated geometry of passages in a packed-bed and the change of gas flow patterns between viscous and molecular regions depending on not only the pressure but also the dimension of passages. In the dynamics, the important factor should be known is the mass flow conductance in pellet packed-bed. In this work, we carried out the experiment for examining the dependence of the conductance on the diameter of particles packed in a column, since the geometrical and dimensional conditions of passages are affected by the size of packing pellets. From the experimental result and its analysis, we clarified the pressure and particle-size dependences of the conductance of hydrogen isotopes in spherical pellet packed-beds.

터보분자펌프(TMP) 배기속도 측정에 관한 고찰

터보분자펌프(TMP)의 특성평가는 ISO, PNEUROP, DIN, JIS, AVS 등 세계 여러 나라의 표준제정기구에서 제정한 국제규격에 그 근거를 두고 있다. 한국표준과학연구원에서는 이러한 국제규격에 기반을 둔 터보분자펌프의 특성평가시스템을 자체 설계/제작하여 그 신뢰성을 확인하기 위해 개발품 및 상용품의 평가에 주력하고 있다. 터보분자펌프의 배기속도 측정방법으로서 기체흐름 영역에 따른 throughput method와 orifice method를 적용하고 있으나 측정게이지, 유량계 및 orifice conductance의 불확도 등 실질적으로 정확한 배기속도를 제시하기 위한 조건들의 제약 때문에 많은 측정오차를 포함하고 있다고 볼 수 있다. 이러한 배기속도의 측정오차를 줄이기 위한 하나의 고찰로서 본 논문에서는 <TEX>$10^{-1}$</TEX> Pa-L/s 영역까지의 유량 주입범위를 가지는 기 구축된 정적법을 이용한 유량주입에 기반을 둔 throughput method를 이용하여 1000 L/s TMP의 측정 능력을 검증하고자 한다. 또한 분자류 영역인 orifice method를 사용할 경우 고진공영역, 미세유량 주입영역으로 진입할수록 커질 수밖에 없는 배기속도 측정 불확도를 최소화시키기 위해 검증된 유량을 이용한 conductance 값을 제시하여, 기 언급한 두 가지 배기 속도 측정 방법의 연속성을 유지하기 위한 실험적인 방법론을 제기하고자 한다. Methods of the characteristics evaluation of turbo-molecular pumps (TMP) are well-defined in the international measurement standards such as ISO, PNEUROP, DIN, JIS, and AVS. The Vacuum Center in the Korea Research Institute of Standards and Science (KRISS) has recently designed, constructed, and established the integrated characteristics evaluation system of TMPs based on the international documents by continuously pursuing and acquiring the reliable international credibility through measurement perfection. The measurement of TMP pumping speed is normally performed with the throughput and orifice methods dependent on the mass flow regions. However, in the UHV range of the molecular flow region, the high uncertainties of the gauges, mass flow rates, and conductance are too critical to precisely accumulate reliable data. In order to solve the uncertainty problems of pumping speeds in the UHV range, we introduced a SRG with 1% accuracy and a constant volume flow meter (CVFM) to measure the finite mass flow rates down to <TEX>$10^{-1}$</TEX> Pa-L/s with 3% uncertainty for the throughput method. In this way we have performed the measurement of pumping speed down to <TEX>$10^{-4}$</TEX> Pa with an uncertainty of less than 6% for a 1000 L/s TMP. In this article we suggest that the CVFM has an ability to measure the conductance of the orifice experimentally with flowing the known mass through the orifice chambers, so that we may overcome the discontinuity problem encountering during introducing two measurement methods in one pumping speed evaluation sequence.

Compensation of Thermal Transpiration Effect for Pressure Measurements by Capacitance Diaphragm Gauge

The thermal transpiration effect shown in intermediate flow and molecular flow regions influences the sensitivity of a capacitance diaphragm gauge (CDG) with a temperature controlled sensor head. This apparent change in the sensitivity of CDG owing to the thermal transpiration effect has to be compensated for precise pressure measurements in the range of lower than 150 Pa. In this study, the method and the uncertainty of the compensation are reported. Seven types of equations for the thermal transpiration effect were compared with the calibration results of high accuracy CDGs by the static expansion system. Takaishi-Sensui equation, Miller equation, and Setina equation show good agreement with the calibration results. The calibration results of CDGs also show that increasing the temperature of the vacuum chamber from 22.5°C to 26.0°C caused decreasing the sensitivity of CDGs by the thermal transpiration effect. The magnitude of the decrease in the sensitivity was from 0.09% for 10 Pa to 0.5% for 0.1 Pa. Such apparent changes in the sensitivity owing to the thermal transpiration effect could be compensated within 0.2% by Takaishi-Sensui equation using parameters quoted from the catalog and the literature values. In addition, this deviation could be reduced to less than 0.1% by fitting Takaishi-Sensui equation using the parameter c or the sensor temperature T2.

An Approximate Equation to the Transmission Probabilities of Conical Tubes

The acurate transmission probabilities in the molecular flow region for conical tubes of various lengths and angles were calculated by solving Clausingintegral equation (IE). An approxmate equationtothe results based on the expression proposed by Füstöss has been derived. The agreementis within 5% of the exact valuesin the whole region.

Conditions for Homogeneous and Rapid Deposition of Si Film on Semiconductor Wafers

The paper investigates the method of improving deposition rate in semiconductor deposition process, while maintaining film thickness uniformity and step coverage in a vertical LPCVD (Low-Pressure Chemical Vapor Deposition) system. In general increasing pressure improves deposition rate, but it decreases uniformity of thickness. The result of experiment and the numerical simulation showed that the non-uniformity of film thickness in high-pressure condition can be improved by controlling flow patterns in the space between wafers. In the molecular flow region (low pressure), the deposition rate and the step coverage were not influenced by the source gas flow rate. In the viscous flow region (high pressure), the step coverage can be improved by increasing source gas flow rate. For the flow the nozzle design and exhaust port location are important. Installation of rings outside of wafers is also effective for the improvement of thickness uniformity.

Sensitivity of Micro Cantilever Mass Sensor Transduced by PZT Film

Piezoelectric thin film transduced micro resonator offers competitive potential applications in mass sensing technology because of its low driving-voltage, self-actuation self-sensation capability and better impedance-matching with electronics. In this paper, the authors fabricated PZT cantilevers with different geometries and PZT thicknesses. Then the authors investigated the essential aspects of the PZT cantilever for mass-detection sensitivity from the viewpoint of mechanical quality factor of the cantilever and piezoelectric induced output of the PZT film. It was found that the mass-detection sensitivity of the cantilever was improved at thicker PZT film under atmospheric conditions by taking advantage of quality factor. The sensitivity can be further improved several times when pressure was reduced into the molecular flow region and the intrinsic region. For a given material properties and structural layer thickness, the cantilever with thicker PZT film was expected to exhibit high open circuit voltage output, while the cantilever with thinner PZT film was expected to show high piezoelectric charge output. In addition, the residual stress of PZT film was found decreased at thicker film. The effects of residual stress in PZT film on cantilever's sensitivity were therefore discussed in this paper.

Energy Dissipation Mechanisms in Lead Zirconate Titanate Thin Film Transduced Micro Cantilevers

A high quality factor (Q-factor) is most desirable for resonant mass sensors because their sensitivity greatly depends on the detectable frequency shift after mass adsorption. The authors fabricated lead zirconate titanate (PZT) thin film transduced micro cantilevers and studied the energy dissipation mechanisms to better understand the essential aspects affecting the Q-factor. It was found that energy dissipation induced by the multi-layered device structure and the PZT thin film was noteworthy even under atmospheric pressure conditions. The effects of the PZT film on the energy dissipation became dominant under reduced pressure. Accordingly, the Q-factors of cantilevers without PZT film became larger than those with PZT film when pressure was reduced into the molecular flow region. The single-layered SiO2 cantilever exhibited the largest intrinsic Q-factor. The electro-mechanical conversion in the PZT film and the thermoelastic damping caused by the property difference between each layer contributed significantly to the energy dissipation.

Flying characteristics in the free molecular region (influence of accommodation coefficients)

To examine molecular gas film lubrication (MGL) characteristics for spacings of several nanometers, the free molecular MGL equation, which assumes that the flow in the lubrication region is the free molecular flow and involves the Poiseuille flow rate and the shear stress coefficient for the free molecular flow region with surface accommodation coefficients as parameters, is established. The usefulness of the free molecular MGL equation for the spacings of less than several nanometers is shown by comparing with the numerically calculated characteristics of flying head sliders using the conventional expression of the MGL equation with accommodation coefficients of running disk and slider, α0 and α1, as parameters. The static pressure generation is found to depend only on the accommodation coefficient of the running disk in the free molecular region.

원판형 드래그펌프 회전자와 고정자 사이의 간극이 성능에 미치는 영향

The pumping characteristics of a single-stage disk-type drag pump (DTDP) are calculated for the variation of the vertical clearance between a rotor and stator by the three-dimensional direct simulation Monte Carlo (DSMC) method. The gas flow mainly belongs to the molecular transition flow region. Spiral channels of a DTDP are cut on the both the upper and lower sides of a rotating disk, but a stationary disk is planar. The interaction between molecules is described by the variable hard-sphere model. The no time counter method is used as a collision sampling technique. The vertical clearance has a significant effect on the pumping performance. Experiments are performed under the outlet pressure range of 0.4∼533 Pa. When the numerical results are compared with the experimental data, the numerical results agree well quantitatively

A study on the pumping performance of the disk-type drag pumps for spiral channel in rarefied gas flow

The pumping characteristics of a single-stage disk-type drag pump (DTDP) are calculated for the variation of the vertical clearance between a rotor and stator by the three-dimensional direct simulation Monte Carlo method. The gas flow mainly belongs to the molecular transition flow region. Spiral channels of a DTDP are cut on both the upper and lower sides of rotating disks, but the stationary disks are planar. The interaction between molecules is described by the variable hard-sphere model. The no-time counter method is used as a collision sampling technique. As a consequence of results, the vertical clearance between a rotor and stator has a significant effect on the pumping performance. Experiments are performed under the outlet pressure range of 0.4–533 Pa. When the numerical results are compared to the experimental data, the numerical results agree well qualitatively.

The properties of B–Sb thin films prepared by molecular flow region PVD process

The present paper is the first description on the electrical and thermoelectric properties of amorphous PVD B 12Sb 2 films prepared using the reaction of decaborane gas with evaporated antimony gas on Si (1900 Å) / SiO x (3700 Å) / Si (100) (625 μm) substrate at the temperature 350°C. Ohmic metals contacts of the film were examined by making evaporated Al, followed by annealing at 200°C. The comparatively high mobility of ∼100 cm 2/V s and high thermoelectric figures-of-merit of ∼10 −4/K were confirmed.

Thermoelectric properties of B12Sb2 films prepared by molecular flow region PVD process

Thermoelectric properties of B12Sb2 films prepared by molecular flow region PVD process

Direct simulation of rarefied gas flows in rotating spiral channels

The pumping characteristics of a two-stage disk-type drag pump from the free molecular flow region to the slip flow region are calculated by the direct simulation Monte Carlo method. Spiral channels are cut on both upper and lower sides of rotating disks. For the molecular collision kinetics, the variable hard-sphere molecular model with the no time counter technique is employed. The Borgnakke–Larsen phenomenological model is adopted for calculation of the rotational energy exchange between the colliding molecules. Experiments are performed under the outlet pressure range of 0.4–526 Pa. Numerical results show good quantitative agreement with the experimental data.