Publications

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An analysis is presented of a method to protect the reticle (mask) in an extreme ultraviolet (EUV) mask inspection tool using a showerhead plenum to provide a continuous flow of clean gas over the surface of a reticle. The reticle is suspended in an inverted fashion (face down) within a stage/holder that moves back and forth over the showerhead plenum as the reticle is inspected. It is essential that no particles of 10-nm diameter or larger be deposited on the reticle during inspection. Particles can originate from multiple sources in the system, and mask protection from each source is explicitly analyzed. The showerhead plate has an internal plenum with a solid conical wall isolating the aperture. The upper and lower surfaces of the plate are thin flat sheets of porous-metal material. These porous sheets form the top and bottom showerheads that supply the region between the showerhead plate and the reticle and the region between the conical aperture and the Optics Zone box with continuous flows of clean gas. The model studies show that the top showerhead provides robust reticle protection from particles of 10-nm diameter or larger originating from the Reticle Zone and from plenum surfaces contaminated by exposure to the Reticle Zone. Protection is achieved with negligible effect on EUV transmission. The bottom showerhead efficiently protects the reticle from nanoscale particles originating from the Optics Zone. With similar mass flow rates from the two showerheads, this system provides efficient protection even when a significant overpressure exists between the Optics Zone and the Reticle Zone. Performance is insensitive to the fraction of incident particles that sticks to walls, the accommodation coefficient, the aperture geometry, and the gas pressure. The showerheads also protect the aperture (and therefore the Optics Zone) during mask loading and unloading. Commercially available porous-metal media have properties suitable for these showerheads at the required flow rates. The benefits of the approach compared to a conceptual EUV pellicle are described.

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Moving-boundary algorithms for the Direct Simulation Monte Carlo (DSMC) method are investigated for a microbeam that moves toward and away from a parallel substrate. The simpler but analogous one-dimensional situation of a piston moving between two parallel walls is investigated using two moving-boundary algorithms. In the first, molecules are reflected rigorously from the moving piston by performing the reflections in the piston frame of reference. In the second, molecules are reflected approximately from the moving piston by moving the piston and subsequently moving all molecules and reflecting them from the moving piston at its new or old position. © 2011 American Institute of Physics.

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An experimental apparatus has been developed to determine thermal accommodation coefficients for a variety of gas-surface combinations. Results are obtained primarily through measurement of the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Measured heat-flux data are used in a formula based on Direct Simulation Monte Carlo (DSMC) simulations to determine the coefficients. The assembly also features a complementary capability for measuring the variation in gas density between the plates using electron-beam fluorescence. Surface materials examined include 304 stainless steel, gold, aluminum, platinum, silicon, silicon nitride, and polysilicon. Effects of gas composition, surface roughness, and surface contamination have been investigated with this system; the behavior of gas mixtures has also been explored. Without special cleaning procedures, thermal accommodation coefficients for most materials and surface finishes were determined to be near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Surface cleaning by in situ argon-plasma treatment reduced coefficient values by up to 0.10 for helium and by ∼0.05 for nitrogen and argon. Results for both single-species and gas-mixture experiments compare favorably to DSMC simulations. © 2011 American Institute of Physics.

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Thermal accommodation coefficients have been derived for a variety of gas-surface combinations using an experimental apparatus developed to measure the pressure dependence of the conductive heat flux between parallel plates at unequal temperature separated by a gas-filled gap. The heat flux is inferred from temperature-difference measurements across the plates in a configuration where the plate temperatures are set with two carefully controlled thermal baths. Temperature-controlled shrouds provide for environmental isolation of the opposing test plates. Since the measured temperature differences in these experiments are very small (typically 0.3 C or less over the entire pressure range), high-precision thermistors are used to acquire the requisite temperature data. High-precision components have also been utilized on the other control and measurement subsystems in this apparatus, including system pressure, gas flow rate, plate alignment, and plate positions. The apparatus also includes the capability for in situ plasma cleaning of the installed test plates. Measured heat-flux results are used in a formula based on Direct Simulation Monte Carlo (DSMC) code calculations to determine the thermal accommodation coefficients. Thermal accommodation coefficients have been determined for three different gases (argon, nitrogen, helium) in contact with various surfaces. Materials include metals and alloys such as aluminum, gold, platinum, and 304 stainless steel. A number of materials important to fabrication of Micro Electro Mechanical Systems (MEMS) devices have also been examined. For most surfaces, coefficient values are near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Only slight differences in accommodation as a function of surface roughness have been seen. Surface contamination appears to have a more significant effect: argon plasma treatment has been observed to reduce thermal accommodation by as much as 0.10 for helium. Mixtures of argon and helium have also been examined, and the results have been compared to DSMC simulations incorporating thermal-accommodation values from single-species experiments.

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The convergence rate of a new direct simulation Monte Carlo (DSMC) method, termed 'sophisticated DSMC', is investigated for one-dimensional Fourier flow. An argon-like hard-sphere gas at 273.15K and 266.644Pa is confined between two parallel, fully accommodating walls 1mm apart that have unequal temperatures. The simulations are performed using a one-dimensional implementation of the sophisticated DSMC algorithm. In harmony with previous work, the primary convergence metric studied is the ratio of the DSMC-calculated thermal conductivity to its corresponding infinite-approximation Chapman-Enskog theoretical value. As discretization errors are reduced, the sophisticated DSMC algorithm is shown to approach the theoretical values to high precision. The convergence behavior of sophisticated DSMC is compared to that of original DSMC. The convergence of the new algorithm in a three-dimensional implementation is also characterized. Implementations using transient adaptive sub-cells and virtual sub-cells are compared. The new algorithm is shown to significantly reduce the computational resources required for a DSMC simulation to achieve a particular level of accuracy, thus improving the efficiency of the method by a factor of 2.

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The convergence behavior of the Direct Simulation Monte Carlo (DSMC) method is investigated for transient flows. Two types of flows are considered: a Couette-like flow, in which an initial velocity profile decays in time, and a Fourier-like flow, in which an initial temperature profile decays in time. DSMC results are presented for hard-sphere argon with Knudsen numbers in the range 0.01-0.4. Low-Knudsen-number DSMC results are compared with Navier-Stokes results. The DSMC discretization errors from finite time step and finite cell size (in the limit of infinite number of computational molecules per cell) are compared with the predictions of Green-Kubo theory for conditions in this regime.

An experimental apparatus is described that measures gas-surface thermal accommodation coefficients from the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Heat flux between the plates is inferred from measurements of temperature drop between the plate surface and an adjacent temperature-controlled water bath. Thermal accommodation coefficients are determined from the pressure dependence of the heat flux at a fixed plate separation. The apparatus is designed to conduct tests with a variety of gases in contact with interchangeable, well-characterized surfaces of various materials (e.g., metals, ceramics, semiconductors) with various surface finishes (e.g., smooth, rough). Experiments are reported for three gases (argon, nitrogen, and helium) in contact with pairs of 304 stainless steel plates prepared with one of two finishes: lathe-machined or mirror-polished. For argon and nitrogen, the measured accommodation coefficients for machined and polished plates are near unity and independent of finish to within experimental uncertainty. For helium, the accommodation coefficients are much lower and show a slight variation with surface roughness. Two different methods are used to determine the accommodation coefficient from experimental data: the Sherman-Lees formula and the GTR formula. These approaches yield values of 0.87 and 0.94 for argon, 0.80 and 0.86 for nitrogen, 0.36 and 0.38 for helium with the machined finish, and 0.40 and 0.42 for helium with the polished finish, respectively, with an uncertainty of ±0.02. The GTR values for argon and nitrogen are generally in better agreement with the results of other investigators than the Sherman-Lees values are, and both helium results are in reasonable agreement with values in the literature.

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Noncontinuum gas-phase heat transfer in two microscale geometries is investigated using two computational methods. The motivation is microscale thermal actuation produced by heating-induced expansion of a near-substrate microbeam in air. The first geometry involves a 1-μm microgap filled with gas and bounded by parallel solid slabs. The second geometry involves a heated I-shaped microbeam 2 μm from the adjacent substrate, with gas in between. Two computational methods are applied. The Navier-Stokes slip-jump (NSSJ) method uses continuum heat transfer in the gas, with temperature jumps at boundaries to treat noncontinuum effects. The Direct Simulation Monte Carlo (DSMC) method uses computational molecules to simulate noncontinuum gas behavior accurately. For the microgap, the heat-flux values from both methods are in good agreement for all pressures and accommodation coefficients. For the microbeam, there is comparably good agreement except for cases with low pressures and near-unity accommodation coefficients. The causes of this discrepancy are discussed. Copyright © 2005 by ASME.

A previously-developed experimental facility has been used to determine gas-surface thermal accommodation coefficients from the pressure dependence of the heat flux between parallel plates of similar material but different surface finish. Heat flux between the plates is inferred from measurements of temperature drop between the plate surface and an adjacent temperature-controlled water bath. Thermal accommodation measurements were determined from the pressure dependence of the heat flux for a fixed plate separation. Measurements of argon and nitrogen in contact with standard machined (lathed) or polished 304 stainless steel plates are indistinguishable within experimental uncertainty. Thus, the accommodation coefficient of 304 stainless steel with nitrogen and argon is estimated to be 0.80 {+-} 0.02 and 0.87 {+-} 0.02, respectively, independent of the surface roughness within the range likely to be encountered in engineering practice. Measurements of the accommodation of helium showed a slight variation with 304 stainless steel surface roughness: 0.36 {+-} 0.02 for a standard machine finish and 0.40 {+-} 0.02 for a polished finish. Planned tests with carbon-nanotube-coated plates will be performed when 304 stainless-steel blanks have been successfully coated.

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Modeling microscale heat transfer with the computational-heat-transfer code Calore is discussed. Microscale heat transfer problems differ from their macroscopic counterparts in that conductive heat transfer in both solid and gaseous materials may have important noncontinuum effects. In a solid material, three noncontinuum effects are considered: ballistic transport of phonons across a thin film, scattering of phonons from surface roughness at a gas-solid interface, and scattering of phonons from grain boundaries within the solid material. These processes are modeled for polycrystalline silicon, and the thermal-conductivity values predicted by these models are compared to experimental data. In a gaseous material, two noncontinuum effects are considered: ballistic transport of gas molecules across a thin gap and accommodation of gas molecules to solid conditions when reflecting from a solid surface. These processes are modeled for arbitrary gases by allowing the gas and solid temperatures across a gas-solid interface to differ: a finite heat transfer coefficient (contact conductance) is imposed at the gas-solid interface so that the temperature difference is proportional to the normal heat flux. In this approach, the behavior of gas in the bulk is not changed from behavior observed under macroscopic conditions. These models are implemented in Calore as user subroutines. The user subroutines reside within Sandia's Source Forge server, where they undergo version control and regression testing and are available to analysts needing these capabilities. A Calore simulation is presented that exercises these models for a heated microbeam separated from an ambient-temperature substrate by a thin gas-filled gap. Failure to use the noncontinuum heat transfer models for the solid and the gas causes the maximum temperature of the microbeam to be significantly underpredicted.

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The ability to detect Weapons of Mass Destruction biological agents rapidly and sensitively is vital to homeland security, spurring development of compact detection systems at Sandia and elsewhere. One such system is Sandia's microseparations-based pChemLab. Many bio-agents are serious health threats even at extremely low concentrations. Therefore, a universal challenge for detection systems is the efficient collection and selective transport of highly diffuse bio-agents against the enormous background of benign particles and species ever present in the ambient environment. We have investigated development of a ''front end'' system for the collection, preconcentration, and selective transport of aerosolized biological agents from dilute (1-10 active particles per liter of air) atmospheric samples, to ultimate concentrations of {approx}20 active particles per microliter of liquid, for interface with microfluidic-based analyses and detection systems. Our approach employs a Sandia-developed aerosol particle-focusing microseparator array to focus size-selected particles into a mating microimpinger array of open microfluidic transport channels. Upon collection (i.e., impingement, submergence, and liquid suspension), microfluidic dielectrophoretic particle concentrators and sorters can be employed to further concentrate and selectively transport bio-agent particles to the sample preparation stages of microfluidic analyses and detection systems. This report documents results in experimental testing, modeling and analysis, component design, and materials fabrication critical to establishing proof-of-principle for this collection ''front end''. Outstanding results have been achieved for the aerodynamic microseparator, and for the post-collection dielectrophoretic concentrator and sorter. Results have been obtained for the microimpinger, too, but issues of particle-trapping by surface tension in liquid surfaces have proven difficult. Subsequent particle submergence into liquid suspension for microfluidic transport has been demonstrated only inefficiently despite significant and varied effort. Importantly, the separate technologies whose development is described, (inertial microseparator, dielectrophoretic corduroy concentrator/sorter) should each, independently, prove greatly useful in a variety of additional applications.

A combined experimental/modeling study was conducted to better understand the critical role of gas-surface interactions in rarefied gas flows. An experimental chamber and supporting diagnostics were designed and assembled to allow simultaneous measurements of gas heat flux and inter-plate gas density profiles in an axisymmetric, parallel-plate geometry. Measurements of gas density profiles and heat flux are made under identical conditions, eliminating an important limitation of earlier studies. The use of in situ, electron-beam fluorescence is demonstrated as a means to measure gas density profiles although additional work is required to improve the accuracy of this technique. Heat flux is inferred from temperature-drop measurements using precision thermistors. The system can be operated with a variety of gases (monatomic, diatomic, polyatomic, mixtures) and carefully controlled, well-characterized surfaces of different types (metals, ceramics) and conditions (smooth, rough). The measurements reported here are for 304 stainless steel plates with a standard machined surface coupled with argon, helium, and nitrogen. The resulting heat-flux and gas-density-profile data are analyzed using analytic and computational models to show that a simple Maxwell gas-surface interaction model is adequate to represent all of the observations. Based on this analysis, thermal accommodation coefficients for 304 stainless steel coupled with argon, nitrogen, and helium are determined to be 0.88, 0.80, and 0.38, respectively, with an estimated uncertainty of {+-}0.02.

A general, approximate expression is described that can be used to predict the thermophoretic force on a free-molecular, motionless, spherical particle suspended in a quiescent gas with a temperature gradient. The thermophoretic force is equal to the product of an order-unity coefficient, the gas-phase translational heat flux, the particle cross-sectional area, and the inverse of the mean molecular speed. Numerical simulations are used to test the accuracy of this expression for monatomic gases, polyatomic gases, and mixtures thereof. Both continuum and noncontinuum conditions are examined; in particular, the effects of low pressure, wall proximity, and high heat flux are investigated. The direct simulation Monte Carlo (DSMC) method is used to calculate the local molecular velocity distribution, and the force-Green's-function method is used to calculate the thermophoretic force. The approximate expression is found to predict the calculated thermophoretic force to within 10% for all cases examined.

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An approach is presented to compute the force on a spherical particle in a rarefied flow of a monatomic gas. This approach relies on the development of a Green's function that describes the force on a spherical particle in a delta-function molecular velocity distribution function. The gas-surface interaction model in this development allows incomplete accommodation of energy and tangential momentum. The force from an arbitrary molecular velocity distribution is calculated by computing the moment of the force Green's function in the same way that other macroscopic variables are determined. Since the molecular velocity distribution function is directly determined in the DSMC method, the force Green's function approach can be implemented straightforwardly in DSMC codes. A similar approach yields the heat transfer to a spherical particle in a rarefied gas flow. The force Green's function is demonstrated by application to two problems. First, the drag force on a spherical particle at arbitrary temperature and moving at arbitrary velocity through an equilibrium motionless gas is found analytically and numerically. Second, the thermophoretic force on a motionless particle in a motionless gas with a heat flux is found analytically and numerically. Good agreement is observed in both situations.

A major cause of semiconductor yield degradation is contaminant particles that deposit on wafers while they reside in processing tools during integrated circuit manufacturing. This report presents numerical models for assessing particle transport and deposition in a parallel-plate geometry characteristic of a wide range of single-wafer processing tools: uniform downward flow exiting a perforated-plate showerhead separated by a gap from a circular wafer resting on a parallel susceptor. Particles are assumed to originate either upstream of the showerhead or from a specified position between the plates. The physical mechanisms controlling particle deposition and transport (inertia, diffusion, fluid drag, and external forces) are reviewed, with an emphasis on conditions encountered in semiconductor process tools (i.e., sub-atmospheric pressures and submicron particles). Isothermal flow is assumed, although small temperature differences are allowed to drive particle thermophoresis. Numerical solutions of the flow field are presented which agree with an analytic, creeping-flow expression for Re < 4. Deposition is quantified by use of a particle collection efficiency, which is defined as the fraction of particles in the reactor that deposit on the wafer. Analytic expressions for collection efficiency are presented for the limiting case where external forces control deposition (i.e., neglecting particle diffusion and inertia). Deposition from simultaneous particle diffusion and external forces is analyzed by an Eulerian formulation; for creeping flow and particles released from a planar trap, the analysis yields an analytic, integral expression for particle deposition based on process and particle properties. Deposition from simultaneous particle inertia and external forces is analyzed by a Lagrangian formulation, which can describe inertia-enhanced deposition resulting from particle acceleration in the showerhead. An approximate analytic expression is derived for particle velocity at the showerhead exit as a function of showerhead geometry, flow rate, and gas and particle properties. The particle showerhead-exit velocity is next used as an initial condition for particle transport between the plates to determine whether the particle deposits on the wafer, as a function of shower-head-exit particle velocity, the plate separation, flow rate, and gas and particle properties. Based on the numerical analysis, recommendations of best practices are presented that should help tool operators and designers reduce particle deposition in real tools. These guidelines are not intended to replace detailed calculations, but to provide the user with a general feel for inherently-clean practices.

This report presents the results of an experimental study of the aerosol produced by the combustion of high-velocity molten-uranium droplets produced by the simultaneous heating and electromagnetic launch of uranium wires. These tests are intended to simulate the reduction of high-velocity fragments into aerosol in high-explosive detonations or reactor accidents involving nuclear materials. As reported earlier, the resulting aerosol consists mainly of web-like chain agglomerates. A condensation nucleus counter was used to investigate the decay of the total particle concentration due to coagulation and losses. Number size distributions based on mobility equivalent diameter obtained soon after launch with a Differential Mobility Particle Sizer showed lognormal distributions with an initial count median diameter (CMD) of 0.3 {mu}m and a geometric standard deviation, {sigma}{sub g} of about 2; the CMD was found to increase and {sigma}{sub g} decrease with time due to coagulation. Mass size distributions based on aerodynamic diameter were obtained for the first time with a Microorifice Uniform Deposit Impactor, which showed lognormal distributions with mass median aerodynamic diameters of about 0.5 {mu}m and an aerodynamic geometric standard deviation of about 2. Approximate methods for converting between number and mass distributions and between mobility and aerodynamic equivalent diameters are presented.

SEMATECH and the Department of Energy have established a Contamination Free Manufacturing Research Center (CFMRC) located at Sandia National Laboratories. One of the programs underway at the CFMRC is directed towards defect reduction in semiconductor process reactors by the application of computational modeling. The goal is to use fluid, thermal, plasma, and particle transport models to identify process conditions and tool designs that reduce the deposition rate of particles on wafers. The program is directed toward defect reduction in specific manufacturing tools, although some model development is undertaken when needed. The need to produce quantifiable improvements in tool defect performance requires the close cooperation among Sandia, universities, SEMATECH, SEMATECH member companies, and equipment manufacturers. Currently, both plasma (e.g., etch, PECVD) and nonplasma tools (e.g., LPCVD, rinse tanks) are being worked on under this program. In this paper the authors summarize their recent efforts to reduce particle deposition on wafers during plasma-based semiconductor manufacturing.

In past five years, Department 1510 has developed a state-of-the-art Aerosol Dynamics Laboratory (ADL). This report documents the current instrumentation and capabilities that exist in this laboratory. The ADL was developed from a variety of sources, with a primary contribution from Department 1510's Independent Research and Development program in aerosol dynamics. Current capabilities of the ADL include: (1) generation of calibration-quality monodisperse particles with diameters between 0.005 to 100 {mu}m, (2) real-time measurement of particle size distributions for particle diameters between 0.01 and 100 {mu}m, (3) in situ, real-time measurement of particle size distributions for particle diameters between 0.3 and 100 {mu}m, and (4) real-time measurement of particle charge distributions for particle diameters between 0.01 and 1.0 {mu}m. 14 refs., 5 figs.

Gravitational forces have been found to be an important factor in defining the particle collection efficiency curve of inertial impactors for large particles. In general it was found that if the parameter {cflx G} = gW/V{sub 0}{sup 2} (g is the gravitational acceleration, W is the nozzle diameter and V{sub 0} is the average fluid velocity at the nozzle throat) in greater than 10{sup {minus}3}, the efficiency curve would shift to lower particle sizes. No effect could be seen for lower values of {cflx G}. 1 ref., 1 fig., 1 tab.