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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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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An aerosol of nanoparticles forms a Knudsen layer when diffusing in a Brownian fashion toward a solid wall. More specifically, the particle number density in the gas by the wall approaches a nonzero value proportional to the flux. An approximate theory for the coefficient of proportionality as a function of the particle sticking probability at the wall and the drift velocity normal to the wall is compared to Langevin particle simulations. The results are used to formulate a boundary condition that enables accurate advection-diffusion simulations of nanoparticle-aerosol transport. © 2009 American Institute of Physics.

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Particle contamination is analyzed for a reticle in the inner pod of a carrier with particular emphasis on the effect of raising the cover of the inner pod before removing the reticle from the carrier at atmospheric pressure (not low pressure). Two mechanisms for particle transport into the gap between the base plate and the reticle are considered: injection and advection-diffusion. It is shown that injection is not an important mechanism but that advection-diffusion transport can carry particles deeply into the gap, where they can deposit on the reticle surface. Closed-form expressions are presented for the transmission probability that particles at the reticle edge are transported inward past the exclusion zone around the reticle perimeter. The gas flow in the gap that occurs during cover-raising is found by numerical simulation, and the closed-form expressions are applied to determine the probability of contamination for different cover-raising scenarios.

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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