Theoretical and experimental evaluation of aerodynamic lenses for producing particle beams of controlled dimensions and divergence

A particle beam is produced when a particle-laden gas expands through a nozzle into a vacuum. This work discusses a method of producing very narrow and highly collimated particle beams. The approach is to pass the particle-laden gas through a series of axisymmetric contractions and enlargements (so called aerodynamic lenses) before the nozzle expansion. Particles are confined closely to the axis alter passing through these lenses. Since particles close to the axis experience small radial drag forces, they stay close to the axis during nozzle expansion and therefore form a narrow particle beam downstream. The major effects that limit the minimum beam width are Brownian motion and lift forces on particles during nozzle expansion. Lift-force effects often occur for non-spherical particles and are often greater than Brownian-motion effects. A particle-beam-forming apparatus consisting of a variable number of lenses in series followed by an accelerating nozzle was developed for the application in a Particle Beam Mass Spectrometer (PBMS). This instrument is to measure ultrafine particles (0.01 {dollar}sim{dollar} 0.5 {dollar}murm m){dollar} in low pressure {dollar}(ge{dollar}0.1 torr) environments such as those in semiconductor processing equipment. The experimental evaluations showed that as more lenses were added the particle beam widths were reduced asymptotically to the minimum values. For spherical particles these minimum values are in good agreement with those predicted from a Brownian-motion model. For non-spherical particles these minimum widths are often much larger than the Brownian limit, which is consistent with theoretical predictions based on lift forces. A Low-Pressure Laser Particle Detector (LPLPD) using aerodynamic lenses was also developed and evaluated in this work. Because of its high particle counting efficiencies {dollar}(sim{dollar}100%) and small flow resistance, it is suitable for detecting particles in exhaust lines of semiconductor processing equipment. This work demonstrates that aerodynamic lenses are an effective means for separating particles from a carrier gas and confining them to the centerline of symmetric flows.