Molecular Beam Sources Fabricated from Multichannel Arrays. III. The Exit Density Problem

Abstract

Although the theory of Giordmaine and Wang adequately predicts the centerline intensity of a molecular beam from a channel source, it is less successful in describing the angular distribution. This deficiency has been ascribed to a nonzero number density at the tube exit. The end conditions chosen by previous workers lead to angular distributions which fail to satisfy total flow and average cosine restrictions. A method of choosing the parameters of the linear density profile which satisfies these integral constraints is described. The computed angular distributions according to the theories utilizing different end conditions differ very little from each other, but represent a clear improvement over Giordmaine and Wang's angular distribution.

Performance predictions for a laser-intensified thermal beam for use in high-resolution focused-ion-beam instruments

“…The tube was implemented in the software by tracing the particles trough the tube assuming inelastic collisions with the walls following a cosinedistribution. The resulting angular distribution was verified against the theoretical prediction [16] and MonteCarlo simulations [26].…”

“…The collimation tube increases the flux density at the MOC entrance and also increases the lifetime of the source. For a heated tube with opening angle θ = r/L s the flux is given by [16] …”

“…The FIB source considered here, as the one of Kime et al [15], therefore uses a Knudsen cell as atomic source. In our case, the Knudsen cell is connected to a heated collimation tube [16,17] which increases the lifetime of the atomic reservoir by more than an order of magnitude and alters the velocity distribution such that even more atoms can be captured in the magneto-optical compressor (MOC). Fig.…”

Design and experimental validation of a compact collimated Knudsen source

“…Depending on the density in the Knudsen cell, interatomic collisions may play a role on the longitudinal (l) or transverse (d = 2 r) length scale of the tube. The importance of collisions is determined by the Knudsen number 4,8 which is defined as the ratio between the mean-free-path λ mf p and the relevant dimension x:…”

“…Such recirculating ovens have been constructed [5][6][7] but are reported to be difficult to operate 3 . A different, and less complex, approach is the use of a heated tube connected to the Knudsen cell [2][3][4]8 . Atoms that hit the wall of the tube are adsorped and, due to the high temperature, emitted again following a cosine angular distribution.…”