A method for constrained optimisation of the design of a scanning helium microscope

Abstract

We describe a method for obtaining the optimal design of a normal incidence Scanning Helium Microscope (SHeM). Scanning helium microscopy is a recently developed technique that uses low energy neutral helium atoms as a probe to image the surface of a sample without causing damage. After estimating the variation of source brightness with nozzle size and pressure, we perform a constrained optimisation to determine the optimal geometry of the instrument (i.e. the geometry that maximises intensity) for a given target resolution. For an instrument using a pinhole to form the helium microprobe, the source and atom optics are separable and Lagrange multipliers are used to obtain an analytic expression for the optimal parameters. For an instrument using a zone plate as the focal element, the whole optical system must be considered and a numerical approach has been applied. Unlike previous numerical methods for optimisation, our approach provides insight into the effect and significance of each instrumental parameter, enabling an intuitive understanding of effect of the SHeM geometry. We show that for an instrument with a working distance of 1 mm, a zone plate with a minimum feature size of 25 nm becomes the advantageous focussing element if the desired beam standard deviation is below about 300 nm.

Neutral Helium Microscopy (SHeM): A Review

“…Researchers often use these simplified expressions to determine the beam's intensity. Over the years, amongst several existing models, often the simpler ones have been favoured, (see for example, [68,69]) despite their not being backed by strong empirical measurements nor by strong theoretical support. In the following paragraphs we review a few popular intensity models from the different families described in Sec.…”

“…Third, the intensity used by Bergin in his helium microscope optimisation paper, published after the Bergen optimisation papers. This intensity uses DePonte et al's centre-line beam intensity (with a correction) [40,68]. This is a model of the second type, in which an empirical formula for the dependency between the virtual source radius and the speed ratio of the beam is used (and therefore an inverse dependency on the speed ratio is introduced).…”

Observation of diffraction contrast in scanning helium microscopy

“…We refer to varying z, while keeping the same point on the sample under the beam, as a z scan. A complication that arises when performing a z scan is that the size of the beam changes as the distance between the sample and the pinhole is varied 21,22 . The range of scattering angles that can be observed is therefore determined by both the available signal level and the largest acceptable illumination area of the helium beam, since resolution of a small feature would require a narrow helium beam.…”

Low-energy electron ionization mass spectrometer for efficient detection of low mass species

“…5 Many helium scattering experiments also require very high-efficiency helium detection in order to, for example, observe weak diffraction peaks 6 or to observe surface correlations using the small number of diffuse atoms that are quasi-elastically scattered. 7 Similarly, in the emerging field of helium microscopy, [8][9][10][11][12][13][14][15] narrow beams of helium are required for high resolution images, which, in turn, reduce the flux of helium dramatically, [16][17][18] again necessitating sensitive detection.…”