Theoretical model of the helium zone plate microscope

Abstract

Neutral helium microscopy is a new technique currently under development. Its advantages are the low energy, charge neutrality, and inertness of the helium atoms, a potential large depth of field, and the fact that at thermal energies the helium atoms do not penetrate into any solid material. This opens the possibility, among others, for the creation of an instrument that can measure surface topology on the nanoscale, even on surfaces with high aspect ratios. One of the most promising designs for helium microscopy is the zone plate microscope. It consists of a supersonic expansion helium beam collimated by an aperture (skimmer) focused by a Fresnel zone plate onto a sample. The resolution is determined by the focal spot size, which depends on the size of the skimmer, the optics of the system, and the velocity spread of the beam through the chromatic aberrations of the zone plate. An important factor for the optics of the zone plate is the width of the outermost zone, corresponding to the smallest opening in the zone plate. The width of the outermost zone is fabrication limited to around 10 nm with present-day state-of-the-art technology. Due to the high ionization potential of neutral helium atoms, it is difficult to build efficient helium detectors. Therefore, it is crucial to optimize the microscope design to maximize the intensity for a given resolution and width of the outermost zone. Here we present an optimization model for the helium zone plate microscope. Assuming constant resolution and width of the outermost zone, we are able to reduce the problem to a two-variable problem (zone plate radius and object distance) and we show that for a given beam temperature and pressure, there is always a single intensity maximum. We compare our model with the highest-resolution zone plate focusing images published and show that the intensity can be increased seven times. Reducing the width of the outermost zone to 10 nm leads to an increase in intensity of more than 8000 times. Finally, we show that with present-day state-of-the-art detector technology (ionization efficiency $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), a resolution of the order of 10 nm is possible. In order to make this quantification, we have assumed a Lambertian reflecting surface and calculated the beam spot size that gives a signal 100 cts/s within a solid angle of 0.02 sr, following an existing helium microscope design.