Off-axis multilayer zone plate with 16 nm × 28 nm focus for high-resolution X-ray beam induced current imaging

Using multilayer zone plates (MZPs) as two-dimensional optics, focal spot sizes of less than 10 nm can be achieved, as we show here with a focus of 8.4 nm × 9.6 nm, but the need for order-sorting apertures prohibits practical working distances. To overcome this issue, here an off-axis illumination of a circular MZP is introduced to trade off between working distance and focal spot size. By this, the working distance between order-sorting aperture and sample can be more than doubled. Exploiting a 2D focus of 16 nm × 28 nm, real-space 2D mapping of local electric fields and charge carrier recombination using X-ray beam induced current in a single InP nanowire is demonstrated. Simulations show that a dedicated off-axis MZP can reach sub-10 nm focusing combined with reasonable working distances and low background, which could be used for in operando imaging of composition, carrier collection and strain in nanostructured devices.

A high-accuracy complex-phase method of simulating X-ray propagation through a multi-lens system

The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X-ray waves through a multi-lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi-lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi-lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi-lens system.