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

In an off-axis geometry, a circular multilayer zone disc is used to locally generate X-ray beam induced currents inside a single InP nanowire. This allows to spatially probe local electric fields at practical working distances and very low background signal.

the high-resolution stage of the GINIX instrument. The sample stage is motorized using piezo scanner by Physik Instrumente Karlsruhe (PI), the MZP stage by stickslip positioners by SmarAct (Oldenburg) for translations, and a piezo-driven Gimbal mount for rotations. For detailed information on the stability and scanning precision see (Osterhoff et al., 2017). The pinhole and the OSA were mounted on piezo scanners by SmarAct (Oldenburg). The diameter of the pinhole was 5.6 µm, the diameter of the OSA was 3.5 µm. The distance of the OSA relative to the focus was 0.44 mm.
At a distance of 5.1 m behind the sample the detector was positioned. A single photon counting Eiger 4m (Dectris Ltd., Switzerland) detector was used with 2068 × 2162 pixels with a pixel size of 75 µm.

P06-Nanoprobe setup
The experiment using the fully illuminated MZP was performed at the PtyNAMI instrument (Schropp et al., 2020) of the Hard X-ray Micro/Nano-Probe at the beamline P06, which is positioned at the PETRA III storage ring. The beamline uses a 2 m long undulator positioned at a distance of 97.5 m from the nanohutch where the experiment was preformed. The undulator beam was monochromatized using a Si (111) channel-cut monochromator to 15 keV. The monochromator is positioned at a distance of 59.1 m from the nanohutch. The distance of the CRLs to the nanohutch is 54 m.
Using the PtyNAMI instrument the pinhole, OSA, MZP and sample were mounted on piezo stages by SmarAct (Oldenburg). The diameter of the central stop was 6 µm, the diameter of the OSA was 3 µm. The distance of the OSA relative to the focus was 0.25 mm.
The diffraction patterns were recorded at a distance of 3.43 m relative to the sample using a single photon counting pixel detector (Pilatus 300k, Dectris Ltd. Switzerland).
The detector has 619 × 487 pixels and a pixel size of ∆ px = 172 µm.

Full Illuminated MZP
The probe of the full illuminated MZP was characterized using ptychography. The measurement was performed at the P06-Nanoprobe beamline (Schroer et al., 2016), as described in the manuscript. A scan was performed with 25 × 51 scan points and an illumination time per frame of 0.2 s. As a sample a Siemens star was used with a smallest feature size of 50 nm. The Siemens star was positioned at a distance of 70 µm relative to the focus. For the reconstruction the ptychography script of the beamline was used. The script is based on the ePIE algorithm (Maiden & Rodenburg, 2009).
In Fig. 1 the results of the ptychographic reconstruction are depicted. In (a) the absorption of the object is shown, in (b) the phase of the object and in (c) the probe in the object plane. The smallest features of the object are well resolved. Further sub-structures are visible in the center of the Siemens star. These sub-structures are not an artifact from the reconstruction process, but real and due to beam damage resulting from a previous experiment.

Off-Axis Illuminated MZP
The probe of the off-axis illuminated MZP was characterized using ptychography.
The measurement was performed at the P10-GINIX beamline (Kalbfleisch et al., 2011), as described in the manuscript. A scan was performed with 41 × 41 scan points and an illumination time per frame of 1.0 s. A lithographic test pattern with smallest structure size of 100 nm was used as a sample. The sample was positioned at a IUCr macros version 2.1.11: 2020/04/29 distance of 350 µm relative to the focus. The diameter of the beam in this plane was about 1.75 µm 2 . For reconstruction our own ptychographic script was used. The script is based on the ePIE algorithm (Maiden & Rodenburg, 2009). In Fig. 2 the results of the ptychographic reconstruction are depicted. In (a) the absorption of the object is shown, in (b) the phase of the object and in (c) the probe in the object plane.
The smallest features of the object are well resolved. The shape of the probe is quiet similar to the shape measured at the detector and is due to the relative large distance between focus and object.

Finite Differences Simulations
Simulations were performed to estimate the focusing properties of an MZP with the exact specifications as the one used in the experiments at the P10-GINIX instrument.
The parameters of the simulated MZP were: 0.92 mm focal length, 784 zones, first inner zone number 14 (equivalent to a diameter of 2.1 µm) 5 nm outermost zone width, 15.6 µm radial size, 2.4 µm optical thickness and a tilting angle of 2.5 mrad. The energy of the illumination was 13.8 keV. The simulations were based on a finite differences (FD) solver (Melchior & Salditt, 2017). To account for the circular shape of the MZP the simulations were performed in three dimensions. The numerical grid parameters were ∆ x,y = 1 nm and ∆ z = 10 nm for the lateral and the propagation directions, respectively. In Fig. 3 As described by (Simpson & Michette, 1984) for the case of round diffractive optics, focus side maxima increase the more zones in the center are not illuminated. Fig. 5 (a) shows the simulated focus of a MZP with the following parameters: photon energy 13.8 keV, focal length 0.92 mm, optical depth 2.5 µm, MZP diameter 16.5 µm, outer most layer width 5 nm, center stop diameter 8.24 µm. All layers are tilted according to the wedge geometry (Yan et al., 2014). Fig. 5(b) shows the focus of an off-axis MZP with the same off-axis gap and the same diameter as the simulated MZP shown in (a). The only difference between the simulated MZP in (a) and (b) is the outer most layer width which is in case of (b) only 2 nm. This is due to the requirement for the simulation that both optics should have the same NA. The simulation were performed using the FD algorithm. In case of (a) the propagation of the field was simulated in a radial coordinate system (Melchior & Salditt, 2017), propagation step size was 10 nm and the lateral grid size was 0.1 nm. In case of (b) an 2D Cartesian coordinate system was used to simulate the propagation of the off-axis geometry. The simulation grid sizes were the same as in (a). The normalized focus profiles from (a)  The large side maxima result in a reduced effective resolution of the focusing optic.
Additionally, also the FWHM of the main focus is slightly smaller for the case of the off-axis illuminated MZP. The intensity is normalized to the maximum intensity of the titled MZP. The focus was simulated using FD in a circular coordinate system (Melchior & Salditt, 2017).
The parameters of the simulated MZPs were: 0.92 mm focal length, 784 zones, 5 nm outermost zone width, 15.6 µm radial size, 2.5 µm optical thickness. The energy of the illumination was 13.8 keV. For the MZP in tilted geometry a tilting angle of 2.5 mrad was assumed. In Fig. 6(a,b) the intensity distributions of both focal points is shown with the same color scaling. The difference of the intensity of the focal spots is a factor of 2.9 as can be seen in the plotted focus profiles shown in Fig. 6(c). This demonstrates the improved focusing efficiency of a MZP based on the tilted geometry compared to a MZP in a flat geometry. MZP off-axis MZP NA 8.7 · 10 −3 8.7 · 10 −3 4.4 · 10 −3 8.7 · 10 −3 D CS 6 µm 12 µm

Flux dependence of the XBIC signal
In Fig.7 the maximum I XBIC is plotted against the photon flux Φ, where the expected linear relation can be observed. Theoretically, I XBIC can be estimated using the equation, I XBIC = qηp abs ΦS (x, y, z) , where q is the charge constant, η is the charge generation yield, p |ΦS(x,y,z)| is the x-ray absorption probability, and S (x, y, z) is the relative spatially dependent charge collection efficiency (Chayanun et al., 2019). The charge generation yield is the ratio between the energy of the x-rays, E, and the ionization energy of the semiconductor , so that η = E/ (Alig & Bloom, 1978). In the case of a very thin sample, p abs can be approximated from p abs = µd, where µ is the absorption coefficient, and d is the thickness of the sample. At the maximum I XBIC from the map, we can assume the maximum charge collection efficiency, and therefore S (x, y, z) = 1 (Chayanun et al., 2019). Consequently, I XBIC as a function of Φ can be written as I XBIC = 1.7062 × 10 −18 · Φ for the x-ray energy of 13.8 keV.
This function is plotted in Fig.7 as a red line. We can observe the difference between the maximum measured and the theoretically calculated I XBIC from the plot in Fig.   7. This low measured XBIC comparing to the calculation was evidenced before in the previous publication. In this experiment, the measured I XBIC is about 20 % of the theoretical calculation, which could attribute to the escaping of those secondary electrons from this nanostructure sample (Chayanun et al., 2019;Stuckelberger et al., 2017).
Hence, we introduced the term for the new charge generation yield of the nanowire compensating the actual yield with the escaping secondary charges. In Fig.8 the radially profiles at different X-ray photon fluxes and bias-dependent XBIC measurements are compared. The profiles are fitted using the Gaussian distribution function and the full-width-half-maximum (FWHM) is defined. The FWHM increases almost linearly with the X-ray photon flux, respectively the XBIC signal.
The same applies to the bias-dependent measurements. Fig. 8. Comparisons of the different radial XBIC profiles. The FWHM of the radial XBIC profiles is plotted against the maximum XBIC signal from the X-ray photon flux variation and the bias-dependent XBIC measurements. The difference between the two measurements can be explained by variations in the intensity of the X-ray beam.

Bias dependent measurements
Beside the XBIC measurements of the off-axis illuminated MZP described in the manuscript, measurements using a full-illuminated MZP at the P10 beamline were performed as well. Therefore the OSA (and the pinhole) were moved out of the beam, since the nanowire device needs more free space in the vicinity of the focus. For a fully illuminated MZP the maximum free space between the focus/sample and the OSA would be below 180 µm, which is not enough for the positioning of the nanowire device.
Equivalent to the bias dependent measurements presented in the manuscript using an off-axis illuminated MZP, bias dependent measurements were performed using the full illuminated MZP. The XBIC maps at different applied biases ranging from −0.5 V to 0.4 V with the increment of 0.1 V and are shown in Fig. 9. The scan was done with 20 nm step size and 0.1 s acquisition time. The I XBIC presents the charge collection of the device. Just like in the figure in the main manuscript the range of the color bar is the same for all maps. For the full illuminated MZP, this results in a bias dependent background signal. This is different for the measurements using the offaxis illuminated MZP presented in the main manuscript, where the color bar range is equal for all maps, and no bias-dependent background signal was observed.
Furthermore, in the case of the fully illuminated MZP, the shape of the nanowire XBIC signal, although similar, is much broader. This is contradictory at first, since the fully illuminated MZP produces a smaller focus. However this is due to the photons from different diffraction orders which also produce an XBIC signal, which then leads to the broadening of the nanowire signal.
This demonstrates for the case of the XBIC measurement in the described experiment, that the slightly larger focus of the off-axis MZP with OSAs and therefore negligible background photons is resulting in a better measurement as the smaller focus of the full illuminated MZP without OSAs and therefore with a background signal.