visible at the very edges of the CCD detector providing NA limited resolution.
Since the radiation damage of the magnetic multilayer systems can be neglected the scattering statistics is improved by increasing dwell time for every scanning step. The basic issue in experiments with long exposure times is the specimen contamination with carbon that occurs due to the interaction of X-rays and residual gases in vacuum chamber.
The carbon layer is built up on the surface of the scanned area that worsen the contrast of the resulting image. Also thermal drifts of the sample during long scans can be an issue causing resolution worsening.
Figure 4.19: Overlap ratio of neighboring illumination spot profiles at the scans with step sizes a) 20 nm and b) 120 nm.
shown. This step size is out of FWHM of illumination profile, but reconstruction results in the same image resolution and contrast. Therefore step size as big as focus spot can be used for imaging of highly scattering samples without affecting the image quality and significantly reducing scanning time. The raster artifacts appear at the scans with the step size of 140 nm, the structures get partially unresolved in figure 4.21 f) when the step size is 160 nm.
Figure 4.20: SEM image of the Siemens Star with smallest structures of 30 nm.
As it is shown a strongly reduced overlap of the neighboring spots in raster scanning leads to the grid artifacts in the image and resolution degradation. It is caused by inhomo-geneous illumination at each scanning spot and, as a result, the lack of scattering signal in overlap region that negatively influences the retrieval process.
Figure 4.21: Ptychographic images obtained with different step sizes of the raster scan: a) 20 nm;
b) 60 nm; c) 100 nm; d) 120 nm; e) 140 nm; f) 160 nm.
4.5.2 Defocus scanning
In order to cover bigger area during ptychographic raster scan not only overlap ratio can be changed but also the size of the illumination spot itself. It is done by shifting the sample out of focus as it is shown in figure 4.22 c). As it was reported in [106] resolution of ptychographic reconstruction isn’t sensitive to the position of the sample relative to the FZP focus plane. Figure 4.22 b) is a simulated illumination profile in defocus position. It has a doughnut like shape, which comes from the divergent light cone of the first order light, and posses an order of magnitude less intensity than in the focus spot (figure 4.22 a), that has to be taken into account. The illumination spot size is estimated asS =δDf, whereδis defocus distance,D- diameter of FZP, andf - focal distance.
The experiment was done by gradually increasing distance from focus position with 5 µmstep moving sample backwards from FZP. Figure 4.23 a) shows image in focus with 120 nm scanning step size and corresponding focus spot size of 122 nm, determined as FWHM. Figure 4.23 b) shows beam profile in 25µmout-of-focus position with 140 nm scanning step size and illumination spot of around 387 nm. In real conditions the spot size might be smaller due to less defined boundaries and possible non-uniformity of the illumination in defocused position. As it was discussed in previous chapter, when the sample is in the focus position and scanned with the step of 140 nm, the reconstruction suffers from grid artifacts since the scanning step is significantly higher than FWHM of the focus spot (figure 4.23 a). In out-of-focus position the reconstruction doesn’t posses
Figure 4.22: Simulated illumination profiles at sample position: a) in focus spot and b) 25µmout of focus position; c) a schematic illustration of the scanning configuration with the sample in focus and out-of-focus positions.
artifacts at 140 nm scanning step and the 30 nm features are resolved as it is seen in figure 4.23 c).
Figure 4.23: Ptychographic images obtained at 800 eV: a) in focus position with scanning step size of 140 nm and b) 160 nm; c) 25µmout of focus with the step of 140 nm and d) 35µmout of focus with the step of 160 nm.
Further increase of defocus distance haven’t showed the same behavior. In figure 4.23 d) reconstruction with the defocus distance of 35 µmand step size of 160 nm has the characteristic grid pattern. Although the 30 nm structures are resolved and the image has better quality in comparison with in focus configuration (figure 4.23 b). The presence of artifacts can be caused by inaccuracy of the initial guess of illumination function. The quality of reconstruction is also affected by a significant drop of the beam intensity in the unfocused illumination spot which reduces scattering statistics.
4.5.3 Resolving power and dwell time
For the estimation of ptychographic resolving power and its correlation with the numerical aperture (NA) of the setup 15 nm structure size Siemens Star (Applied Nanotools) was imaged. The scan was done at energy 708.4 eV and 9 cm detector distance that results in NA with 12.5 nm output pixel size. Therefore the smallest structures of the inner circle would result in around 1 pixel size in the reconstructed image. Figure 4.24 shows amplitude and phase reconstructions of clearly resolved Siemens star that proofs that we get NA limited resolution.
Figure 4.24: Siemens star with 15 nm wide inner circle structures imaged by ptychography: a) amplitude and b) phase reconstructions.
As it was discussed, in order to increase scattering statistics in diffraction the data dwell time per each scanning point should be increased. The main effect on the recon-structions is the increase of the contrast that improves the visibility of imaged features. In figure 4.25 the graph shows the dependance of ptychographic reconstruction contrast on the dwell time for a highly scattering sample, i.e. Siemens star, and low scattering mag-netic domain structure multilayer Ta(5)/[CoFeB(1.5 nm)/MgO(2 nm)/Ta(3 nm)]15. The
contrast of amplitude image was estimated as a Michelson contrast [107]:
Contrast= Imax−Imin
Imax+Imin, (4.11)
whereImaxandIminrepresent the intensities of bright and dark regions, respectively. In the first case the change of the contrast doesn’t not have a strong dependance on the dwell time, relative rise is within 2%that is still in the range of standard deviation error. There-fore high scattering from the morphological edges of the Au features provides sufficient photon count statistics and signal to noise ratio even at 50 ms dwell time. At the same time, we see that magnetically scattering sample has 20%contrast change between 100 and 500 ms dwell times. At the higher dwell time values the exponential curve gets into plateau evidencing that further increase will not improve image quality.
Figure 4.25: Contrast dependance of ptychographic amplitude images on scanning dwell time. The blue curve represents contrast change of magnetic domain sample obtained at Fe-edge 708 eV, the red curve - Siemens Star with 30 nm structures at energy 800 eV. The curves are fitted with expo-nential fits. The error bars are determined as standard deviation within 5 contrast measurements.
The observed behavior proves that quality of ptychographic reconstruction is mainly defined by the scattering properties of the sample itself and can’t be endlessly improved by the change of signal accumulation time. As it was shown the increase of dwell time for charge scattering samples doesn’t improve the reconstruction quality, extremely high
scanning time rather can cause the sample drift and carbon layer formation on the sample surface. For the further ptychographic measurements optimized dwell time values of 300-400 ms for pure magnetic contrast samples and 100-200 ms for charge scattering samples are used.