Imaging the Structure and Properties of 2D Materials with 4D-STEM

Abstract

Two-dimensional materials are usually imaged with low beam energies to minimize sample damage but limiting spatial resolution to ~1 Å. With the recent advances in detector technology [1] and reconstruction algorithms [2], the resolution limits are now dominated by counting noise through the maximum allowable dose, either by radiation damage to the sample, or by recording times. In particular, ptychographic phase retrieval algorithms offer an approach to using all of the scattered electrons-potentially enhancing both the resolution and dose-efficiency beyond what is possible with conventional imaging modes. The intrinsically thin nature of 2D materials greatly aids the modelling of the scattering process needed for phase retrieval. We have previously shown how in-focus ptychography enables imaging at more than double the diffraction limit of the lens [3]. Here we also show how out-of-focus ptychography (Figure 1) improves the dose efficiency compared with ADF STEM (Figure 2a), simultaneously providing a four-times-faster acquisition, double the information limit and double the precision (Figure 2b). By combining our design of electron microscope pixel array detector (EMPAD) [1] which has the dynamic range to record the complete distribution of transmitted electrons at every beam position, and a ptychographic phase retrieval algorithm to process the data, we have been able to increase the spatial resolution well beyond the traditional lens limitations reaching a 0.39 Å resolution for MoS2, at the same dose and imaging conditions where conventional imaging modes reach only 0.98 Å.[3] However, in-focus ptychography, like conventional STEM, is not well suited to imaging large areas at high spatial resolution-as the resolution is increased, the number of samples required grows quadratically in dwell time or dose. Operating out-of-focus decouples the resolution and real-space sampling requirements [2,4,5], provided the detector has sufficient dynamic range and pixels. While simulations have shown the out-of-focus reconstructions to have better convergence at low dose, compare to in-focus [3], in practice this was not the case when simple initial probe estimates were used. With improved probe diversity, we have been able to image 120 nm fields of view with 0.69 Å resolution at 80 keV producing 6000x6000 pixel images. Figure 2 shows the dose dependence and resolution of out-of-focus ptychography on WS2 monolayers. Figure 2d shows the precision with which we can measure S-S or W-W bond lengths, both in ptychography and ADF STEM, showing a roughly factor of two advantage for ptychography over ADF at the same dose.