(a, b) HIM images of freestanding CNMs on TEM grids, illustrating the importance of the background. Both images show the same sample mounted differently. The arrows point to the same positions as a guide to the eye. (c) CNMs on a TEM grid with a bright background and substantial membrane charging. (d) CNMs are imaged on a dark background with negligible membrane charging. (e) Schematic cross-section and superimposed line profile of the image greyscale values along the dotted line in (c) with the primary He + beam and secondary electrons emitted from the CNM and the sample holder depicted at three exemplary locations. The values of the line profile (grey curve) are a measure of the amount of detected secondary electrons. Detailed information on all HIM images are given in Supporting Information File 1, Tables S1 and S2. 

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... nanomembranes (CNMs) are extremely thin and homogeneous two-dimensional objects consisting of a monolayer of laterally cross-linked molecules. They are made by exposing a self-assembled monolayer (SAM) of aromatic molecules with electron [1] or soft X-ray irradiation [2], which results in the cross-linking of neighbouring molecules into a CNM of molec- ular thickness. The CNM is then released from its substrate by dissolving the latter [3]. The thickness, chemical composition, and density of the original SAM determine the mechanical properties, such as elasticity and porosity, as well as the chem- ical composition of the resulting CNM. The freely suspended CNMs are made by transferring the cross-linked SAM from its substrate to a holey structure, such as a metal grid. The resulting CNM is approximately as thick as the original SAM and can span macroscopic areas; thus far, freestanding CNMs of up to 0.5 × 0.5 mm 2 have been fabricated. The electrical conductivity of the CNM can also be tailored, as pyrolysis results in a gradual transformation into graphene [4-6]. CNMs have potential for many technical applications, such as filters [7], sensors [4], resists [8], nanosieves [9], or “lab-on-a-chip” devices [10]. Many aspects regarding the fabri- cation, modification and functionalization of homogenous as well as patterned CNMs are compiled in a recent review [11]. Optical microscopy is suitable for imaging CNMs on SiO 2 /Si wafers [12], but on other substrates, CNMs are not (or only barely) visible. In particular, it is not possible to directly image freestanding CNMs by regular optical microscopy. Indirect optical methods require the attachment of particles, fluorescent dyes [13], metallic nanostructures [14] or other suitable indica- tors that are detectable by optical microscopy. In addition, optical imaging with a Mirau interferometer allows the detection of the vibrational modes of bare CNMs with a resolution limited by the light wavelength [15]. The imaging of CNMs with higher magnification requires charged particle microscopy techniques such as scanning electron microscopy (SEM) or helium ion microscopy (HIM). As illustrated in Supporting Information File 1, Figure S1, SEM shows a low signal-to-noise-ratio for freestanding CNMs, espe- cially at higher magnifications, due to charging issues [4,16]. This tends to be destructive for freestanding membranes. For example, an attempt at imaging perforated CNMs with SEM failed due to charging-induced rupture during the imaging process [9]. On the other hand, HIM is very well-suited to image CNMs with high signal-to-noise-ratio at high magnification. In this report, we will show examples that support this statement. We demonstrate the effect of charging on HIM images as well as the effectiveness of the HIM charge compensation mechanism. The principle of operation of HIM as well as a recent overview of HIM-related reports can be found elsewhere [17]. In short, HIM utilizes a focussed beam of He + ions that scans the sample surface. The image is usually obtained by the detection of secondary electrons. The imaging of insulating samples may lead to positive charging due to the emission of secondary electrons as well as the exposure to positive He + ions. A major advantage of HIM is its ability to compensate for sample charging by employing an electron flood gun in an alter- nating manner. In this way, the sample is exposed to electrons between scans of subsequent image lines or frames. There is scarce literature on HIM imaging of ultrathin membranes. Many researchers have examined graphene, where the main focus was on the modification and production of small structures and circuits [18-22]. The thickness of graphene is comparable to CNMs, but a fundamental difference is its high conductivity, which eases charged particle imaging. Small flakes of hexagonal boron nitride (h-BN), an insulating ma- terial that shares similarities with graphene, were imaged in a comparative study [23]. Therein, it is shown that HIM is more sensitive and consistent than SEM for characterizing the number of layers and the morphology of 2D materials. It was also shown that HIM is very sensitive in characterizing supported, thin organic layers due to its high surface sensitivity [24,25]. For imaging with the HIM, the most important characteristics of CNMs are that they are ultrathin ( ≈ 1 nm) and electrically insulating. Due to the low thickness, the high surface sensitivity of the HIM is well suited to obtain CNM images with high signal- to-noise-ratio. It is also important to note that the helium beam easily penetrates the CNM and also strikes objects below the freestanding membrane, for example, the sample holder. Figure 1 shows an example of this effect. The images in Figure 1a,b show the same sample: a hexagonal TEM grid is mounted in a sample holder (visible in the four corners of the images) which has a mm-sized, circular opening. The CNM partly covers the TEM grid and the white arrows indicate CNM- covered regions. Although both HIM images were taken with the same ion acceleration voltage and similar ion currents, the contrast in the images appears almost inverted. This difference relates to the background: In Figure 1a, the main part of the grid is placed closely over the homogeneous metal surface of the sample holder. An edge of the sample holder surface is visible as a bright strip running from the top to the lower right of the image. These background features are visible in the HIM image as He + ions impinge upon the sample holder behind the grid and eject secondary electrons that reach the SE detector without being blocked. In Figure 1b, the sample holder background is not visible as the path of the secondary electrons emitted from the sample stage to the detector has been blocked by mounting the grid on top of a deep cavity, which acts like a Faraday cup. Thus, in Figure 1b, the uncovered openings of the grid appear dark in all parts of this image. To guide the eye, white arrows in Figure 1a,b depict the same position in the sample. Note that regardless of the CNM grid mounting, in both cases, a fast evaluation regarding the area of intact CNMs is easily obtained due to the large field of view (of more than 2 mm), high depth of view, and high contrast between bare and CNM-covered grid meshes. The recording time of such images is less than one minute. Another effect, which substantially changes the appearance of the CNM image, is electrostatic charging of the ultrathin, insulating membranes. In Figure 1c,d HIM images with and without charging artefacts are compared. A schematic cross-section of the sample as well as a superimposed line profile of the image greyscale values in Figure 1c corresponding to the white dotted line is given in Figure 1e. An empty grid opening on the left is followed by a partial and a fully covered opening. CNM charging due to the positively charged He + ion beam and the emission of negatively charged secondary electrons can only result in positive charging regardless of the secondary electron yield of the CNMs. A positively charged sample will hinder the emission of secondary electrons. Therefore, positively charged CNMs will appear dark in HIM images. This is observed in Figure 1c where the freestanding regions of the membranes are dark, while the membrane regions directly in contact with the copper grid appear much brighter. In the latter, secondary electrons are also emitted from the underlying copper grid and charges in the CNM are neutralised by the metallic support. This combination of effects yields a high contrast between the CNM-covered and non-covered regions. However, the struc- tural details of the CNMs cannot be investigated under such imaging conditions. An interesting image feature appears in partially covered meshes: the edges of freestanding CNMs are brighter than intact CNMs, as illustrated in the area near the centre of the dotted line. This effect is explained by considering that secondary electrons are emitted from the sample support rather than from the freestanding CNMs itself, as schematically depicted in Figure 1e. The intact CNMs completely block the path of such secondary electrons to the detector while partially ruptured CNMs do not. The reduction of the beam current, the dwell time per pixel, the use of frame averaging as well as charge compensation can reduce or completely avoid the charging of insulating membranes. These imaging parameter changes resulted in Figure 1d, which does not show any notable charging effects. Here, the sample was mounted in a way that no secondary electrons from the sample holder could reach the detector. A small rupture in the CNM reveals a high contrast between the bright CNM and the dark background. Under these imaging conditions, fine details on the top of freestanding CNMs can be observed. For example, small pores and folds are visible. A collection of different CNMs on hexagonal copper grids is presented in Figure 2, exhibiting the different types of features that are visible in HIM images. From these images, one intu- itively obtains an impression of the detailed shape of the copper grid and the CNM on top. In Figure 2a larger folds on the upper side of the image and one rupture in the centre are visible. Figure 2b is an example of a membrane rolling up at a rupture, showing the high flexibility of CNMs. Small folds like those in Figure 2c are frequently observed, while wrinkling of the freestanding membrane (Figure 2d) is less often observed. Examples of very large, freestanding CNMs are given in Figure 3. The ≈ 1 nm thin membranes are self-supporting over a distance of ≈ 0.5 mm, which are to date among the ...