Contrast modes in a 3D ion transmission approach at keV energies

We present options for visualizing contrast maps in 3D ion transmission experiments. Simultaneous measurement of angular distributions and flight time of ions transmitted through self-supporting, single-crystalline silicon foils allows for mapping of intensity and different energy loss moments. The transmitted projectiles were detected mainly for random beam-sample orientation using pulsed beams of He ions and protons with incident energies 50 and 200 keV. Differences in contrast, observed when varying the projectile type and energy, can be attributed to sample nuclear and electronic structure and bear witness to impact parameter dependent energy loss processes. Our results provide a base for interpretation of data obtained in prospective transmission studies when for example using a helium ion microscope.


Introduction
Thin self-supporting targets permit analysis of their composition and structure in transmission, gaining additional information in comparison to other spectrometric and spectroscopic approaches. Various probes, based on different particles, have been employed. Scanning transmission ion microscopy using MeV primary ions (STIM) is analogous to scanning transmission electron microscopy and several modes for contrast imaging were investigated with the emergence of microbeams in the 80s [1][2][3]. However, for MeV ions the beam spot size is limited, typically to µm [4,5] with a few studies with nanometre beams existing [6]. Even at much lower keV energies, the short wavelength of helium ions still results in a reduced diffraction limit for helium ions compared to electrons. Recently, a new imaging technique, the helium ion microscope (HIM) based on keV ion beams has been introduced. It offers high spatial resolution (<0.5 nm), large depth of field, and the ability to image nonconductive samples [7][8][9]. Along with secondary electron detection, it has so far been shown that contrast can be achieved by detecting primary and secondary ions scattered or sputtered from the sample surface [10]. For thin samples, however, a majority of incident helium ions is transmitted through the sample, i.e. >90 % of the helium ions scatter in forward direction, whereas only ~5 % or less are scattered in an angle larger than 90°. Due to this property, detection of ions in transmission would enable imaging of thin samples with low fluence drastically reducing the amount of sample damage to bulk and surface by introducing defects from small and large angle nuclear scattering and due to effective sputtering by keV ions, respectively [11].
Contrast in any transmission microscope using ions is related to either lower intensity as particles are scattered away or the energy loss that the projectile suffers during the passage through the sample. In the dark field mode Woelh et al. showed the advantages of detecting transmitted ions for quantitative imaging over conventional transmission electron microscopy (TEM) [12]. In the broad-beam setup introduced by Mousley et al. the intensity distribution patterns could also be related to the surface morphology [13]. Energy loss contrast originates either from different stopping, different thickness, or different scattering, i.e. different angular distribution for a given energy loss. The most commonly observed contrast comes from the variation of sample thickness and materials. However, even for a monoatomic compound of constant thickness, the intensity and the energy loss can show a dependence on the sample orientation if the target is crystalline. For MeV ions, the energy loss is known to show a strong impact parameter dependence, due to impact parameter dependence of inner-shell excitations [14][15][16][17] resulting in reduced loss along low-index crystal directions. Also, the intensity distribution of transmitted He projectiles is affected by these channelling and blocking effects, which can enhance or reduce the particle fluence in specific directions [18]. In a recent work Lohmann et al. showed that, even at energies typically employed in the HIM, the energy loss experienced by primary ions can depend strongly on the ion trajectories, due to a pronounced impact parameter dependence of the mean charge state [19,20].
Particle optics and dimension constraints in transmission approaches using the HIM are still a challenge for direct mapping of energy loss of transmitted ions. Wang et al. have constructed a transmission channelling setup for a He ion microscope [21], and recently, Kavanagh et al. used this setup to acquire transmission images showing an intensity contrast pattern [22].
In this work, we show how sample structure affects intensity as well as energy loss and its higher moments for both helium ions and protons transmitted through thin, self-supporting, single-crystalline silicon foils. For this aim, we simultaneously record angular distributions and particle energy and present different ways to obtain and visualize contrast, which is considered to be useful for potential future investigations using helium ion microscopes in transmission mode.

Experiment and data analysis
Experiments were performed with the time-of-flight medium energy ion scattering (TOF-MEIS) setup at Uppsala University [23,24]. Based on a Danfysik implanter, a chopped beam of atomic ions was provided to the experimental chamber, while maintaining a beam spot size smaller than 1x1 mm 2 and beam angular divergence better than 0.056°. The current impinging on the sample is 2-3 fA with a beam pulse width of 1 ns to 2 ns and a repetition rate of 31.25 kHz. In the present study, we focus on protons and 4 He + primary ions as they feature maximum relevance for the HIM. The initial ion energies range between 50 and 200 keV. Projectiles are detected after transmission through 200 nm thin, selfsupporting Si (100) foils. The angular distribution of transmitted particles is recorded with a large, position-sensitive microchannel plate detector with diameter 120 mm from RoentDek [25]. The detector covers a solid angle of 0.13 sr, and the position of particles is determined with help of two perpendicular delay lines. The ion energy, after transmission through the sample, is measured via its flight time.
The acquisition software COBOLDPC (Computer Based Online offline Listmode Dataanalyser) stores the data in a list mode file format [25]. Every time event can consist of up to five incidents (hits or noise) while every hit is assigned a XY position and flight time [26]. The assignment of the position is made from the time difference of the signals appearing at the two ends of each delay-line anode.
When loading the file to the COBOLD interface, data is processed by an inner algorithm with conditions defined by the user. Custom changes in the source code allow us to extract an ASCII file containing a list of events holding position coordinates and the associated energy of the particle derived from its time-of-flight value. Multiple hits are rare and are, for the sake of simplicity of coding, excluded.
By binning the data in three dimensions, i.e. in energy and two spatial dimensions, statistical manipulation becomes accessible. Every spatial bin contains thus an energy distribution histogram of particles arriving at the same detector position. These histograms permit extraction of statistical values such as the most probable energy or the mean energy as well as its standard deviation (SD). These variables can be assigned to their respective position and plotted as 3D maps as the one shown in Figure 1. Spatial binning is for statistical reasons chosen as 0.5 mm, corresponding to an angular resolution ~0.1°. Spatial intensity distribution maps are normalized to the maximum value. Energy is binned with 1 keV steps, with regard to the fact that the detector energy resolution for all used projectiles should be better than 1 keV.

Results
For the primary beam oriented perpendicular towards the Si (100) surface, channelling allows the majority of the ions to propagate in a straight direction encountering no large-angle collisions. Intensity mapping on the detector features an intense peak in the centre with lower intensity surrounding it, which is formed by ions that escaped the channel and experienced scattering by larger angles than the critical angle for channelling [27] (see Figure 2). Some of these trajectories become a subject to blocking, which for 200 keV He, results in observable weak streaks along low-index planar channels.
The same effect is taking place for 50 keV He, however, due to the wider angular distribution, it is not visible within the angle covered by the detector.   As described in the previous section, it is possible to calculate the mean energy of the ions detected for the same dataset. This representation is equivalent to plotting the energy loss experienced. Figure   3 b) shows the resulting spatial energy distribution of detected projectiles, i.e. virtually the same data as in Figure 1 but in 2D. With respect to the intensity distribution, the energy map gives a clearly different, and more pronounced contrast. It is readily visible that the ions lose significantly less energy along channelled trajectories compared to random trajectories. Also, more channels are visible and structures observed show a higher resolution. and literature [19,28]. In contrast, data for 50 keV protons does not show any clear contrast in the energy distribution, which goes beyond a weak contrast that originates from reduced sample thickness towards the [100] direction, i.e. the lower left corner of the detector.

Discussion
Contrast in intensity reveals information about the crystal structure and about the scattering processes experienced by the projectiles. As shown for 50 keV He, even though the beam is aimed towards the centre of the detector, the maximum intensity can be observed in close-by channels and planes. We observe a clear dependence of the intensity distribution on both initial energy and projectile charge.
As the scattering cross section increases for lower energy and increasing Z1, steering of the projectiles along crystallographic axes and planes becomes more likely. This can be observed for 50 keV He where the projectiles are exiting the crystal from mostly low-index channels. At 200 keV, however, these channels become less accessible due to significantly decreasing critical angles which eventually results in predominant blocking from the same crystallographic features. Nevertheless, a significant number of ions are entering higher index channels located close to the beam due to the smaller, and thus more probable, deflection angles necessary (the bright spots around the central position). Also, 50 keV protons experience less scattering than helium at the same energy, and tend to propagate in a straight direction. The channelling into higher index axes is found more pronounced than in the case of 200 keV He. This behaviour can be well understood qualitatively, as both the Rutherford cross section but also the here more applicable screened potential predicts the scattering cross section for 50 keV protons to be found between those for 200 keV and 50 keV He ions. For a more quantitative discussion, one could compare the half-widths of the angular distributions with predictions for the channelling half angle [27] or perform Monte-Carlo-simulations. Such angular distributions can, however, not be obtained from the present samples, but would require amorphous foils. but increases to about 0.9 at 200 keV [19]. The gradual contrast observed diagonally towards the left corner in the Figure 3 d) is a result of increased length of the particle trajectory through the sample, which is expected to be max 10 % over the whole angular span of the detector.
In light of the discussion above, one can attempt to carefully interpret the map of the standard deviation of the mean. At first, however, one should discuss a statistical issue in the calculation of SD that needs to be handled before visualizing the data. Detector areas with low count intensity, in combination with background noise, i.e. white noise at the channel plate detector, can result in huge standard deviation thus saturating the final contrast. Therefore, a threshold of a minimum of 100 counts per pixel, selected as described above, was applied as a condition for visualization. This standard deviation can be understood as a form of energy straggling of ions with possibly different trajectories inside the crystal, but similar final angular deflection. One could expect such contrast to be visible at the edges of the axial and planar channels i.e. in the transition regime from channelling to random geometry, with qualitatively very different trajectories (analogy to the skimming effect described for backscattering [31]), resulting in signal broadening. There are, however, other contributions from e.g. higher angle scattering and dechannelling that complicate the straightforward interpretation of the observed contrast. As a result, the observed distributions are far from what is commonly considered as energy loss straggling, i.e. close to Gaussian distribution of the observed particle energies. In turn, the specific sample structure will have a huge influence on how data can be interpreted. As such, an interpretation of straggling maps, due to the huge amount of mixed information they contain, is expected to be only meaningful based on complete pictures from both intensity and energy distributions.