Atomic-scale effects behind structural instabilities in Si lamellae during ion beam thinning

Since atomic-scale building blocks determine functionality in nanotechnology, understanding physical processes at this scale is crucial for the discipline. One of the most important means for achieving this knowledge is aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM),^1,2 a method which allows determining the positions of atomic columns of a structure with accuracy higher than interatomic distance in solids.^3,4 HRTEM requires thin, unbent samples which ideally should contain no amorphous surface layer. Moreover, in nanotechnology, it is mandatory to achieve sample preparation with a sub-μm precision in all dimensions. These standards cannot be reached using traditional mechanical preparation methods such as mechanical milling, and thus the focused ion beam (FIB) technique, where the sample is milled into a thin lamella through sputtering, needs to be used instead.

The current development in AC-HRTEM is to lower the voltage from the usual 200–300 kV to well below 100 kV,^5–10 in order to minimize displacement damage in fragile samples.¹¹ So far, predominantly low-dimensional materials such as graphene,^5,8,10 hexagonal boron nitride,⁶ and carbon nanotubes⁷ have been studied at low electron beam voltages by HRTEM. In the future, however, there will be a demand to extend these low-voltage studies to conventional materials, which similarly suffer from knock-on damage at higher voltages. This trend of lowering voltage entails an increasingly stringent requirement for sample thickness, which must not surpass the extinction length of the electron beam (∼few nm). However, the conventional FIB thinning method is limited to thicknesses above ∼20 nm. The dominant effect behind this limitation is the shrinkage of the lamella in height during milling: Thinning a lamella down to a thickness of 20 nm may induce several μm of shrinkage in the vertical direction.¹² The underlying physical reasons for this observation are currently not known, because an atomic-scale description of the thinning process has hitherto not been presented. Additionally, the conventional method is hampered by specimen warping, an uneven thickness profile, and often heavy amorphization.

Although irradiation effects in Si have been studied for decades, the work has concentrated on bulk Si samples.^13–16 Moreover, earlier computational work on FIB processing of similar nanosystems has been restricted to simulation setups which severely reduce the applicability of the obtained results to the problem addressed in the present study. On the one hand, some studies have employed less detailed models based on Monte Carlo simulation of sputtering and redeposition on a three-dimensional grid.^17,18 Unfortunately, such models lack real atomic resolution and hence do not account for, e.g., amorphization, which alone renders them powerless for the topic at hand. On the other hand, previous molecular dynamics (MD) simulations motivated by FIB milling have employed geometries restricted to a single surface with no deformation of the sample allowed,^19–21 thus yielding comparatively limited insight into the process. To uncover the mechanisms responsible for the deleterious effects on the lamella under conventional FIB thinning, we performed a classical MD study of the FIB thinning process in conjunction with experiments. Using the findings from our experiments and simulations, we show that the empirically observed limit of 20 nm for the conventional thinning method is a result of geometric sputtering effects due to the finite sharpness of the ion beam, dominant at low energies (∼1 keV), and of atomic-scale effects at the very top part of the lamella, significant at high energies (∼30 keV). We further explain why these mechanisms are not present in a recently proposed double-tilt method,²² which thus allows the thinning process to proceed beyond the conventional limit.

The experimental setup and the conventional FIB thinning method are described in Appendix  A. The effect of ion beam tails, discussed below, is demonstrated in Appendix  B. Here, we focus first on studying experimentally the deleterious shrinkage effect on a lamella during FIB thinning. In principle, creating a wedge-shaped lamella would show shrinkage versus thickness in a straightforward experiment. However, the structural stability of such a geometry is reduced fast during thinning, and warping of the sample occurs. Therefore, we instead thinned a co-planar Si lamella in a double-wedge configuration (Fig. 1): Material was removed from one side by milling at a horizontal tilt of 4° and from the other side at 1° but with a vertical rotation of 0.5°. The resulting lamella thus gets gradually thinner from bottom to top and from right to left with the very thin areas restricted to the top edge to limit warping. Milling parameters for the fabrication were identical to the single-edge experiment of Appendix  B. For a given material and set beam conditions the absolute thickness of the lamella can be estimated from scanning electron microscope (SEM) image contrast.²³ In the secondary electron SEM image of Fig. 1, the thickness gradient of the lamella manifests in a contrast gradient with the thin areas appearing lighter.

Based on purely the milling geometry, the thin top-edge of the created double-wedge lamella should be straight, as shown in the schematic illustration of Fig. 1. Instead, we observe a strongly falling edge indicating that the removal of lamella material in the vertical direction is greatly increased when the thickness drops below a certain threshold. Furthermore, very thin areas (< 10 nm) are notably absent in the wedge lamella. In fact, we could not find any experimental conditions that would have allowed us to create a very thin Si edge using 30 keV Ga ions. We tried shortening the line dwell time/milling depth to reduce the corner rounding – to no avail. Reducing the beam current and thus sharpening the beam did not prove a viable option either since the resulting milling times were excessive, leading to problems from stage drift. Consequentially, we can unfortunately not draw any quantifiable conclusions from the thinning experiments except that we were not able to create very thin areas, and that there is a thickness-dependent vertical shrinkage effect for the thinnest parts of the structure.²⁴ 

In order to understand the unexpected shrinkage of the lamella below the threshold thickness, an atomic-level description of the irradiation process is required. Our MD simulation setup, designed for studying ion irradiation effects on the top edge of a short section of a thin Si lamella, is visualized in Fig. 2. In all simulations, the studied system size was 65 nm in the vertical (z) direction and 10 nm in width (x-direction), periodic boundaries being applied in the latter dimension to mimic a much wider lamella edge. The beam, assuming a Gaussian distribution with a standard deviation of 2.5 nm in both the x and y-direction, was directed at the edge of the lamella at an angle of 1°. The thickness of the edge was controlled by the size of the system in the y-direction (S_y ∈ [3, 10] nm). The simulation setup is further detailed in Appendix  C, and the performed runs are described in Appendix  D.

In Fig. 3, we plot sputtering yield Y as a function of edge thickness for 1 keV and 30 keV Ga⁺ irradiation as given by two different Si–Si interaction potentials (Appendix  C). The data is clearly grouped by the beam energy: The thickness of the system seems to have no systematic effect on the results. On average, the 30 keV beam produces a Y of 7.1 ± 0.2 atoms/ion, whereas the 1 keV beam gives 0.98 ± 0.05 atoms/ion, as averaged over all system sizes and potentials. To better understand whether the irradiation energy leads to other differences beyond those in Y during the milling, we carried out an extensive analysis of different physical effects occuring during the process. For all simulated cases, the initial positions of sputtered atoms were determined after each irradiation event. Secondly, the center of mass of the system in the y-direction CM_y was calculated as a function of the z-coordinate. Thirdly, the degree of amorphization of each system was determined likewise as a function of z using structure factor analysis.²⁶ 

Our analysis shows that the 1 keV beam results in the smoothening of the initially abrupt upper corner of the edge, which would lead to milling of the edge upon continued irradiation. The corner is amorphized, and sputtering is mainly from the impact region. However, the effect of the 30 keV beam, as presented in Fig. 4, is more interesting. At this beam energy, the ⩾7 nm structures bend toward the edge onto which the beam is aimed. This is verified by the diagrams showing the center of mass in the y-direction as a function of the edge height, which clearly reflect what is seen in the snapshot of the final state of each system. Also, the apparent amorphization seen in the snapshots is confirmed by the quantitative amorphization analysis. Sputtering is induced over the entire front face of the system and somewhat at the back face also. For edges <7 nm, however, almost no bending is observed at the dose of 500 ions. Instead, the system simply shrinks vertically as a result of the ion bombardment. Correspondingly, sputtering for the thinnest structures is no longer predominantly off the front face but also significant off the back of the structure.

Based on the results presented above, it would seem that the 30 keV beam induces mainly bending and modest shrinking in the thicker edges (⩾7 nm) and predominantly shrinking in the thinnest edges. This inference is supported by studying the evolution of the atomic structure of the 10 and 3 nm edges as a function of the 30 keV irradiation dose, as presented in Figs 5(a) and 5(b), respectively. As the dose increases, the 10 nm system bends toward the corner where the beam is incident, whereas the 3 nm system shrinks by nearly 10 nm in height as the dose is brought to 1000 ions. The explanation for these two distinct modes of behavior can be found by considering the positions of sputtered atoms in each case and taking into account the resulting surface tension. As noted above and as seen in Fig. 4, sputtering for the ⩾7 nm edges occurs mainly off the front face of the structure. Therefore, the system will relax, i.e., minimize its free energy to a local minimum, by contracting the front face in the vertical dimension, hence pulling the structure into a forward-bent position. Correspondingly, when atoms are sputtered evenly off both the front and back faces, as for the <7 nm edges, the bending behavior is taken over by the shrinkage of the system in the vertical direction, as the structure relaxes by contracting along the entire thickness.

Note that the above-described bending is not the same phenomenon as the deleterious warping observed experimentally in the sample during conventional FIB thinning. The empirical warping happens in the opposite direction relative to the beam, and throughout the bulk of the lamella. Perhaps counterintuitively, the bending as described by our simulations will actually appear as shrinkage of the lamella top in the experiments. This is because the tilted structure is etched away more efficiently by the incoming ions than the originally straight-standing one. Obviously, this erosion process is very difficult to observe experimentally, and has therefore not been detected before. One example of how the erosion might proceed is presented below in Fig. 5(d). Here a large density of deposited energy on the top of the bent structure causes hundreds of atoms to sputter with a single ion hit and leads to the subsequent straightening of the lamella edge. For the extreme case of lamella edges <7 nm, sputtering from both the front and back faces simply constitutes another mechanism of shrinkage.

Focusing on the described bending of the edge in more detail, it can be seen in Fig. 5(c) that an 8 keV ion beam is energetic enough to induce bending in the 10 nm structure, whereas at 1 keV the edge is left standing upright. Looking at the bent structures in Figs 4 and 5(a), it can be discerned that the top part of the bent structure is as if bent around a hinge at a well-defined height on the back face of the structure, as illustrated explicitly by the horizontal line in Fig. 5(a). This point is roughly around the area where the amorphization starting from the front face of the structure reaches the back face, which is where the originally rigid crystalline back wall gives way to the contracting force on the front face of the system. Such a mechanism is functional only when the system is thin enough to allow for the amorphization to proceed all the way through the structure. For sufficiently thick structures this does not happen. We emphasize that this does not require a complete amorphization of the structure. Instead, it is enough if the damage reaches the back face at one location. This may happen outside the collision cascade, as was shown recently.²⁷ 

To predict the minimum attainable thickness of the lamella top edge according to this erosion mechanism, we performed a set of SRIM runs with Ga⁺ incident on a Si target at an angle of 1° at energies from 1 to 30 keV. To quantify the effect of the ions in the y-direction, we calculated the sum of ion range and straggle for the different energies (Fig. 6). To first assess how these results compare with MD data, we noted that for the 10 nm thick edge, the thickness of the amorphous layer in our MD simulations in the y-direction is 3 to 5 nm for 1 keV ions, and for 8 keV ions the thickness already surpasses 10 nm. A comparison of these two points to the SRIM results in Fig. 6 shows that the SRIM results give roughly half the thickness of the amorphous layer. The difference is due to the fact that in the SRIM calculations only ions incident on the front face of the structure are included, whereas in the MD runs, ions incident on the very top of the structure are simulated as well. Another factor possibly contributing to this discrepancy is a recently predicted damage flow mechanism in amorphous Si.²⁷ Taking into account this factor of two difference leads to the prediction that at 30 keV, lamella edges of thicknesses ⩽26 nm will be subjected to bending into the beam and hence catastrophic erosion. This explains why very thin lamella edges were completely absent in our experiments using the 30 keV Ga ion beam.

Regarding the warping seen in the experiment, the likely explanation for the phenomenon is to be found from previous studies of Si wafer curvature as brought on by ion implantation:²⁸ As the FIB is used to mill the face of the lamella, the surface region is amorphized, which causes the region to expand and hence to bend the lamella in the observed manner. The relevant scale for the effect is much larger than that in the present MD simulations. Furthermore, the mechanism relying on surface tension producing the bending toward the beam is dominant in our study over volume changes due to amorphization. The volume change of Si upon amorphization is predicted to be positive (as in experiment) for EDIP and negative for SW,²⁹ but nevertheless both potentials reproduce the bending of the top part of the lamella edge in the same direction. In our simulations, this is due to the small size of the structures; the smaller a system is, the higher its surface area to volume ratio, and hence any surface effects are pronounced in smaller systems.

In conclusion, we have experimentally demonstrated the well-known fact that a FIB milling energy of 30 keV cannot be used to create very thin lamellae (<∼20 nm) within the conventional thinning approach. Our simulations reveal that this limitation is a fundamental one, being due to atomic-scale effects at the top edge of the lamella which lead to the erosion of the structure under the ion beam. Specifically, we predict that an edge of thickness ⩽26 nm will be subject to catastrophic erosion through the lamella top edge bending into the beam. This effect can be reduced by lowering the beam energy, but the lower the energy, the more significant the effects of the beam tails become (Appendix  B). Together these two mechanisms of shrinkage lead to the lower limit of 20 nm for the thickness of the lamella during conventional FIB thinning. Our results explain why the alternative double-tilt approach (Appendix  E) is free of these harmful effects, and can be used for preparing extremely thin samples of good quality for current and future AC-HRTEM studies.