Towards atomically precise manipulation of 2D nanostructures in the electron microscope

Despite decades of research, the ultimate goal of nanotechnology--top-down manipulation of individual atoms--has been directly achieved with only one technique: scanning probe microscopy. In this Review, we demonstrate that scanning transmission electron microscopy (STEM) is emerging as an alternative method for the direct assembly of nanostructures, with possible applications in plasmonics, quantum technologies, and materials science. Atomically precise manipulation with STEM relies on recent advances in instrumentation that have enabled non-destructive atomic-resolution imaging at lower electron energies. While momentum transfer from highly energetic electrons often leads to atom ejection, interesting dynamics can be induced when the transferable kinetic energies are comparable to bond strengths in the material. Operating in this regime, very recent experiments have revealed the potential for single-atom manipulation using the Angstrom-sized electron beam. To truly enable control, however, it is vital to understand the relevant atomic-scale phenomena through accurate dynamical simulations. Although excellent agreement between experiment and theory for the specific case of atomic displacements from graphene has been recently achieved using density functional theory molecular dynamics, in many other cases quantitative accuracy remains a challenge. We provide a comprehensive reanalysis of available experimental data on beam-driven dynamics in light of the state-of-the-art in simulations, and identify important targets for improvement. Overall, the modern electron microscope has great potential to become an atom-scale fabrication platform, especially for covalently bonded 2D nanostructures. We review the developments that have made this possible, argue that graphene is an ideal starting material, and assess the main challenges moving forward.


Introduction: a new tool for nanotechnology
Although based on physical principles it should be possible to assemble matter atom-by-atom, only few attempts at such manipulation have been successful. The first and so far only methods to truly achieve this goal are scanning probe microscopies (SPM), scanning tunneling microscopy (STM) in particular. STM is able to resolve the atomic structure at conducting surfaces by measuring the tunneling current to an atomically sharp tip. Voltage pulses from the tip also allow atoms to be picked up from one potential energy minimum and placed at the location of another one on a flat surface 1 , or moved to a vacancy in a surface layer 2 . Similarly, the interaction between the tip of an atomic force microscope (AFM) and surface atoms can lower migration barriers, allowing manipulation even at insulating surfaces 3 . However, despite many impressive demonstrations such as quantum corrals 4 , atomic-scale memories 5 , and designer atomic lattices 6 , these techniques are by nature limited to relatively weakly bound surface adatoms or vacancies.
In transmission electron microscopy (TEM), on the other hand, the scattering of highly energetic electrons passing through the sample is used for imaging. The mass of electrons makes TEM fundamentally different from optical microscopies: since electrons carry significant momentum, they can eject atoms from the structure being observed. Although the quantum mechanical scattering of relativistic electrons from the Coulomb potential of a nucleus is a complicated process in its fine details, the ejection event can be adequately described as an elastic collision between one imaging electron and one nucleus of the target material. This electron beam damage is typically a detrimental side-effect, prompting a push towards lower acceleration voltages to avoid degrading or destroying conducting samples for which this is the dominant damage mechanism. However, atom-number-conserving changes can be stochastically induced when the transferable kinetic energies are comparable to bond strengths in the material. A crucial advantage compared to SPM is that these energies are on the order of ten electronvolts in light-atom materials even for modest electron acceleration voltages. This potentially allows atoms with strong covalent bonds to be manipulated.
Since the entire field of view is uniformly irradiated in TEM, it is difficult to control the dose at the atomic level. However, in scanning transmission electron microscopy (STEM), pre-specimen condenser lenses are used to focus the electrons into an atomically small beam, which is rastered over the sample while the scattered intensity is recorded to form an image. In modern aberration-corrected instruments, the size of the beam spot (full-width at half-maximum) is only on the order of 1Å 7, 8 , making it possible to essentially direct the dose at individual atomic columns. These developments have given STEM the technological maturity to become a promising candidate for a fundamentally different tool for atomically precise manipulation. Indeed, some of us recently published the very first experimental demonstration of this process 9 .

Scanning transmission electron microscopy: enabling developments
While STM has allowed routine atomic resolution imaging since the 1980s, the non-destructive imaging of individual atoms by STEM only became widespread recently. The challenge was a pernicious property of electron optical systems, whereby no rotationally-symmetric electron lens of the type commonly used to form atomic-sized probes can eliminate spherical and chromatic aberrations 10 . The development of aberration correctors in the 1990s finally overcame this technical barrier, and electron microscopy instrumentation has seen enormous advances over the last two decades 7,8,[11][12][13][14][15][16][17] , making atomic resolution possible in most materials 18,19 . Further, the identification of the exact chemical structure is also possible, especially in low-dimensional materials. The elemental composition can be revealed by direct Z-contrast imaging 20 (since the scattered intensity is proportional to the atomic number) or through energy dispersive X-ray spectroscopy 21 , whereas electron energy loss spectroscopy (EELS) [22][23][24][25][26] can additionally reveal the exact bonding configuration. Non-destructive imaging of a range of materials has meanwhile been enabled by lower electron acceleration voltages 16,20,24 , yet still retaining atomic resolution.
Early aberration-corrected instruments were, however, too sensitive to focus the electron beam on a single atom for extended periods of time, and typical residual vacuum pressures in the instrument columns led to chemical etching 27 . Sample stability is very important for EELS mapping, but particularly crucial for single-atom manipulation where the electron dose needs to be accurately directed. These challenges have been largely addressed in the latest generation of instruments, leading to remarkable sample stability. Stage drift can be as low as 0.1Å per minute, and, thanks to improved vacuum, beam damage in pristine graphene is completely suppressed at electron acceleration voltages below 80 kV 27, 28 .

Graphene: advantage of two dimensions
Concurrently with improvements in STEM, the discovery of graphene 29 has provided ideal samples for atomic resolution studies 30 . Not only is monolayer graphene highly conductive, which effectively mitigates other damage mechanisms such as radiolysis and ionization, it also has remarkable electronic and mechanical properties 31 . These are theoretically well understood, and possible to accurately model from first principles using modern computational techniques.
The greatest advantage of graphene for manipulation experiments is its reduced dimensionality. The two-dimensional atomic structure can be directly imaged and atomic species easily identified, both of the material itself as well as any present impurities 20 . Even in cases where a projected image may be ambiguous, as when a heavier impurity atom such as Si 32-34 or P 35 buckles out of the plane, EELS can be used to unambiguously identify the precise nature of the bonding. Further, the electron dose can be predominantly directed at single atoms, apart from probe tails, i.e. the spreading of the intensity envelope of the electron beam beyond its sharp maximum 36 . Aberration-corrected beams are so finely focused that if the dose is directed at a single carbon atom in graphene, we estimate that only 0.3% impinges upon the other two neighbors of an impurity (integrated beam intensity based on the electron probe shape measured in 36 ). Since the relevant atom-scale dynamics are caused by electron impacts on a specific carbon atom 34 , this precision is crucial for control.
The reduced dimensionality also considerably simplifies both the physical interaction between the beam and the sample, and the analysis of the recorded image data. Each electron interacts only with a quasi-2D electron density, and predominantly scatters from the electrostatic potential of a single atomic nucleus. Besides simplifying theoretical descriptions of the interaction, the atomic structure can thus be directly and unambiguously identified from the scattered signal. This stands in stark contrast to three-dimensional crystals, where the complex interactions between the probe electrons and the sample, and the precise real-time reconstruction of its three-dimensional lattice from projected images present daunting challenges for atomically precise control 37 .

Atom-scale dynamics: state-of-the-art
In addition to spatial resolution, understanding dynamics requires collecting information in the time domain. Atomic motion that happens on femto-to-picosecond timescales is several orders of magnitude too fast to capture using conventional instruments, and even dedicated ultrafast techniques are limited to nanosecond timescales for real-space imaging far from atomic resolution 38, 39 . However, if the probability (i.e. cross section) of an electron-beam-driven process is low enough compared to the irradiation dose rate, each event can be individually distinguished. This enables their statistical treatment as a Poisson process 34 , allowing experimental interaction cross sections to be extracted and compared to simulations.
In the case of graphene, there is a growing body of work on the controlled creation 40 and annihilation 41 of defects, and etching and edge shaping directed by the electron beam 42, 43 . However, our focus here is on non-destructive (atom-numberconserving) manipulation. Fundamentally, such reversible beam-driven processes in graphene can be divided into two categories: bond rotation events and impurity dynamics.
Most of the former observations have been of all-carbon structures, ranging from the creation and annihilation of the double pentagon-heptagon defect (controversially 44 called "Stone-Wales defect" in the current literature) in pristine graphene 30,45 and bond rotations at a graphene edge 46 to the migration of dislocation cores 47, 48 and divacancies 36, 49,50 , and the transformation of grain boundaries 41 . The bond rotation process is also responsible for the healing of the so-called flower defect under electron irradiation 41 . Crucially, in all of these cases, the structural changes in the material can be explained through rotated carbon-carbon bonds, understood to occur due to a single impact from an electron to one of the involved carbon atoms 51 . In Fig. 1, we present examples for some of these cases, pointing out the individual bonds that have rotated between the frames when possible.
In contrast to observations of bond rotations, only a handful of examples of beam-driven and non-destructive impurity motion in graphene are known. These are the movement of the trivalent Si substitution via an out-of-plane bond inversion process 34 , the rotation of a Si trimer in a divacancy 52 , the atomic motions in a Si 6 cluster in a pore 53 , and the jumping of a bivalent N between two equivalent bonding sites across a single vacancy 54 . Although not previously discussed, we have observed both B and N substitutions to also undergo lattice jumps similar to Si (data from published experiments 32, 54, 55 ). Fig. 2 illustrates each of these processes, with the impurity atoms appearing brighter than the carbon atoms of the lattice due to their higher atomic number (apart from B, which appears dimmer). In the case of the trivalent Si impurity, a physical mechanism to direct the atom-scale dynamics is known 34 , pointing a way for atom manipulation experiments.

Electron irradiation: physics of manipulation
The highly energetic electron can transfer a maximal amount of kinetic energy when it backscatters from the electrostatic potential of an atomic nucleus. For typical relativistic velocities this process occurs on the 10 −21 s time scale, allowing it to be treated as an instantaneous event even compared to electron dynamics. When the transferred energy is larger than what is required to remove an atom from the immediate vicinity of its lattice site (called the displacement threshold), knock-on damage occurs.
At room temperature, pristine graphene is damaged 27, 28 at electron acceleration voltages above 80 kV (corresponding to an experimentally estimated 28 displacement threshold of 21.14 eV), even leading to the amorphization of the material 49 during extended experiments at 100 kV. Excitations in highly conductive graphene are damped extremely fast, and each impact can thus be accurately described as a perturbation of the equilibrium state 28 . How well this assumption holds for imperfect structures needs to be confirmed, but early indications show a puzzling discrepancy with theoretical expectations for the rate of bond rotations under 60 kV TEM observation 56 , as well as at impurity sites as we discuss below.
For atomic-scale manipulation of structures with impurities, mass is important since heavier heteroatoms receive less energy in a momentum-conserving interaction with an electron. However, carbon atoms next to an impurity tend to be more weakly bound than atoms of the bulk, leading to their preferential ejection 57 . This effect can impose a direction for atomic motion caused by sub-displacement electron impacts. For three-coordinated Si impurities in graphene irradiated by 60-keV electrons, these considerations result in a striking effect 34 . Although electrons of such energy are unlikely to cause outright damage, they can momentarily displace the C neighbor of Si. In the resulting dynamical out-of-plane process revealed by modeling 34 (Fig. 3a), the Si relaxes into the vacancy created by the impact on C, which is pulled back into the lattice on the opposite side. This makes the switching of places of the Si and C-reminiscent of flipping a digital bit from one state to the other one-highly directional and enables control over it 9,34 . In the case of bond rotations, the process is very similar 51 (Fig. 3b). For bonds in defective graphene structures 36 , rotations that lead to rare atomic configurations (such as carbon rings with four or fewer atoms) are less likely to occur than those involving only pentagons, hexagons and heptagons. Hence, it should be possible to control the atomic structure by placing the electron beam on top of the bond one wishes to rotate to maximize the electron dose on the two involved atoms. To our knowledge, control of bond rotations has not been attempted. However, we recently showed that by iteratively placing the electron probe on top of a selected carbon neighbor, it is indeed possible to "pull" a silicon impurity through the graphene lattice 9 .

First principles modeling: pushing the limits
Modeling atomic dynamics accurately over the picosecond timescales required to extract displacement thresholds is demanding. Most computationally affordable tight-binding (TB) models have failed to yield accurate thresholds for 2D materials with 3/12 non-carbon atoms, necessitating the use of more expensive density functional theory (DFT) for dynamical simulations (e.g. N-doped graphene 57, 58 , hexagonal boron nitride (hBN) 59,60 ). These studies have established DFT-based molecular dynamics (DFT/MD) as the most reliable way to theoretically estimate the displacement threshold energies.
In addition, at electron energies near the threshold, the vibration of nuclei in the direction of the beam become important in activating otherwise energetically prohibited processes 27, 28 . By modeling the atomic motion via a quantum description of lattice vibrations, it is possible to estimate the cross section of the knock-on process. When the velocity distribution in the perpendicular direction was included in the model, the probability of displacements from 12 C and 13 C graphene could be directly predicted from theory 28 . However, all of the tested exchange correlation functionals (including some with a description of the van der Waals interaction) seem to overestimate the displacement threshold, with the closest match within 0.3 eV (1.4%) of the best-fit experimental threshold. Although this agreement is good enough that the DFT-derived displacement cross section values are within experimental uncertainties, this is achieved by selecting the functional providing the closest match rather than the physically best motivated theoretical model. The explicit phonon calculations required are also only feasible for small numbers of atoms, making it difficult to extend precise analyses to systems with impurities. For their displacement, discussed below, we thus merely correct the mass term in the mean square velocity with the impurity mass.
With these caveats in mind, in Table 1 we show our reanalysis of published data using the latest out-of-plane vibration model 28 . For the case of N 57 and Si 34 , we find discrepancies of 1.7 and 4.1 eV in the simulated thresholds for the ejection of C atoms neighboring the impurity. Using data collected on B during the experiments described in 55 , we find discrepancies of 2.1 and 4.5 eV for B and C ejection, with the theoretical thresholds leading to negligible displacement rates. Calculating cross sections with a 50% increased mean square velocity of vibrations would reduce the discrepancies, but even such a high correction does not bring the consistently underestimated theoretical cross section values into agreement with experiment.
Finally, we have occasionally observed the ejection of the N impurity itself upon intense spot irradiation at 60 keV, hinting at the possibility of dose-rate dependence at impurity sites that is not included in the modeling, or to the occurrence of rare chemical etching events. The most serious discrepancy with current theory, however, results from the observed rate of reversible jumps of a pyridinic N dopant across a vacancy 54 . The thermal barrier for such a transformation is at least 4 eV 61 , leaving beam activation as the only plausible mechanism even in high temperature experiments (we have once also observed the same event at room temperature). The experimental rate calculated from seven consecutive jumps corresponds to a cross section of over 30 barn, whereas DFT/MD modeling fails to reproduce the event (the jump is only initiated for in-plane momentum transfers that are unphysically large for the experimental geometry), let alone quantify its probability.
The physical reasons behind such differences need to be understood and the theoretical treatments correspondingly improved to provide accurate predictions for manipulation experiments. Apart from neglecting vibrational impurity modes, the remaining inaccuracy of DFT/MD could be due to one or more of the presently necessary approximations: 1) the system size is limited due to the computational cost; 2) the simulation timestep is likewise limited, possibly leading to cumulative errors in the integrated equations of motion 64 ; and 3) the description of the dynamics may be inadequate either due to the approximation of exchange and correlation, or the lack of time-dependence of the electronic degrees of freedom.
Although the out-of-plane buckling of silicon 32 (or phosphorus 35 ) provides a strong asymmetry for the atomic motion even for momentum transfers completely perpendicular to the plane, for impurities with planar bonding geometries such as N and B, in-plane components of the momentum either from the electron impact or from phonons (or contraction of bonds at the moment of the impact due to the vibrations) may be required to explain the observed dynamics. A coordinated experimental and theoretical effort should be able to bring light on these issues.
A related but different topic where first-principles or other type of quantitative modeling has not even been attempted is radiation damage by ionization or electronic excitations (also known as radiolysis) 65 . Although irradiation effects in graphene seem to be adequately described solely by the knock-on effect 28 , as the materials zoo is extended-especially if soft matter and molecular structures are included-radiolysis becomes important. Ionization damage is already the most obvious hindrance for manipulation of non-graphene materials, and our understanding of radiation damage is inevitably incomplete without its quantitative understanding. Isotope-labeled hBN or transition metal dichalcogenides would make for excellent systems to isolate radiolysis from knock-on damage, especially when supplemented with experiments combining these materials with graphene to mitigate ionization 66,67 .

Outlook: paths forward
To develop STEM into a practical manipulation technique, in addition to better modeling of beam-induced dynamics, improvements in sample preparation and the automation of manipulations are required. In our view, Si impurities in graphene provide the most promising system for initial experiments, as shown in Fig. 4. In this case, the process of moving the Si atom in graphene was carried out by manually directing the beam. While this is how also the first successes of STM were achieved, it is impractical to fabricate complex nanostructures in such a manner. Fortunately, the modern computerized STEM is well-suited for automation, and the required software tools can be swiftly developed, along the lines discussed in 9, 37 .

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Sample quality presents another obstacle for large-scale manipulation. Even a single atomic layer of contamination prevents such experiments, and finding clean areas, especially those that contain heteroatoms 26, 35 , is difficult. Even when such areas are found, contamination often gathers under the beam and obscures the surface 68 . Finally, a sufficient quantity of heteroatoms need to be introduced into the lattice in the first place, but without causing significant structural damage or contamination. Ion implantation is a particularly promising technique, but contamination remains a serious issue 26,35 . Cleaning the samples outside the microscope vacuum 69, 70 seems insufficient for ideal samples, since atmospheric exposure will be particularly detrimental to the chemically more reactive impurity sites. In situ heating of samples appears more promising, either in a dedicated sample holder with a resistive heating element 54 , via Joule heating 71 or using a laser 72 .
Current literature almost exclusively provides examples of reversible electron-beam driven dynamics in graphene, largely because of its availability and robustness as an electron microscopy specimen. However, there is no fundamental reason why other 2D materials 73 could not host similar processes. If ionization damage can be mitigated, possibilities include 2D SiO 2 74 , silicene 75 and phosphorene 76 , which all share bond-rotation-type defects with graphene. Other candidates could be directed vacancy or impurity atom migration in transition metal dichalcogenides 77 .
Finally, although two-dimensional crystals are ideal for manipulation due to their relative simplicity both experimentally and theoretically, the penetration of an electron beam through a sample offers the possibility of bulk manipulation. The methods and tools developed in 2D would largely translate to materials more generally, allowing us to eventually tackle the full complexities of three-dimensional crystals 37 .

Conclusion
The challenges that we have discussed above are significant, but so is the current rate of progress. The rewards, however, are even greater: all properties of a material are determined by its chemical structure, whose precise control would allow these to be designed at will within the bounds given only by the laws of physics and material stability. Electron beam manipulation will in the near future allow the creation and tailoring of covalently bonded 2D nanostructures, with a further possibility of extending the technique to 3D. Initial experiments could for example target designed molecules embedded within graphene 78 , plasmonic nanoantennas 79 , and novel quantum corrals 80 . Once established, atomically precise manipulation in the electron microscope will open a new playground for materials science and engineering at the ultimate limit of control. a b Figure 3. Mechanisms for single-atom manipulation in graphene revealed by modeling. The carbon atom undergoing out-of-plane dynamics caused by the nuclear backscattering of a single electron is colored black (and the silicon in panel a, yellow). By focusing the electron irradiation on the desired atom (denoted by the red circle in the first frame), it is possible to direct the dynamics. a) The silicon-carbon bond inversion (simulation published in 34 ). b) The Stone-Wales bond rotation (momentum transfer at an 12.5 • angle, simulation published in 51 ). Table 1. Comparison between experiment and theory for atomic displacements from graphene, its impurities, and their carbon neighbors. Conversions between threshold energies T d (in eV) and cross sections σ (in barn) are based on the McKinley-Feschbach approximation 62 with the experimental (exp) electron energy E e . The influence of out-of-plane velocities at room temperature is included via the phonon dispersion of pristine graphene 28 , scaled where applicable by the mass of the impurity atom. Theoretical values (sim) are based on DFT/MD 28, 34, 57 with the PBE functional 63 (better match was obtained for pristine graphene with another one 28 ). No events were observed either experimentally or in the simulation when "-" is shown. The last column cites the publication describing the experiments from which the data was extracted. KO refers to a knock-on event, X-graphene refers to graphene with heteroatom dopants of element X, N sub/pyr refers to substitutional/pyridinic nitrogen bonding, and C@X refers to a carbon atom neighboring dopant X.

Electron beam manipulation
Proof of principle experiment Bottom: Proof-of-principle experiment (MAADF detector, 60 kV, time between frames 15 s). In the first frame, the three-coordinated Si impurity selected for manipulation is denoted by the dashed circle. In the following frames, the solid dots denote the location of the manually parked electron beam, the solid arrows the cumulative single-site jumps, and dashed arrows jumps over more than one site. (Adapted with permission from 9 , Copyright 2017 Elsevier B.V.)