Directly controlling the position of a single dopant atom offers opportunities for quantum engineering, such as quantum computing, (10,11) optoelectronics, (12) or catalysis. (13,14) Bismuth was recently identified as a potentially superior candidate for donor-based quantum computing, (15−20) and its large atomic number relative to Si makes Bi an ideal test subject for addressing difficulties related to single-atom manipulation in three-dimensional crystals. However, incorporation of Bi into an (isotopically purified) Si film is problematic (21−24) because Bi is almost insoluble in Si due to the large difference in covalent radius. (25) Moreover, as evidenced by the efforts in the STM-based approach, (4) progress in directed single-atom manipulation is hindered by the limited experimental means to address single atoms within a solid. Even elementary questions such as “where exactly are the dopants?” often remain unanswered, and accurate placement and determination of dopant locations below the surface, therefore, remains a key challenge. (26−28)

In Richard Feynman’s famous 1959 lecture, he proposed the idea of building nanoscale devices by directly arranging atoms “the way we want” and indicated the need for an improved electron microscope. (1) These ideas were reflected in the recent suggestion to use an electron beam to directly manipulate materials at the atomic scale. (2) However, such an undertaking requires precise control over the size and position of the electron probe, which has only recently become possible through aberration correction. The current state of the art in manipulation at the atomic scale includes the positioning and imaging of single atoms, (3) or even atomic scale surface lithography, (4) using scanning tunneling microscopy (STM) and atomic force microscopy (AFM), (5,6) performed upon two-dimensional surfaces. Recently, promising results for control of substitutional Si atoms found in two-dimensional single-layer graphene films have been demonstrated in a scanning transmission electron microscope (STEM). (7−9) Ultimately one wishes to achieve controlled positioning of individual atoms, especially impurities, within a three-dimensional crystal, but no method for targeted manipulation of a specific atom within such a structure exists.

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Here we demonstrate both the growth of heavily Bi-doped Si(111) and Si(100) thin films by solid-phase epitaxy and the ability to controllably move and place the Bi dopants below the surface of a Si crystal at room temperature using STEM. This capability was indicated by two findings from our density functional theory (DFT) calculations: (1) the strain induced by the Bi dopant lowers the Si vacancy enthalpy of formation, allowing for Si vacancies to be preferentially created adjacent to the large Bi atoms, and (2) there is no significant energy barrier for the Bi atom to hop into these vacancies once they have been formed. Using the electron beam, we exploit this phenomenon to direct and place the Bi dopants in specific columns within an oriented Si crystal. We explored the effect of the sub-ångstrom-sized electron beam on single dopants in aberration-corrected STEM at various accelerating voltages between 60 and 200 kV. By using an accelerating voltage of 160 kV, which is close to but above the knock-on damage threshold of silicon, we achieve control of dopant placement while reducing damage to the surrounding crystal. The method presented in this work is an indispensable step toward the fabrication of functional single-atom devices through the direct positioning of single dopants within a three-dimensional material.

Z-contrast STEM images of a Bi-doped Si(111) layer grown using nonequilibrium solid-phase epitaxy (see versus 3.5 eV in pure Si) due to the strain induced by the dopant ( 1 Figure shows-contrast STEM images of a Bi-doped Si(111) layer grown using nonequilibrium solid-phase epitaxy (see Methods ). Plan view images along the [111] direction ( Figure 1 a) show well-dispersed Bi atoms distributed over the sample. A cross-section view ( Figure 1 b) ([110] direction) confirms the presence of a nominally 10 monolayer (ML) thick Bi-doped Si layer (1 ML = 0.31 nm). When imaged at high magnification in a 200 kV STEM ( Figure 2 a), we find that some dopants exhibit “streaks” in their intensity, and others are only partially visible. This effect is not rooted in microscope instabilities, but arises because the dopant atoms move during the image scan. (29) To confirm this inference, Figure 2 b shows a selection of frames extracted from a fast sequence of larger images taken at 200 kV. Supporting Figures S1–S3 show a similar selection of frames, but for images acquired at 60, 100, and 160 kV. The apparent interaction of the beam with the dopants is enabled by beam-induced Si dynamics. For a 200 kV accelerating voltage, the maximum amount of energy that can be transferred to a Bi atom in a single elastic collision is less than 2.5 eV, (30) whereas the diffusion barrier for Bi inside Si is about 4.1 eV, (31) implying that, even at the highest beam energy used here, direct energy transfer to Bi is insufficient to cause the Bi mobility. However, because the Si atoms are lighter, significantly more energy (up to about 18 eV at 200 kV) can be transferred to Si in a single elastic collision, for which the bulk knock-on damage threshold is roughly 12.5 eV, corresponding to an accelerating voltage of about 140 kV. (32) At accelerating voltages below the knock-on damage threshold of Si (100 and 60 kV) we see almost no dopant movement ( Supporting Figures S2 and S3 ). Using DFT calculations we found that the Si vacancy enthalpy of formation is significantly lower at sites adjacent to substitutional Bi atoms (1.5 eV3.5 eV in pure Si) due to the strain induced by the dopant ( Supporting Figure S4 ). Further, we used the nudged elastic band method to calculate the energy barrier for a Bi to hop into such a vacancy to be only about 40 meV, meaning that such a hop readily occurs thermally. When a single atomic column is irradiated by an electron beam with an energy above the knock-on damage threshold of the crystal, there is a high probability that an atom will be displaced from its lattice site. In the case that all atoms had the same bonding environment, they would have a similar probability of being displaced, depending on the local irradiation (taking into account the 3D propagation of the beam). In general, surface atoms are most likely to be removed from the lattice because they have fewer bonds. In the case where the Si is strained by a neighboring Bi atom, reducing the vacancy enthalpy of formation nearby, these atoms are more likely to be displaced or may even attract existing vacancies. We conclude that the electron beam can easily generate Si vacancies adjacent to substitutional Bi atoms and, through regulated beam motion, enable controlled movement of single Bi atoms to adjacent lattice sites.

Figure 1 Figure 1. Z-contrast STEM images of the Bi-doped layer on a Si substrate. (A) Si(111) view of dopants well dispersed over the sample. (B) Si(110) cross-section view. A thin Bi-doped layer is clearly visible below the surface, but not inside the substrate. Note that the thickness gradient in the STEM specimen gives an overall increase in intensity moving away from the surface and that there is some contamination on the (rough) microscope sample surfaces. (C) High-magnification image of Si(110) with bright Bi-containing atomic columns clearly visible.

Figure 2 Figure 2. Z-contrast images showing nondirected beam-induced motion of Bi dopants in Si(110). (A) Single slow-scanned image of the doped layer recorded with an electron dose of about 1.3 million electrons/Å2. Occasional localized streaks running in the horizontal direction indicate dopants moving during the image scan. (B) Four panels from the same region extracted from a set of fast-sequential frames acquired at 200 kV, with a nominal dose of 100 000 e/Å2/frame. Dopants move to different positions over the sequence of images.

In Figure 3 we demonstrate the experimental ability to control the dopant movement and selectively place single Bi atoms within a Si crystal. The frames displayed in Figure 3 are extracted from the video shown in Supporting Movie 1 . To direct the dopant movement, we used controlled positioning of the electron beam operated at 200 kV. First a high-angle annular dark field (HAADF) image is acquired ( Figure 3 a) to act as a survey image. With the scanning stopped, the electron beam is manually positioned near a column containing a Bi atom. A path is then traced by stepping the electron beam from column to column ( Figure 3 c–f). A survey image afterward reveals that the Bi atom has followed the movement of the beam, ending up in the designated position ( Figure 3 b). In fact, two Bi atoms are moved into the column where the beam was last positioned: one that was targeted for directed placement and one that was located in an adjacent column before beam positioning. The intensity of this column after Bi positioning is higher than either of the Bi-containing columns previously, indicating that two Bi atoms are occupying the column. Remarkably, this directed movement is highly reproducible, as shown in Supporting Movies 1–3 . Significantly, the Bi atom appears to be on the Si column and stable at the new position. Nudged elastic band DFT calculations ( Supporting Figure S5 ) show that this behavior is not consistent with the motion of Bi atoms along the surface, in which case they are adsorbed in hollow sites (between columns) on the surface.

Figure 3 Figure 3. Electron-beam-directed placement of a Bi atom in Si(110). At 200 kV the Bi dopant, indicated with a white circle, is moved several unit cells by following the path of the electron beam (marked with white dashed arrows). Blue circles indicate the reference Bi dopants that do not move between frames. (A) Image acquired before dopant movement. (B) Image acquired after directed dopant movement. (C–F) Frames showing the location of the electron beam as it was used to guide the Bi atom. Image scanning was paused, and the electron beam was manually moved to direct the Bi dopant. Frames selected from Supporting Movie 1.

We now use the electron beam to assemble atomic-scale structures. In Figure 4 , we show that several Bi atoms in a single region can be individually repositioned into neighboring columns, demonstrating precise control of dopant placement within a two-dimensional projection of a three-dimensional crystal. In Figure 4 , some untargeted Bi atoms randomly move due to repeated scans at 200 kV, consistent with our previous observations. However, this random movement does not negate the fact that we demonstrate controllable positioning of targeted Bi dopants. By lowering the beam energy closer to the knock-on damage threshold of Si, we reduce the vacancy formation probability per incident electron, allowing for better placement of single atoms. In Figure 5 , we have reduced the accelerating voltage to 160 kV to draw a triangular dopant lattice composed of six regularly spaced Bi atoms in projection ( Figure 5 b). Supporting Figure S6 shows an estimate of the Bi dopant depth based on a 10 nm thick Si crystal. Supporting Movie 3 shows the process of manually assembling this more complex atomic structure. While there are still technical hurdles toward optimizing the accelerating voltage of the microscope and dopant concentration of the samples, these results demonstrate that the electron microscope can be used as a tool for building device architectures at the atomic scale ( Figure 4 ) and nanoscale ( Figure 5 ) inside a three-dimensional Si matrix.

Figure 4 Figure 4. Example of controlled dopant movement using the STEM electron beam at 200 kV. (A) Image acquired before any Bi movement. Only one Bi atom is located within the marked white diamond region. (B) Image acquired after directing several Bi atoms to a small area. At least five Bi dopants are now located within the marked white diamond region. The dashed circles indicate atoms directly positioned, and the dashed square indicates an atom that did not move. Dopant manipulation occurred over a period of 9 min with periodic scanning to form images, which gives some additional random dopant movement.

Figure 5 Figure 5. Assembly of a triangular dopant lattice. By reducing the accelerating voltage to 160 kV, we create fewer Si vacancies, allowing us to assemble a complex structure with the electron beam. (A) Distribution of Bi atoms in a Si(110) crystal before atom manipulation. The dashed circles indicate Bi atoms directly positioned to form a triangular lattice. (B) Triangular dopant lattice assembled by directing the placement of six Bi atoms, illustrating control over direct atom placement within a Si crystal. Frames extracted from Supporting Movie 3.

Although it is reasonable to assume that we are creating a chain of vacancies through the Si crystal, we never observe a Bi atom moving freely back along the path traced by the electron beam. This suggests one of two further steps is occurring: Either an interstitial Si, created through the knock-on process, fills in the vacancy left by the Bi atom or the vacancy rapidly diffuses away from the dopant atom. Point-defect studies published in the literature suggest that either mechanism is plausible. However, the conventional wisdom regarding point-defects in Si has been acquired primarily through methods that apply a more uniform amount of energy to a macroscopic Si wafer. (33−35) Here, we use a focused electron beam to supply energy to a very small portion of the sample, approximately one atomic column at a time. The system will therefore lack the energy for long-range defect migration, either away from or toward the Bi dopant; thus the interstitial Si will be near enough to allow vacancy–interstitial recombination, filling in the vacancy left by the Bi and preventing backward diffusion. (33)

The accurate placement of donor atoms currently presents a major challenge for the synthesis of quantum devices. (11) Here we demonstrate the ability to control the positioning of individual Bi atoms within a two-dimensional projection of a solid, providing a powerful method for fabricating atomically precise samples of doped silicon. Supporting Figure S7 shows as-positioned dopants after time without electron beam exposure. The lack of movement of the dopants when not exposed to the electron beam demonstrates the potential of this method to produce stable structures. Supporting Table S1 includes the success rate of dopant positioning. On the basis of 226 recorded attempts at dopant positioning, we achieve a success rate of about 75%, although the combination of imaging and motion available in the STEM allows multiple attempts to move dopants to the desired location.