Supplementary Figure 1 Atom gating results for Sn and Si a-b STM images showing Sn atom transfer by atom gating. The cross indicates where the tip is

Transcription

1 Supplementary Figure 1 Atom gating results for Sn and Si a-b STM images showing Sn atom transfer by atom gating. The cross indicates where the tip is approached during atom gating. c-d STM images showing Si atom transfer by atom gating. The presence of two Si adsorbates in adjacent HUCs leads to the formation of a Si tetramer, which is located over the central dimer of the Si(111)-(7x7). The white dashed triangles and rhombus mark the initial (a and c) and final (b and d) locations of adsorbates transferred by gate control.

2 Supplementary Figure 2 Distance dependence of AFM/STM observables during atom gating a Typical <I t (z)> curves acquired at V s =-500mV, revealing the evolution of the current (left axis) and conductance (right axis) during Au atom gating as a function of the tip-sample relative displacement. b Variation of the energy dissipation as a function of tip-sample distance, simultaneously measured with <I t (z)> during Au atom gating. Note that the onset of the Au atom jumps during gating is accompanied by the enhancement of the dissipation signal, and the value reaches 0.6 ev/cycle at close approach. c Typical short-range force versus distance curve in the retraction, which is converted from the f(z) curve as depicted in Fig. 2b of the main manuscript. The curves are divided into three characteristic parts, having different slopes in the retract <I t (z)> curve. Regions indicated by i, ii, and iii correspond to contact, transition, and tunneling regime, respectively. Blue lines along the vertical axis split the regions. The dotted curves in (b) demonstrate the expected dissipation signal at sufficiently low temperatures. The orange and black dotted curves in (c) correspond to expected F SR (z) curves on a Au diffusing surface and on Au trapped below the tip, respectively. The inset schematics in (c) show the two situations.

3 Supplementary Figure 3 Influence of the accompanied atom/clusters on appearance of Ag clusters in STM images a STM images showing the influence of Ag atom transfer into a NS close to the existing Ag cluster formed at the unfaulted-huc of Si(111)-(7x7). b The line profiles traversing over the Ag clusters on the images showing Ag 11 (black), Ag 12 (red), Ag 12 with an additional Ag atom diffusing within the surrounding NSs (blue), and Ag 11 with Ag 3 cluster (green). Note that the presence of the Ag 3 cluster neighboring the existing Ag 11 cluster modifies the topographic height of the center cluster due to surface electronic modification, whereas a single Ag atom neighboring the Ag 12 does not.

4 Supplementary Figure 4 Snap shot STM images of Ag clusters taken from Supplemental movie 7 Upper panel (a-c) shows the isolated Ag 3, Ag 4, and Ag 5 clusters. Lower panel (d-f) shows Ag 11 structure accompanied by the formation of Ag 3, Ag 4, and Ag 5.

5 Supplementary Figure 5 STM images of Pb 3 Si cluster with two different configurations assembled by atom gating a STM image showing the Pb 3 Si isomer. b STM image showing the stable form of the Pb 3 Si cluster, which is transformed from the Pb 3 Si isomer in (a). Note that this transformation is irreversible. Once the stable structure is formed, the transition back to the isomer never occurs.

6 Supplementary Table 1 Acquisition parameters Data Mode Set point V s [mv] f 0 [Hz] k [N/m] A [Å] Fig. 1b and 1c Static-STM 30 pa Fig. 1d and 1e Static-STM 50 pa Fig. 1f and 1g Dynamic-STM 40 pa Fig. 1h and 1i Dynamic-AFM -2.1 Hz Fig. 2a Static-STM Fig. 2b and S2 Dynamic AFM/STM Fig. 3a Static-STM 30 pa Fig. 3d Static-STM 40 pa Fig. 4a-d and S3 Static-STM 50 pa Fig. 4e-k Static-STM 30 pa Fig. 4l-o Static-STM 30 pa Fig. S1a and S1b Dynamic-STM 20 pa Fig. S1c and S1d Static-STM 40 pa Fig. S5 Static-STM 30 pa Movie 2 Dynamic-STM 40 pa Movie 4 Static-STM 30 pa Movie 5 Static-STM 30 pa Movie 6 Static-STM 50 pa Movie 7 and Fig. S4 Static-STM 30 pa Movie 8 Static-STM 30 pa Movie 9 Static-STM 30 pa

7 Supplementary Note 1 Single atom diffusion within a half unit cell (HUC) of the Si(111)-(7x7) surface The observation of diffusion of single Ag atom within a HUC of the Si (111)-(7x7) surface was previously reported by variable temperature scanning tunneling microscope (STM) and DFT calculations [1]. Single adsorbate atom on the 7x7 surface travels among the various adsorption sites over the surface potential minima in a HUC at room temperature (RT); these minima are known to be multi-coordinate sites rather than the tops of Si adatoms and rest atom sites. It was shown that the appearance of a HUC associated with a single Ag adsorbate in STM image is changed under the low temperature condition. At a lower temperature, fuzzy aspect of a HUC turns into an asymmetric pattern, showing only one bright protrusion due to the suppression of the thermal diffusion of adsorbate atom. Consequently, the single adsorbate atom is located on one of the particular adsorption sites. However, it is still difficult to be ensure that the observed pattern is related with a single atom, because the STM images of adsorbate atoms are influenced by the electronic effect. Therefore, theoretical investigations combined with the STM images were performed. By comparing simulated and measured STM images, it was revealed that the appearance of the single adsorbate at this particular site in STM images was well reproduced by the DFT calculations involving single Ag atom at a multi-coordinate site. Thus, it was concluded that the bright/fuzzy aspect of a HUC at RT is indeed the result of frequent hopping of single adsorbate atom among various adsorption sites offered by the surface at much faster rates than that of the scanning speed of the STM tip.

8 Supplementary Note 2 Atom gating by STM Single atoms deposited on the Si(111)-(7x7) surface, such as Au, Ag, Pb, Sn, and Si, thermally diffuse within HUCs at RT. They can travel among various potential minima within the HUCs; these potential minima are known to be multi-coordinate sites rather than the tops of Si adatoms and rest atom sites [1-3]. The rate of interdiffusion between two HUCs is extremely lower than that of intradiffusion within a HUC [4-7]. A potential energy barrier existing between two NSs suppresses the adsorbate diffusion across the boundary. Thus, we can regard HUCs as nanospace (NS) arrays confining the adsorbate atoms that are diffusing at RT. We found that the transfer of an adsorbate diffusing within a NS to an adjacent NS can be induced by the tip proximity near the border, but slightly shifted away from the NS where the diffusing atom is located. The gate associated with the potential energy barrier that hinders the mobility of adsorbates between NSs can be opened by the tip proximity. This gate-opening process can be facilitated by the tip through a local energy barrier reduction near the limit that allows a thermally activated process between the NSs, enabling the adsorbate atoms to hop across the boundary of two NSs (atom transfer). This process is a purely mechanical effect caused by the formation of chemical bonds between the outermost apex atom and the adsorbate atom trapped on the surface, which induces a strong modification in the energy landscape for the adsorbate atom. The Supplementary movie 1 demonstrates the principles of atom gating in a static STM. The surface-energy potential of two neighboring NSs is depicted as two blue boxes separated by a gate i.e., a potential energy barrier. Single adsorbate diffusion within one of these NSs is indicated by an orange ball. When the tip approaches the boundary slightly shifted from the center, the single adsorbate hops across the boundary. The adsorbate is then trapped at a local surface potential minimum created by the interaction with the tip, which results in the formation of an atomic junction as discussed in the main manuscript. Atom gating is a highly controllable technique that can be applied to various adsorbates and surfaces possessing periodic NS arrays. Here, we demonstrate in detail various atom transfer processes by the gating method. Supplementary movie 2 shows the sequence of atom gating for a single Pb atom. The transfer of Sn and Si atoms between two adjacent NSs using the atom gating method is also demonstrated in Supplementary Figure 1. The HUCs involving single Sn and Si atoms appear brighter, with noiselike features, resembling the previous observations [8-10]. The gating operation for a single Sn atom by STM tip is shown in Supplementary Figure 1a and 1b. The Sn atom can be successfully transferred between two NSs by bringing the tip close enough above the position marked by the cross in Supplementary Figure 1a. The same procedure can be applied to the Si adsorbates. One of the Si adsorbates in Supplementary Figure 1c is transferred into the adjacent NS. As soon as two Si atoms are adsorbed in the neighboring HUCs, a Si tetramer is spontaneously formed at the boundary region of the HUCs, as shown in Supplementary Figure 1d. Si tetramer was previously observed as a self-assembled cluster [8,11]. Two Si atoms originate in two Si adsorbates while the other two Si atoms are originally center Si adatoms. The details will be discussed elsewhere.

9 Supplementary Note 3 Experimental evidence of the Au atom trapping below the tip by the chemical bonding force The stochastic fluctuations of current around z=1.2 Å in the retraction curve (i.e., transition region of Fig. 2(a) of the original manuscript) clearly separate two characteristic regions: trapping region at closer distances and free diffusion region at far tip-sample distances. In the transition region, the current fluctuates by more than one order of magnitude. This change can be explained by the consecutive trap and release of the adsorbate below the tip. When an adsorbate is locally trapped below the tip, the effective tip-surface distance is reduced by the height of the adsorbate, typically 1 Å. The trapped region (z<1.2 Å) can further be divided into two separate regions, namely, plateau-like region (0.7 Å<z<1.2 Å) and compressed region (z<0.7 Å). The current in compressed region exhibits distance dependence while it is constant in the plateau region. Furthermore, the noise level in these regions shows clear difference. While the noise level is about 10 % in compressed region, it is about 1 % in the plateau region. The apparent difference in the noise level can be attributed to the difference in the stability of the atomic junction formed between tip and adsorbate/surface system. The chemical bond established between the tip and adsorbate/surface system in this plateau region involves only the foremost atom of the tip and the adsorbate Au atom on the surface, rather than the surrounding Si adatoms and second layer atoms in the tip. This is a strong evidence that the stable atomic junction is maintained in the plateau region. On the other hand, current noise increases at the compressed region because the junction is unstable due to the onset of repulsive interaction force and the additional contribution from the surrounding atoms on the surface as well as the second layer atoms in the tip.

10 Supplementary Note 4 Conductance through single atomic junction We determined the conductance (G) at the tip-au-surface atomic junction. We obtained G=2.2 x 10-4 G 0 as the quantized conductance through a single Au atom junction (see Fig. 2a of the main manuscript). Experiments with different atomic junctions formed between the Au atom and several different tips provide G values in the range of 10-4 to 10-3 G 0. These values are much smaller than those obtained in pure gold atomic junctions [12] where the conductance is close to 1 G 0. Furthermore, the conductance measured over the bare Si surface with various different tips is around G=2 x 10-2 G 0 [13]. The low observed conductance probably originates from the energy level mismatch between Au and Si surfaces, which in turn results in a much smaller transmission coefficient than the one observed in a perfect ballistic transport. This observation can be understood by the electron scattering at the junction. It has been reported that the scattering arising from the mismatch of electron wavefunctions at the tip-surface interface causes the transmission probability through a conduction channel deviated from 1 [14]. The incoming electron wave is reflected due to the orbital energy level mismatch in the junction.

11 Supplementary Note 5 Mechanism of atom gating in dynamic AFM/STM To shed some lights on the mechanisms underlying the gating operation, we performed force-distance spectroscopy measurements during atom gating using an atomic force microscope (AFM). In dynamic AFM/STM mode, the tunneling current flows instantaneously at a close tip-surface distance during cantilever oscillation. A time-averaged tunneling current (<I t >) is then detected since the bandwidth of the current-to-voltage converter is usually much smaller than the resonance frequency of the cantilever [15]. The simultaneously measured distance dependence of <I t > and the energy dissipated from the cantilever during the gating of the Au atom are shown in Supplementary Figure 2a and 2b, respectively. Our AFM was operated under constant oscillation amplitude using the frequency modulation detection method [16]. The additional excitation energy supplied to the cantilever to maintain the oscillation amplitude during the tip-sample interaction is related to the energy dissipated in the system. We note that the f(z) curve acquired simultaneously is displayed in Fig. 2b of the main manuscript. When the oscillating tip approaches the surface for the atom gating operation, <I t > varies exponentially with distances (see the black curve in Supplementary Figure 2a). Then, discontinuous jumps are observed at z=0.3 Å in all signals (see black curves), due to a Au atom hop from the original NS to the adjacent NS located below the tip. During retraction (red curve), <I t > smoothly decreases without fluctuation, whereas in the static STM case fluctuation does occur (see Fig. 2a of the main manuscript). The disappearance of the observed fluctuations in the <I t (z)> curve acquired with dynamic AFM/STM can be attributed to the averaging effect of the cantilever oscillation. The measured tunneling current is averaged over many oscillation cycles. Once the Au atom is transferred to the NS below the tip, the trapping and release of the Au atom are repeated due to the large cantilever oscillation amplitude used in our experiments. This consecutive trap/release cycles of the Au atom accompanied by the large amplitude oscillation will be wiped away when the closest tip-sample distance is out of the interaction region. Supplementary movie 3 schematically demonstrates the AFM-based gating process, revealing the trapping and release of an adsorbate under the oscillating tip. To further explicate in detail our observations during atom gating, we have divided the <I t (z)> curve in retraction into three different regions, which are determined by the observed differences in their slopes; perfect trapping and release [(i) z 1.2 Å], transition from contact to tunneling [(ii) 1.2 Å<z<1.7 Å], and free diffusion region [(iii) z 1.7 Å]. These interaction regimes are separated by blue lines along the vertical axis in Supplementary Figure 2. In the perfect trapping regime (region i), <I t > decreases with smaller slope by increasing tip-sample distance. In this interaction regime, the formation and collapse of the tip-au-surface atomic junction are repeated for every tip oscillation cycle, and the ballistic electron current would flow through the junction at the lower turning point of tip oscillations. In the transition regime (region ii), the slope of the <I t (z)> curve is larger than that of the perfect trapping regime, and more importantly the Au atom is not trapped in every cantilever oscillation cycle. This part of the <I t (z)> curve corresponds to the fluctuated region of the I t (z) curve obtained with static STM, which was demonstrated in Fig. 2a of the main manuscript. The stochastic fluctuations of the current as observed in

12 the static STM are smoothed out by the averaging effect over multi cantilever oscillation cycles in the dynamic AFM/STM, not in a single oscillation. The Au atom trapping rate varies from 100 % at 1.2 Å to 0 % at 1.7 Å as the tip-sample distance increases. In the regime at z>1.7 Å (i.e., free diffusion region iii), the chemical bond arising between the Au atom and the tip is completely broken, and the tip cannot trap the Au atom anymore. Consequently, the Au atom thermally diffuses within the NS all of the time at any tip height in the cantilever oscillation cycle. The <I t > value changes by almost one order of magnitude when the tip is retracted from the perfect trapping to the totally free-diffusing region. By further increasing the tip-sample distance, <I t > decreases by following the basic tunneling law, i.e., the <I t > varies exponentially with distance. It is worth mentioning that, in the free diffusion regime (region iii), the <I t (z)> curve acquired during the tip retraction does not match the one obtained during the tip approach (see Supplementary Figure 2a). This disparity is caused by the Au atom diffusing within the HUC below the tip during retraction, which does not exist during tip approach. The topographic and electronic structure modifications induced by the Au atom diffusion on the surface enhance the tunneling current upon retraction, as is clearly apparent in Supplementary Figure 2a. The simultaneously measured energy dissipation channel provides additional insights into the dynamic evolution of the atomic junction during Au atom trapping and release. The onset of the Au atom trapping and release during gating is accompanied by the enhancement of the dissipation signal, reaching a value of 0.6eV/cycle at the closest approach (see Supplementary Figure 2b). The observed behavior can be attributed to the adhesion mechanism of dissipation as previously proposed in Refs [17-21], where a double-well potential energy surface causes energy dissipation. In our studies, the trapping and release of the Au atom causes a hysteresis in the interaction force during the approach and retraction cycle and this hysteresis produces the dissipation signal. The thermally diffusing Au atom is trapped below the tip at a certain tip height during the tip approach in one oscillation cycle. Then, the Au atom is released from trapping by the tip to start diffusion at a higher tip position during retraction. The atomic scale dissipation as observed in dynamic AFM is usually associated with instabilities at the tip-surface interface at close proximity [19-21]. Here, it is clear that the dissipation is caused by the trapping and release of the Au atom by the tip. This result provides direct evidence for the observed enhancement of the dissipation signal due to such structural rearrangements, and further supports the triggering mechanism of the gating as a purely mechanical effect. Force spectroscopy measurements also enable us to quantify the tip-adsorbate/surface interaction forces during atom gating. We can estimate the threshold force associated with the atom trapping and the chemical bonding force that can stabilize the atomic junction formed between tip and the surface. The short-range force contribution in f(z) was obtained by subtracting the long-range background contribution, which was estimated from the approach f(z) curve, from the retract f(z) curve. Then, the interaction force was obtained from the f(z) curve using the inversion procedure [22]. The short-range force (F SR ) during the retraction of the tip after Au atom hopping from neighboring NS by atom gating is depicted in Supplementary Figure 2c (which is the same curve as in the inset of Fig. 2b of the main manuscript). We obtained a threshold force of -0.1 nn, which is the force required to trap a single diffusing Au atom by the tip. This force value was estimated at a distance where the Au atom starts to diffuse freely without any tip trapping (i.e., z=1.7 Å). This particular interaction distance associated with the force threshold was determined from the characteristic slope of the <I t (z)> curve simultaneously acquired with the f(z) curve (compare Supplementary Figure 2a and 2c).

13 The F SR (z) curve displays a local minimum at z=1.2 Å, which roughly corresponds to the plateau region in the I t (z) curve obtained with the static STM shown in Fig. 2a of the main manuscript. It is therefore plausible to relate the force at z=1.2 Å to the force required to maintain the atomic junction. From z=1.7 Å to z=1.2 Å, the energy dissipation increases significantly while no dissipation is detected within measurement error at z 1.7 Å. The presence of energy dissipation indicates that the interaction force at this characteristic region (transition region ii) is nonconservative. The force hysteresis accompanied by the significant dissipation is likely to hinder the estimation of the short-range force required to maintain the atomic junction. Based on the adhesion mechanism of dissipation, we can estimate this force and explain the observed dissipation changes in the junction. As mentioned above, the reversible structural instabilities result in two different solutions in force on approach and retraction. These force solutions ( real forces) over a cantilever oscillation cycle, as expected for this nonconservative interaction, are sketched by the dotted curves in Supplementary Figure 2c. While the orange dotted curve represents the force curve that is expected for the diffusing Au atom within a HUC, the black dotted curve represents the force expected on the Au atom trapped by the tip, i.e., the tip-au-surface interaction force in the junction. The latter one is more attractive. At a sufficiently low temperature, one can assume that both forward and backward forces in a cantilever oscillation cycle follow the orange dotted curve until the closest tip-surface distance in the cantilever swing is larger than 1.2 Å. Once the closest tip position enters the region of z 1.2 Å, the force distance curve displays hysteresis, as shown by the gray arrows in Supplementary Figure 2c. During tip approach, the force curve follows the orange dotted curve at z>1.2 Å, then jumps at z=1.2 Å. After this point, the force follows the black dotted curve at z<1.2 Å, where the Au atom is trapped below the tip. The force continue to follow the black dotted curve, then another force branch with a larger attractive force minimum appears, which we discuss below. In retraction, the F SR (z) curve follows the black dotted curve until z<1.7 Å, where the Au atom is still trapped below the tip. A sudden jump in the force curve occurs at z=1.7 Å, and then it follows the orange dotted curve at z>1.7 Å where the Au atom diffuses in the HUC below the tip. In this situation, a steplike increase in the dissipation signal can be expected at z=1.2 Å, as shown by the dotted orange lines in Supplementary Figure 2b. The value of the dissipated energy at z=1.2 Å should be consistent with the area enclosed by the force hysteresis cycle (i.e., the orange and black curves encased by gray arrows in Supplementary Figure 2c). The experimental force curve converted from the f(z) curve in region ii and region iii must coincide with the expected forward curve on the diffusing Au atom, i.e., the orange dotted curve in Supplementary Figure 2c. At the contact regime (region i), the force extraction is not straightforward, as discussed previously [17]. In the case of a room temperature experiment, the transition between two energy branches becomes more complicated, making the force estimation difficult even at region ii. Trap and release becomes stochastic in region ii, leading to a random switch between two energy branches. Actually, the dissipation gradually increases in this interaction region instead of the steplike behavior (see Supplementary Figure 2b). To connect the expected forward/backward real forces to the measured force is not a straightforward matter anymore. We have discussed this situation in detail before [21]. The relationship between the expected forward/backward force and the force converted from the measured f, as well as the dissipation signal at RT, are discussed on the basis of the experiments and first principle calculations. At RT, the measured force in region ii should sit between the two branches such that the values at 1.7 Å and 1.2 Å coincide with those of the orange and black curves, respectively. Thus, the measured force corresponds to the curve smoothly connecting two branches of real forces, as we assumed in Supplementary Figure 2c. Therefore, we can

14 conclude that the chemical bonding force between the tip and the Au atom to stably maintain the atomic junction at z=1.2 Å is close to F SR =-0.6 nn. Since the value is in the class of a chemical bonding force [23], the gating mechanism can be attributed to a purely mechanical effect. At even smaller tip-surface distances (region i), the second force minimum appears in the F SR (z) curve. This force minimum is probably caused by the configuration change in the atomic junction due to atomic relaxations induced by the tip-au-surface interaction. As the tip moves closer to the surface, second-layer atoms on the tip-apex contribute to the interaction, resulting in a more attractive force. The further increase of the dissipation signal at z<1.2 Å is related to the onset of an additional dissipation channel, which stems from the tip apex or surface atom modifications [19-21]. However, this atomic junction is relatively less stable than the junction formed in the plateau region of the main manuscript.

15 Supplementary Note 6 Assembly of gold clusters Nanometer-sized Au clusters supported on surfaces have a wide range of applications, such as catalysts and single-electron transistors, as discussed in the main manuscript. To reveal the special properties of these fabricated clusters in practical applications, it becomes important to construct ordered and well-defined cluster arrays with a defined number of atoms. Nanoclusters constructed from a well-determined number of atoms may provide affirmative evidence of the unique size-dependent properties of clusters in nanocatalysis. This information is also important for computational modeling of the structures of fabricated clusters. Atom gating allows us to assemble Au clusters atom-by-atom into predesigned composition and sizes. Supplementary movies 4 and 5 show the assembly sequences of Au clusters in a faulted-huc and an unfaulted-huc of Si(111)-(7x7) surfaces, respectively. The transfer directions of the individual Au atoms that will form the Au N clusters are indicated by the blue arrows in the movies. Single Au atoms in the STM images look similar to those in previous STM images [24-25]. It appears that the two different HUCs (i.e., faulted and unfaulted-hucs) occupied by single Au atoms appear to be different from each other. Corner (center) adatoms look brighter than center (corner) adatoms in the faulted-huc (unfaulted-huc) involving single Au atoms in the filled-state STM images. The Au 5 and Au 6 structures spontaneously change their conformations among equivalent forms by following the threefold and/or the mirror symmetry of the surface. These changes are highlighted as Conformational change in Supplementary movies 4 and 5. Au 7 to Au 11 clusters in the faulted-huc exhibit a threefold symmetry in STM images and are similar to self-assembled clusters previously observed [26-27]. Three corner adatoms remain almost intact without participating in the chemical bond formation with Au atoms. When more Au atoms are added to Au 12, a bond between cluster atoms and the Si corner adatoms starts to form, thus breaking the apparent threefold symmetry. Some Au N clusters also form constitutional isomers just after one Au atom is added to the existing Au N-1 clusters. These isomers then spontaneously transform into stable structures in an irreversible manner. These clusters include the same number of atoms but exhibit different structures. The observed irreversible structural changes of clusters are specified as Stabilization in the movies. It is important to note that the lifetimes of the isomers differ between faulted and unfaulted-hucs, suggesting different interaction characteristic with the clusters.

16 Supplementary Note 7 Assembly of silver clusters Ag clusters on the Si(111)-(7x7) have been extensively investigated by STM in recent years [28-32]. Here, we reveal the results of our investigations into Ag clusters formed on the Si(111)-(7x7) surface, which are not discussed in the main manuscript. We compare the stability of the Ag clusters with that of Au clusters. Supplementary movies 6 and 7 show the assembly sequences of Ag clusters by the atom gating method. The single Ag atoms in the STM images look similar to those in previous STM images [1,30]. The two different HUCs that accommodate single Ag atoms appear differently in the STM images. Corner adatoms look brighter than center adatoms in the faulted-huc including single Ag atoms, while corner and center adatoms look similar in the unfaulted-huc in the filled-state image. Our investigations revealed that the stability of these Ag clusters is different from that of the Au clusters formed with an identical number of atoms, although Ag lies in the same chemical group as Au. The Ag atoms of the Ag 1 -Ag 2 structures show quick thermal diffusion with much faster speed than the scanning speed of the STM tip. On the other hand, Ag 3 exhibits two different adsorption configurations, one with a relatively stable form and the other showing quick thermal fluctuations during STM scanning. These structural differences, which are apparent in the STM images, suggest the existence of two metastable configurations of cluster-surface system having slightly different adsorption energies. The Ag 4 cluster shows a partly fluctuated feature, which indicates that some Ag atoms are hopping within the cluster. The stability of some of these structures differs between faulted and unfaulted-huc. While the Ag atoms in Ag 5 form a stable structure in an unfaulted-huc, Ag 5 in a faulted-huc frequently changes its configuration among three equivalent orientations, which reflects a surface threefold symmetry. Structure fluctuations due to quick thermal diffusion can also be seen accompanied by the conformation change of Ag 5. The Ag 6 structure remains very stable, and no indication of changes was observed in their appearances within the experimental time scale. The cluster structures of Ag 7 -Ag 9 undergo extensive conformational changes among three equivalent orientations, reflecting the surface threefold symmetry. The Ag 10 structure shows fuzzy features in an unfaulted-huc, in contrast to its appearance in a faulted-huc, which indeed remains stable even at high temperature [32]. Ag 11 - Ag 12 are stable and their conformations do not change. As we mentioned in the main manuscript, Ag N for N 13 never formed in an unfaulted-huc. The unfaulted-huc can accommodate at most 12 Ag atoms. The transfer of an additional Ag atom into a NS adjacent to the Ag 12 cluster does not induce clustering with the existing Ag 12 cluster. The Ag atom thermally diffuses among three NSs surrounding the Ag 12 cluster. This means that while the additional Ag atom can hop into the NS occupied by the Ag 12 cluster, it quickly hops out. As seen from the line profiles in Supplementary Figure 3, the center Ag 12 cluster is not affected by the additional Ag atom, which passes through the NS that is occupied by the Ag 12. This implies that the diffusing Ag atom does not spend enough time in the NS occupied by Ag 12 to modify the cluster electronic states. When two Ag atoms are put into a NS adjacent to Ag 12, Ag 3 is formed instead of Ag 2, and it diffuses among surrounding NSs in a concerted way. This suggests that a single Ag atom is dissociated from Ag 12 and is merged with Ag 2 to form Ag 3. The center cluster becomes Ag 11. Ag 11 accompanied by the formation of Ag3 appears differently from isolated Ag 11. Rather, the structure looks similar to that of Ag 12 with a small difference in the brightness of the image contrast (see Supplementary Figure 3). When one more Ag atom is

17 added into a faulted-huc adjacent to the center cluster, the Ag atom is combined with Ag 3 to form Ag 4 (see Supplementary movies 6 and 7). Ag 4 does not show inter-ns diffusion, and forms a stable cluster structure. When more Ag atoms are added into Ag 12, the Ag atoms diffuse into the faulted-huc occupied by Ag 4, leading to the growth of a second cluster in the faulted-huc. Another type of cluster formation through Ag atom diffusion between neighboring clusters is also observed without a tip-induced effect. Individual Ag atoms dissociated from the larger clusters diffuse into the neighboring HUC to enlarge the neighboring cluster. For example, Ag 11 at the unfaulted-huc and Ag 7 at the faulted-huc are transformed into the two Ag 9 clusters at the neighboring HUCs (see Supplementary movie 6).

18 Supplementary Note 8 Cluster-induced gate opening In the course of cluster assembly, it is revealed that larger clusters tend to attract individual adsorbates from the neighboring NSs into the NS where they are located without a tip close-proximity effect. This is the general trend for various adsorbate atoms studied here. This suggests that the presence of a large cluster in a NS has a strong electronic influence on the surrounding gates, and dictates the magnitude of the activation barriers for the diffusion of adsorbates from the nearest neighboring NSs. This tendency implies a long-range attractive interaction between an adsorbate and a cluster in adjacent NSs, which promotes atom aggregation as reported in previous investigations [4,33,34]. According to the previous theoretical investigation [33], a cooperative diffusion mechanism was proposed to explain the observed tendency to aggregate adsorbate metals on semiconductor surfaces at RT. The presence of a cluster in a NS creates anisotropy in the energy landscape at the borders surrounding the NS. The energy barrier associated with the gate between NSs is effectively reduced by the presence of the clusters without a tip-induced effect, opening the surrounding gates for adsorbate diffusion. These results shed light on the principles governing the cluster formation process on a Si surface.

19 Supplementary Note 9 Identification of the center cluster accompanied by the formation of Ag 3, Ag 4, and Ag 5 Based on the comparison with an isolated Ag 3 structure, we have identified the Ag 3 structure adjacent to the Ag 11 [see Supplementary Figure 4(a) and 4(d)]. In Supplementary Figure 4(a), a STM image of isolated Ag 3 structure is shown. The HUC involving Ag 3 structure appears as two bright protrusion. In Supplementary Figure 4(d), we show a STM image of two Ag cluster arrays adjacent to each other; one in unfaulted (center cluster) and the other in faulted-huc, respectively. The cluster adjacent to the center cluster looks identical to the isolated Ag 3 shown in Supplementary Figure 4(a), although they are located at different HUCs. The Ag structure in the faulted-huc and its counterpart in the unfaulted-huc look almost the same. From this comparison, it appears that the side cluster is Ag 3, thereby the center cluster can be assigned to Ag 11. In a similar way, we have identified the center cluster accompanied by the formation of Ag 4 and Ag 5. When one Ag atom is put into a NS adjacent to Ag 11 accompanied by Ag 3, Ag 4 is formed [see Supplementary Figure 4(b) and 4(e)]. When one more Ag atom is put into a NS adjacent to Ag 11, Ag 5 is formed [see Supplementary Figure 4(c) and 4(f)], and the center cluster remains as Ag 11. The Ag 4 structure is not so stable, and shows thermal fluctuation. In short, we can clearly identify the center cluster surrounded by the other Ag clusters as the Ag 11 by atom counting.

20 Supplementary Note 10 Assembly of multi-element clusters Predesigned multi-element clusters can be fabricated by the atom gating technique. Despite the wide range of technical applications of atomically well-defined multi-element clusters, their assembly at RT has not been demonstrated yet. The investigation of the structure and the stability of these bimetallic clusters can contribute to our understanding of the interaction between the doped atom and the metal clusters, i.e., the so-called synergistic effect [35], which determines the reaction rates. Supplementary movie 9 demonstrates the assembly sequences of Au N Pb clusters. Individual Pb adsorbates diffusing within a NS can be distinguished from single Au adsorbate on STM images. The results of these investigations reveal that the presence of the single Pb atom in the host clusters drastically changes the stability of a given cluster. As we mentioned in the main manuscript, other group elements can also be used to constitute bimetallic clusters. Supplementary Figure 5 demonstrates an example of a bimetallic cluster assembled from the group IV elements involving Pb and Si atoms. The accommodation of a single Si atom into an existing Pb 3 cluster results in the formation of Pb 3 Si isomer, as shown in Supplementary Figure 5a. This isomer then spontaneously transforms into the stable form (see Supplementary Figure 5b). The appearance of Pb 3 Si is different from those of Pb 3 and Pb 4, although both Pb and Si belong to the same chemical group IV. This indicates that the difference in the covalent radius of the elements also influences the manner of cluster formation as well as the stability of the clusters. In short, atom-by-atom fabrication of multi-element clusters with various combinations and with a defined number of atoms by the proposed method can find important applications across a diverse range of fields, including nanomagnetism and nanocatalysis. Magnetic elements can be confined within a NS on the Si(111)-(7x7) surface, for instance, Mn [36] and Co [37]. A nanomagnet can be fabricated atom-by-atom to investigate the size and shape dependence of a magnetic moment. The nanoclusters that exhibit magnetic properties can be designed from nonmagnetic materials or elements [38]. The combination of this method with exchange force microscopy [39] allows us to investigate the cluster size dependence of the magnetic moment. In a catalysis field, this technique can also contribute to the realization of the influences of cluster size on catalytic reactivity, as proposed by Haruta [40]. This method, when combined with Kelvin probe force microscopy [41,42], would be useful for detecting the charge states of the fabricated clusters that can help to clarify the role of the electron transfer between clusters and the supporting surface in catalytic reactivity. Furthermore, the dependence of the reaction rate on the cluster composition can be investigated by exposing the man-designed clusters to different gas sources, as investigated on self-assembled nanostructures [43,44].

21 Supplementary Note 11 Assembly of lead clusters This supplementary material demonstrates another example of atom clusters that are fabricated using Pb atoms in a group IV element; these atoms are tetravalent as Si atoms. Supplementary movie 8 shows the assembly sequences of Pb N clusters in a faulted-huc. The single Pb atom in STM images looks similar to those in previous STM images [4]. While the contrast in the filled-state image of the faulted-huc including the single Pb atom is homogeneous, in the unfaulted-huc the center adatoms look slightly brighter than the corner adatoms. This is related to the difference in diffusion properties between the two HUCs. Pb clusters are more stable than Au and Ag clusters because their interaction with surface Si atoms is stronger. Pb 4 -Pb 6 look similar to each other and have a mirror symmetry. These structures closely resemble the self-assembled clusters previously observed in [45]. Despite their resemblance in the STM images, however, the number of Pb atoms forming the clusters and the structural model constructed from the first principle calculations are not consistent with our results. In that study, the number of Pb atoms in the cluster was assigned as seven, and the optimized model structure suggests that Pb atoms replaced the corner Si adatoms. On the basis of force spectroscopic measurements [46], we have identified the atomic species over the corner site as Si adatom rather than Pb atom. The results of this study will be presented elsewhere.

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