Electron Orbital Contribution in Distance‐Dependent STM Experiments

Scanning tunneling microscopy (STM) is one of the most powerful techniques for the analysis of surface reconstructions at the atomic scale. It utilizes a sharp tip, which is brought close to the surface with a bias voltage applied between the tip and the sample. The value of the tunneling current, flowing between the tip and the sample, is determined by the structure of the surface and the tip, the bias voltage, and the tip‐ sample distance. By scanning the tip over the surface, a tunneling current map is produced, which reflects the local atomic and electronic structures. This chapter focuses on the role of the tip‐surface distance in ultrahigh vacuum STM experiments with atomic and subatomic resolution. At small distances, i.e., comparable with interatomic distances in solids, the interaction between the tip and the surface atoms can modify their electronic structure changing the symmetry of the atomically resolved STM images and producing unusual features at the subatomic scale. These features are related to changes of the relative contribution of different electron orbitals of the tip and the surface atoms at varying distances.

STM is based on quantum tunneling of electrons from atoms present at the surface of a sample to the front atom of an STM tip (or vice versa) through the vacuum gap. Because of the exponential distance dependence [34], the tunneling current drops approximately by one order of magnitude with every 1 Å increase in the tip-sample separation. Because of the strong distance dependence, more than 90% of the current can be localized on only two, closest to each other, tip and surface atoms. This provides unique spatial resolution of STM, reaching the picometer scale [15,[22][23][24] and allowing even direct imaging individual electron orbitals at certain tunneling parameters [22][23][24][25][26][27][28]. However, the ultimate orbital resolution could rarely be achieved in experiments because of simultaneous contribution of different electron states of the tip and the surface atoms and nonideal geometries of the tips used. Probing particular atomic orbitals with STM is further impeded by possible modifications of the tip and surface electronic structure at very small tunneling gaps (2.0-5.0 Å), generally required for atomically resolved STM imaging.
The role of different electron states and tip-surface distance in high-resolution STM imaging has been discussed since 1980s. Apparently, the first anomalous distance dependence of the STM contrast was reported in reference [35]. Afterward, the distance dependence has been studied in a number of works [22,23,27,28,[36][37][38][39][40][41][42][43][44][45][46]. However, because of complexity of the theoretical calculations for realistic tip-surface systems and experimental studies with precise control of the tunneling gap and the tip state, there is still no detailed knowledge about the role of particular electron orbitals in the distance-dependent STM experiments. This chapter is focused on the experimental and theoretical studies of the role of the tip-sample distance in STM experiments with atomic and subatomic spatial resolution which can pave the way to selective probing particular electron orbitals, controllable chemical analysis at the atomic scale, and surface imaging with picometer lateral resolution.
between the simulated and experimental images for numerous atomically resolved STM studies.
The ultimate lateral resolution R within the Tersoff-Hamann approach [47] is defined by the formula R = d ⋅ 2k −1 , where d is the distance between the interacting tip and surface atoms and k -1 ≈ 1 Å. The limit of the lateral resolution for a tip-sample distance of 4.5 Å should be about 3 Å. The theory [47] predicts an enhancement of the spatial resolution with decreasing tipsample distance but cannot explain the large atomic corrugations in STM images of metal surfaces [49][50][51] and the experimentally observed sub-Ångström lateral resolution [7,[22][23][24], even at tunneling gaps in the range of 2.0-2.5 Å. The former can be explained either by the tip and surface atom relaxations [37] or by decisive contribution of higher momentum (l) electron states with nonzero momentum projections on the z-axis (m ≠ 0 states) [52][53][54][55][56]. For example, calculations by Tersoff and Lang for different tip atoms (Mo, Na, Ca, Si, and C) suggest that atomic corrugations on the same surface can vary by one order of magnitude depending on the relative contribution of the electron states with different values of l and m [52].
To get more general description of the tip structure and to clarify the role of particular electron orbitals in STM imaging, Chen introduced the so-called derivative rule [54], where the tunneling matrix elements, corresponding to individual orbital contributions, are proportional to the z derivatives of the surface atom wave functions at the center of the tip apex atom. The total tunneling current can be calculated by summing up all individual contributions of the electron orbitals with different values of l and m [54]. According to the theory [54,55], d z 2 and p z tip electron states can be responsible for enhanced atomic resolution and large corrugations on metallic surfaces. For the tips having m = 0 electron states at the apex, the simulated STM images should correspond to the surface DOS distribution, similar to the s-wave tip. This assumes that the best STM tips should possess either d z 2 or p z electron states at the apex. At the same time, the m ≠ 0 tip states (e.g., d xz , d yz , d xy , and d x 2 -y 2 ) can provide enhanced atomic corrugations and intra-atomic effects at small distances [53][54][55][56]. For example, d xz , d yz , d xy , and d x 2 -y 2 electron orbitals at the apex can produce twofold and fourfold split subatomic features, respectively, instead of a single atom at very small tunneling gaps [56]. The dependence of atomic corrugations on the tunneling gap resistance, calculated for different electron orbitals by Sacks [56], suggested that d z 2 and m ≠ 0 d-orbitals can produce enhanced corrugations in comparison to the s-state. Furthermore, the corrugations can substantially increase with decreasing gap resistance.
The improvement of the lateral resolution of the SPM to the picometer scale [7,[22][23][24][57][58][59][60], observation of orbital channels in tunneling conductance [61], and subatomic contrast in SPM experiments [22][23][24][25][26][27][28][29][30][31][32] led to the development of new theories accounting for the distance dependence of the electron orbital contribution [62,63], energy-dependent combinations of the tip orbitals [64][65][66][67][68], and effects of inter-and intra-atomic interference of the electron orbitals in the tunneling junction [69][70][71][72][73]. Recently, the revised Chen's derivative rule, accounting for the orbital interference effects, has been proposed by Mandi and Palotas [74], who considered the realistic electronic structure and arbitrary spatial orientation of the tip minimizing the computational efforts. Their results showed that the electronic interference effects have a considerable effect on the STM images. As an example, in certain cases a tip with a mixture of s and p z electron states can provide even higher spatial resolution than pure p z -orbital tip [74].

Electronic structure of realistic tips at small tunneling gaps
Although the developed theories can provide a correlation between experimental and theoretical images in certain cases, they rarely take into account possible interaction-induced changes of the tip orbital structure at very small tunneling gaps. It has been demonstrated recently [62][63][64]75] that electronic structure of the transition metal tips and relative weights of different d-orbitals in the tip's DOS near E F strongly depend on the tip element, tip cluster size, and local environment around the tip. In particular, it has been shown that d z 2 -orbital is more sensitive to the local environment and the tip cluster size than m ≠ 0 d-orbitals (d xz , d yz , d xy , and d x 2 -y 2 ) [63]. The electronic structure of different transition metal tips can nonequally depend on the tip-surface distance [63,75]; therefore, determination of the most suitable tip for particular surface can be crucial for reaching highest spatial resolution in the experiments. Stimulated by the subatomic resolution AFM experiments [33], Wright and Solares calculated the electronic structure of the tungsten tips with different crystallographic orientations in proximity to different surface clusters [75][76][77]. The calculations showed that the experimental SPM images with subatomic resolution [22][23][24]33] were, most probably, related to the tip electronic structure, which could become asymmetric at small tip-sample distances because of the tip-sample interaction. The stability of the tungsten tips was found to be dependent on the crystallographic orientation of the apex. In particular, W[001] tip did not substantially relax even at the tip-sample distance of 1.50 Å, while [011]-and [111]-oriented tungsten tips were stable only at gaps above 2.25 and 2.50 Å, respectively.  tips. These areas of increased charge density (dark red color) reveal the twofold and fourfold symmetry representatives of each tip's crystallographic orientation. However, for the W[111] tip, the areas of increased density do not reveal the threefold symmetry proposed from the crystal symmetry consideration [33]. These results suggest that the highest spatial resolution can be achieved in STM experiments using W[111] tips which have symmetrical charge density distribution along the tip axis even at relatively small distances from the surface. In contrast, W[001] and W[011] tips can produce subatomic features at small tip-sample distances [22][23][24] but can be more suitable for scanning tunneling spectroscopy (STS) experiments demanding high tip stability.

Role of atomic relaxations at small tip-surface distances
An enhancement of the lateral resolution and atomic corrugations with decreasing tip-surface distance was anticipated from the theories [47,56] omitting possible relaxations of the interacting tip and surface atoms. Additionally, the topographic contrast in STM experiments can be enhanced at small distances because of the tip and surface atom relaxations reported for the first time almost three decades ago [49]. The role of elastic effects in high-resolution STM experiments on close-packed metal surfaces was thoroughly studied in Ref. [37]. To evaluate possible corrugation enhancement related to atomic relaxations, the simulations were performed on Cu(111) and Al(111) surfaces at different tip configurations and tunneling gaps [37]. The relaxations were found to be substantially stronger for Al(111) because of the higher elasticity of the aluminum surface. As a result, the atomic corrugations in the simulated images of Al(111) increased almost by one order of magnitude (from 10 to 70 pm) with decreasing distance from 600 to 400 pm. The calculations [37] explain the anomalously high corrugation amplitudes observed in numerous STM experiments on metal surfaces. The large outward relaxations of the surface atoms under typical tunneling conditions can lead to atomic corrugations which can hardly be explained from the electron DOS and simplified theoretical considerations [47,56]. The corrugation enhancement was proved on different metal surfaces; therefore, one can anticipate the validity of the work [37] for other metals, although the effect cannot be so well pronounced as calculated for aluminum surface scanned by an aluminumterminated tip.

Reduction in tunneling current channels with decreasing tip-surface distance
First observations of the tunneling current channels associated with different electron orbitals were reported almost two decades ago [61]. However, their role in STM imaging at different gaps is still not clear. Recent theoretical studies showed that relative contributions of different electron orbitals can be substantially modified because of tip-sample interaction changing the tip and surface DOS near E F [62-64, 75, 78-80]. For example, Figure 1 demonstrates the distinct asymmetry of the [001]-and [011]-oriented tungsten probes appearing only at small gaps when the overlap of the orbitals of the interacting tungsten and helium atoms takes place [75]. Figure 2 shows the theoretical calculations demonstrating a drastic reduction of the DOS near E F associated with the Si(111)7×7 surface atom interacting with the [001]-oriented tungsten tip [79]. The interaction modifies the electronic structure of the surface atom at distances below 4.75 Å, as shown in Figure 2  [ Figure 2(b)]. Then, the vertical adatom displacement decreases until it reaches its initial value at a tip-sample distance of 3 Å. The electron DOS isosurfaces calculated for different tip-sample distances [ Figure 2(a)] show the typical charge density distribution of the Si(111)7×7 surface at 6.0 Å, a charge transfer from the adatom to neighboring surface atoms at 4.75 Å, the suppression of the adatom dangling bond at 4.5 Å, and the chemical bond formation at 3.0 Å that prevents the electron transport between the tip and the surface at small distances. The W[001] tip electronic structure remained practically unchanged in this tip-sample distance range. Note that calculations of Jelinek et al. [78] were carried out at low voltages, corresponding to probing the p z -states dominating in the Si(111)7×7 surface DOS near E F . Therefore, it can be assumed that the overlap of the silicon p z -orbital with the tungsten tip orbitals is responsible for the strong modification of the tunneling current as shown in Figure 2(d). Furthermore, one can expect similar phenomena in other systems where the electron transport occurs through p z electron orbitals.
Recent theoretical calculations of the tunneling current between an STM tip and a single Cu/Co atom adsorbed on a Cu(001) surface [62] have shown that conductance in these systems can be decomposed into several orbital contributions. The tunneling probabilities of these individual channels can provide the information about the modifications of the adatom's DOS caused by the tip-adatom interaction. The calculations revealed that the d z 2 -orbitals of the interacting atoms in such systems are especially sensitive to the tip-adatom distance because they start to overlap at larger distances. The DOS associated with the d x 2 -y 2 -orbitals starts to decrease at smaller tunneling gaps and the total reduction at distances between 4.0 and 2.5 Å for this orbital is smaller in comparison with that of the d xz -, d yz -, and d z 2 -orbitals. At tip-sample distances exceeding 3.0 Å, the channels contributing to the most of the tunneling current were generally related to hybrids of s-and d z 2 -orbitals. The contribution of m ≠ 0 electron states increased with decreasing distances.

Electron orbital resolution in distance-dependent STM experiments
The first STM images with the atomic orbital resolution were obtained at the beginning of 1980s. For example, typical images of the Si(111)7×7 surface [5] correspond to direct visualization of the p z surface orbitals. Similar selective visualization of the atomic orbitals at certain tunneling conditions was achieved on other semiconducting surfaces [17]. The control of the orbital contribution on multicomponent metal surfaces is more difficult. Up to date, several STM studies demonstrating subatomic, electron orbital contrast have been published. In several cases, the observed features were related to direct visualization of the electronic structure of the tip atom by more localized surface atomic orbitals [22][23][24][25][26][27][28]. However, some STM studies revealed asymmetric subatomic features associated with the m ≠ 0 electron orbitals of the surface atoms [30,81]. The STM studies presented in this section can be important for optimizing the tunneling parameters for high-resolution STM imaging and shed light on the gap resistance dependence of atomically resolved STM images and chemical contrast observed on metallic and semiconducting surfaces.

Tip orbitals resolved using p z states of the Si(111)7×7 surface atoms
SPM imaging with subatomic resolution was first claimed by Giessibl et al. [31] who reported the AFM images of the Si(111)7×7 reconstruction demonstrating a regular twofold splitting of the surface atomic features. This was explained by direct visualization of the two atomic orbitals of an Si[001] tip atom by the p z -orbitals of the surface atoms. This is schematically shown in Figure 3(b). Later studies [28] showed that qualitatively the same asymmetric features can be resolved with STM using a silicon-terminated tungsten tip. Figure 3(a) demonstrates the change of the contrast in the STM experiments [28] with decreasing tunneling gap resistance. Note that precise structure of the tip apex, responsible for the subatomic contrast in both SPM experiments [28,31], was unknown because of the tip preparation procedure. Therefore, the origin of the subatomic features in the Si(111)7×7 SPM images was disputed in a number of papers [82][83][84][85][86][87]. Alternative explanations based on the feedback loop artifacts [83], presence of a carbon atom at the apex [86], and visualization of the surface atoms' backbonds [87] were proposed. Nevertheless, independent theoretical calculations [31,32,82,84] support the possibility of direct visualization of the asymmetric charge distribution around the [001]-oriented Si tip atom [ Figure 3(b)] at small (2.5-4.0 Å) tip-surface separations. This is in agreement with the gap-resistance-dependent STM experiments [28]. Figure 3(a) demonstrates that the twofold splitting of the adatoms becomes discernible only at small bias voltages (small distances), while at large negative voltages a (7×7) pattern with with well-resolved adatoms, rest atoms, corner holes, and single-atom defects are observed, which is only possible with extremely sharp single atom-terminated tips [88]. The effect can hardly be explained by the formation of a two-atom terminated apex and visualization of the surface atom backbonds because deep corner holes, rest atoms, and single atom defects on the surface were simultaneously resolved even at low gap resistances. The double features become sharper and change their appearance from symmetric to asymmetric with decreasing gap resistance, as shown in Figure 3 (c) and (d). The shape of the double features could be changed both by increasing tunneling current at fixed voltage and decreasing voltage at the same current [28]. The asymmetry of the double features at small gaps can be explained by the relaxation of the apex atom, as shown in Figure 3(b). The distance between the two maxima of the double features decreased from 2.7 to 2.2 Å with decreasing gap resistance from 7.5 to 2.5 GΩ and then increased to 2.75 Å with further decreasing gap resistance from 2.5 to 1.25 GΩ. The decrease of the distance between the subatomic maxima is in line with the theoretical spatial distribution of the two sp 3 dangling bonds at the [001]-oriented silicon apex [32]. The increase of the splitting at smaller distances can be related to tip-sample interaction modifying the electronic structure of the apex atom and inducing lateral relaxations of the tip and surface atoms in near-to-contact regime.
Herz et al. applied a Co 6 Fe 3 Sm tip for high-resolution STM experiments on the Si(111)7×7 surface [25]. They utilized a dynamic-STM mode with an oscillating probe to reduce the lateral forces in tip-sample contact and increase the tip stability at extremely small tunneling gaps. At some tunneling parameters, the adatoms were resolved as extremely sharp spherically symmetric features surrounded by lower lying crescents. These asymmetric features, observed at small gaps, were explained by a convolution of the p z -orbitals of the surface atoms and the f z 3 -orbital of an Sm atom at the apex tilted to the surface normal by 37°. The validity of this interpretation was supported by the theoretical calculations in an assumption of the tilted Sm f z 3 tip orbital [25].

Distance dependence of the W[001] tip orbital contribution in STM experiments on graphite
The selection of the tip orbital responsible for high-resolution STM imaging has been demonstrated in references [22][23][24]. The electron orbitals of the graphite surface atoms were used to study the relative contribution of the [001]-oriented single crystalline tungsten tip orbitals at different distances ( Figure 5). To avoid apex contamination, W[001] tips were cleaned by flash heating and ion sputtering in ultra-high vacuum (UHV) before the distancedependent experiments. The transmission electron microscopy (TEM) studies proved the fabrication of the [001]-oriented nanopyramids with well-defined structure at the apexes [24].   Figure 5(c)] demonstrates that these images reproduce the electronic structure of the same tip atom modified with decreasing tip-sample distance. The two and fourfold split features in Figure 5 cannot correspond to the threefold symmetrical graphite surface. At the same time, the observed two and threefold split features cannot be related to the tip atom backbonding because of the symmetry of the W[001] tip used in experiments. The subatomic features can only be explained by a direct visualization of the tip atom's electronic structure modified by the tip-sample interaction at small tunneling gaps. According to the tunneling currents, the observed transformation of the asymmetric features took place in the narrow range of tipsample distances of the order of 0.1 Å. The actual distance could be slightly above this value because of the tip and surface atom relaxations at small distances [37].
At certain tunneling parameters (voltages and gap resistances), the shapes of the subatomic features in the STM experiments reproduced the electron density distribution associated with the d z 2 -, d xz -, and d xy -orbitals in the tungsten atom. This can be explained by a major contribution of particular electron orbitals of the tip atom at certain tip-sample distances [ Figure 5(a)]. According to Figure 5(c), the relative contribution of the d xz -and d xy -orbitals increases with decreasing gap resistance. PDOS calculations for the fully relaxed "W[001] tip-graphite" system [ Figure 5(b)] demonstrate a suppression of the tip d z 2 electron orbital near E F at distances below 2.5 Å because of the overlap with the carbon orbitals. The domination of the tip d xy electron orbital near E F is observed in a narrow range of the tip-surface distances between 2.2 and 2.5 Å, which is in agreement with the current values in Figure 5(c). The surface imaging by the tungsten d z 2 -orbital can be realized at tunneling gaps between 2.5 and 4.0 Å, while d xy electron orbital can yield a maximum contribution to the tunneling current at distances between 2.2 and 2.5 Å. The appearance of the asymmetric features is related to the interactioninduced modification of the PDOS associated with different d-orbitals of the tungsten tip atom.
The DFT calculations [ Figure 5

(b)] and distance-dependent STM experiments [Figure 5(c)]
show the correlation between the spatial distribution of the atomic orbitals (in particular, extension in the z-direction) and the order of their suppression with decreasing tip-sample distance. The suppression of the further protruded in the z-direction electron orbitals with m = 0 can increase the contribution of the m ≠ 0 electron states at small gaps. Figure 5 demonstrates that picoscale spatial resolution and even direct imaging of the transition metal d-orbitals using the p-orbitals of light elements can experimentally be achieved. Figures 3-5 correspond to probing the tip electronic structure by the surface atomic orbitals. Similar STM experiments revealing the tip atom's subatomic structure with decreasing tunneling gap have recently been reported for several tip-sample systems [89][90][91][92]. Figure 6(a) shows the STM image of the Cu(014)-O surface measured with a polycrystalline tungsten tip [30]. This image reveals one bright atomic row within the four-atom-wide terraces [see the model in Figure 4(a)]. The atomic features within the well-resolved copper row have two maxima separated by approximately 1 Å [ Figure 6(b)] reproducing the electron density distribution in the Cu d xz atomic orbital. According to the TB calculations [ Figure 6(c)], the DOS associated with the d xz -orbitals of the surface copper atoms is maximal for the fourth (down-step) copper row of each terrace suggesting that visualization of one atomic row within the terraces can be achieved if the surface d xz -orbitals yield the largest contribution to the tunneling current. Similar to the STM experiments with the W[001] tips [22][23][24], this can be reached at small bias voltages and small tip-sample distances, where the d xz -orbital channel dominates in the tunneling current. The STM image with one well-resolved row with double features (Figure 6(a)) can be explained by imaging the d xz -orbitals of the Cu(014)-O surface using the d z 2 -orbital of a tungsten tip atom.

STM imaging of graphite (0001) using a [111]-oriented diamond tip
Conductive diamond tips, generally considered as AFM probes, can provide carbon atomic orbitals for imaging with picometer lateral resolution ( Figure 5) and high apex stability at small tunneling gaps. It has been demonstrated that high spatial resolution can be achieved in STM experiments with the boron-doped single crystal diamond tips [93].   Figure 7(e, f) and the charge density map presented in Figure 7(g) were calculated at a tipsample distance of 4.5 Å where the atomic and electronic structures of the tip and surface atoms are not substantially modified by the interaction [93]. The excellent agreement between experimental and theoretical images suggests that the highest resolution was achieved with the diamond probe at tunneling gaps of 3.5-4.5 Å where the tip did not strongly interact with the surface. This result shows the advantages of the oriented single crystal diamond probes: their structure is stable and well defined while high lateral and vertical resolution can be achieved at larger tunneling gaps comparing to typical tip-sample distances used in experiments with transition metal tips. Calculations of the partial DOS associated with the electron orbitals of the diamond probe and graphite surface atoms at different tunneling gaps (Figure 8) show that electronic structure of the interacting atoms is modified at tip-sample distances below 3.0 Å. The overlap of the tip and surface atomic orbitals leads to decrease in the PDOS associated with the p z -orbital of the graphite surface atoms when the diamond tip atom is positioned directly above the surface atom [ Figure 7(a, right panel)]. The suppression of the surface atom's p z -orbital at small tunneling gaps (d < 2.5 Å) is in qualitative agreement with the results of the theoretical calculations for the Si(111)7×7 surface interacting with the W[001] tip shown in Figure 2 [78]. If the diamond tip atom is positioned above the hollow site (left panels in Figure 8), the overlap of the front tip atom and the surface orbitals does not take place even at small distances. Therefore, the change of the PDOS of the tip and surface atoms is minor even at the tunneling gaps of 1.5 Å. According to the calculations [93], the electronic structure of the diamond probe is defined by a mixture of the carbon s and p-states with domination of the p x -and p y -orbitals, responsible for the STM imaging (Figure 7).

STM experiments with functionalized tips terminated by a light element atom
The experiments with the diamond tip (Figure 7) show that an enhancement of the spatial resolution can be achieved using conductive tips having molecules or light element atom at the apex. During the recent years, a number of high-resolution STM studies performed with the conductive tips functionalized by different light elements have been reported [57-59, 89, 96-103]. These studies generally demonstrated an enhanced contrast in the STM experiments with the light element-terminated probes, especially, at small tip-surface distances. For example, the lateral resolution at the level of intramolecular chemical bonds has been reached in STM experiments using molecule-terminated probes [58,59]. In the recent theoretical work [101], the high resolution in experiments with the functionalized probes was explained by significant apex atom relaxations toward the local minima of the interaction potential at small distances. However, the tip functionalization procedures are generally not capable of producing stable apexes with well-defined structure. These tips could produce substantial noise [58] and asymmetric subatomic features [89] at small tunneling gaps. Besides, STM images measured with the molecule-terminated tips can strongly depend on the precise orientation of the molecule at the apex and the bias voltage [102,103] that can complicate the interpretation of the atomically resolved STM data. Figure 9 demonstrates the picometer lateral resolution achieved in high-resolution STM studies of graphene/SiC(001) system [7] using a [111]-oriented single crystalline tungsten tip. Theoretical calculations shown in Figure 1 suggest that the front atom of the W[111] tip should possess symmetric charge distribution along the tip axis even at small tip-sample distances. Although the W[111] tips were found to be the least stable from three possible low-index crystallographic orientations [75], they can produce higher spatial resolution in STM experiments without possible tip structure effects which can be observed with the W[001] tips ( Figure 5). Indeed, although high spatial resolution was achieved on the quasi-freestanding graphene grown on SiC(001) with the stable W[001] tips [24], the best resolution was obtained with the W[111] tip [7]. Figure 9(a) demonstrates the rippled morphology of graphene on SiC(001) with the lateral and vertical dimensions of the ripples of about 30-50 and 1 Å, respectively. Figure 9(b) and (c) demonstrates random picoscale distortions of the carbon bond lengths, which are very close to the values calculated for the freestanding graphene monolayer [104]. The contrast in Figure 9(b) and (c) was adjusted to enhance the picometer scale bond length distribution. The picometer lateral resolution obtained in the RT STM experiments (Figure 9) corresponds to the best standards of the SPM and can be compared with the resolution achieved in the recent AFM experiments [96].

Conclusions
The spatial resolution on the level of individual electron orbitals corresponds to the ultimate resolution of the SPM. During the last decade, a number of SPM studies demonstrating selective visualization of individual electron orbitals and subatomic contrast have been published. The experimental and theoretical works conducted during the recent years demonstrate that selective imaging of the surface electron orbitals can only be achieved at finely adjusted bias voltages and tip-sample distances. Therefore, for the development of the electron orbital imaging capability, the stability of the tip-sample separation should be maintained at the level of 1 pm or below. Distance-dependent STM imaging with electron orbital resolution can lead to further improvement of the lateral resolution down to the picometer scale and development of the chemical-selective imaging of complex multicomponent surfaces.