Morphology of Bi(110) quantum islands on epitaxial graphene

Proximitized 2D materials present exciting prospects for exploring new quantum properties, enabled by precise control of structures and interfaces through epitaxial methods. In this study, we investigated the structure of ultrathin coverages formed by depositing high-Z element bismuth (Bi) on monolayer graphene (MLG)/SiC(0001). By utilizing electron diffraction and scanning tunneling microscopy, ultrathin Bi nanostructures epitaxially grown on MLG were studied. Deposition at 300 K resulted in formation of needle-like Bi(110)-terminated islands elongated in the zig-zag direction and aligned at an angle of approximately 1.75∘ with respect to the MLG armchair direction. By both strain and quantum size effects, the shape, the orientation and the thickness of the Bi(110) islands can be rationalized. Additionally, a minority phase of Bi(110) islands orthogonally aligned to the former ones were seen. The four sub-domains of this minority structure are attributed to the formation of mirror twin boundaries, resulting in two potential alignments of Bi(110) majority and minority domains with respect to each other, in addition to two possible alignments of the majority domain with respect to graphene. Notably, an annealing step at 410 K or lowering the deposition temperature, significantly increases the concentration of the Bi(110) minority domain. Our findings shed light on the structural control of proximitized 2D materials, showcasing the potential for manipulating 2D interfaces.


Introduction
Heteroepitaxy is a well-known approach to the targeted change of properties of solid crystalline surfaces [1].The structure and morphology of such epitaxial coverages depend on the individual properties of both materials and physical growth conditions, but it is also the main factor determining the characteristics of the entire coverage-substrate system.Modern technologies make it possible to obtain rather extreme heteroepitaxial systems in which both the substrate and the coverage are monolayers or consist of several layers of different atoms [2,3].In this sense, heteroepitaxy has been successfully used for the functionalization of graphene by deposition of mono/multilayers [4].
The extraordinary qualities of graphene are fascinating.However, it is also an exciting prospect to expand the range of these properties, in particular through functionalization.As an example, significant efforts have been made to increase the negligible spin-orbit interaction in graphene [4].For this purpose, the effect of proximity (i.e.contact) with materials with strong spin-orbit interaction was used.A good candidate in this case is the heavy semimetallic bismuth (Z = 86), which is characterized not only by strong spin-orbit splitting but also by spin-split surface electronic states [5,6].Due to the large Fermi wavelength (≈30 nm) the quantum size effect is pronounced in Bi films/clusters as well [7].In addition, we can expect topological insulator properties from monolayer bismuth [8] and edge states of Bi nanoribbons [9].It is also interesting that the Bi monolayer can even have ferroelectric properties [10].The spin polarized surface states of Bi enable the injection of spin polarized currents into graphene by inducing ferromagnetism in it [11].In combination with the long spin diffusion length in graphene, for which values larger than 100 µm have been reported [12], this makes the system an ideal candidate for spintronic applications for quantum computing.Moreover, when a band gap is opened in graphene, e.g. by wrinkling induced stress, Bi/graphene heterostructures show enhanced photoelectric activity making them a candidate for the use in photodetectors and photocatalysts [13,14].
For these reasons, it is not surprising that the structure of bismuth coatings on graphene has already been the focus of many experiments [15][16][17][18].In particular, it was found that small ultrathin coverages of Bi on graphene are island-like and have the structure of α-bismuthene [19], i.e. the structure of Bi(110) possessing three main domains oriented along the armchair directions of graphene with two subdomains misoriented by about ±2 • .The Bi(111) phase, β-bismuthene [19], arises at higher bismuth coverages (approx.⩾ 7 bilayers Bi(110) [16]).The Bi(110) islands were also found to be elongated into the armchair directions of graphene [16,18], while the islands of the Bi(111) phase have a triangular shape [16].However, the conditions under which previous experiments were performed were somewhat different.Takahashi et al deposited Bi on triple-layer graphene/SiC at 100 • C [15], while in other experiments, monolayer graphene was used as the substrate at room temperature (RT) [16,18].In [15], the experiment was performed on a substrate containing a mixture of monolayer graphene and buffer layer areas.Therefore, it is obvious that conducting thorough and consistent studies to reveal the details of the structure of ultrathin Bi coatings on graphene formed by the same methodology is desirable and expedient.
This paper presents the results of detailed morphological studies by high resolution low energy electron diffraction (LEED) and scanning tunneling microscopy (STM) of bismuth island nanocoatings formed on monolayer graphene/SiC at RT and 100 K (with and without annealing) depending on the average coverage Θ of deposited bismuth (0.6 ⩽ Θ ⩽ 3.6 bilayers (BL)).In the last section we propose a structural model of the Bi(110) islands and their alignment on graphene.

Experimental methods
The high resolution LEED (using a spot profile analyzing LEED system) and STM measurements were performed in ultra high vacuum (UHV) systems operating at base pressures of ⩽1 × 10 −8 Pa and at substrate temperatures of 77 K and 300 K for LEED and STM, respectively.As substrates epitaxial monolayers of graphene (MLG) grown on either 4H-SiC(0001) (LEED) or 6H-SiC(0001) (STM) crystals, prepared ex-situ by heating the SiC crystal in an Ar atmosphere, were used [20].The samples were degassed inside the UHV chambers at 500 • C in order to remove contaminants before deposition.Bi islands were grown in-situ at a sample temperature of 300 K, unless otherwise noted, by evaporation of Bi from a Knudsen cell at a rate of 0.23 BL (with respect to Bi(110)) per minute.The amount was controlled by a quartz crystal microbalance.The thickness calibration was done by observing the conductance oscillations during the deposition of Bi on a Bi(111) film on Si(111) at a substrate temperature of 12 K, and then converting the result from Bi(111) bilayers (1BL = 1.14 × 10 15 atoms cm −2 ) to Bi(110) bilayers (1BL = 1.85 × 10 15 atoms cm −2 [15]).The Bi layers were investigated as deposited and after an annealing step at 410 K for 30 min.

Results and discussion
This section is structured as follows: In the first subsection, the dominant Bi(110) structure, which consists of islands elongated in the armchair direction of graphene, is discussed.In the following, this structure will be referred to as the majority structure.In the second subsection, an additional Bi(110) structure, which is rotated by approximately 90 • with respect to the majority structure, is discussed.This structure consists of islands elongated in the zig-zag direction of graphene, that are mainly formed during an annealing step and are always connected to a majority island.It will be referred to as the minority structure.In the third subsection, we propose a structural model including both structures.

Bi(110) majority islands elongated in the graphene armchair direction
Bi adsorbed on monolayer graphene at 300 K grows predominantly with a Bi(110) surface termination as evident from the LEED image in figure 1(a), at least for a coverage below 7 BL [16].Due to the rectangular symmetry of the Bi(110) surface and the hexagonal symmetry of the graphene layer, there are three equivalent Bi(110) domains rotated by 120 • with respect to each other, marked in figure 1(a) in red, green and blue, respectively.In each of these cases the longer Bi(110) axis in reciprocal space, i.e. the shorter axis in real space, which corresponds to the zig-zag direction of Bi(110) (see also the inset of figure 2(c)), is aligned approximately with the armchair direction of graphene.However, it is misaligned by ±(1.75 ± 0.5) • , resulting in two sub-domains, as already observed by Takahashi et al [15], and indicated by solid and dotted lines in figure 1(a).For reference, figure 1(b) shows the LEED image for a Bi coverage of 0.15 BL, where the Bi spots are barely visible, i.e. the image shows essentially the graphene/SiC pattern.
The comparative STM study in figures 2(a) and (b) for an average Bi coverage of 0.6 BL and 2 BL, respectively, shows that the adsorbed Bi grows as needle-like islands elongated in the armchair direction of graphene.These islands are (110) terminated, as confirmed by the atomically resolved image, which is shown in the inset of figure 2(c) and was taken on top of one of the needle-like islands.In addition, a small proportion of Bi(111) islands, recognizable by their triangular shape, is observed (approximately 3% of the total coverage), as seen, e.g.close to the center of figure 2(b).
The height distributions corresponding to the STM images in figures 2(a) and (b) are shown in figures 2(c) and (d), respectively.At an average coverage of 0.6 BL the island growth is still mostly two dimensional, with 2 and 3 BL being the dominant island heights.Approximately 24% of the surface is covered by Bi islands.At an average coverage of 2 BL the islands have grown in height, so that now 3, 4 and 5 BL are the most common island heights.However, still only approximately 43% of the surface is covered by Bi, indicating a Volmer-Weber growth mode.
The observed preference for full bilayer, i.e. even monolayer heights is in line with earlier studies [23].In particular, the 2 BL high islands are very stable as they show a comparatively wide band gap in scanning tunneling spectroscopy [23].These so called 'magic' heights are related to the electronic structure arising from quantum confinement effects.As the thickness of a film is reduced to the nanometer scale, the confinement of the electrons at the island/substrate and island/vacuum interfaces leads to the formation of discrete electronic quantum well states.Their energy depends on the island sizes, in particular the height, since it is usually the smallest dimension.The formation of the most stable islands (with 'magic' height) is directly related to the lowering the total energy of the islands through moving the occupied electronic levels far from the Fermi energy.As an example, such an effect was observed for Pb islands on Cu(111) [24], Pb layers on epitaxial graphite [25] and Bi islands on quasi-crystal alloys [26].The needle-like structure is mainly a result of the lattice misfit along one direction so that strain effects are limiting the width.This is supported by the detailed analysis of the lattice parameter as well as the structural models presented below.
For the purpose of studying the structure of the Bi(110) islands in more detail, high resolution LEED images recorded at an electron energy of 90 eV are depicted in figures 3(a)-(d) for average coverages between 0.6 BL and 3.6 BL.This energy turned out to be ideal in order to investigate the structure of the adsorbed Bi.The streaks through the Bi(110) spots, which become increasingly pronounced with increasing Bi coverage, indicate that the periodicity perpendicular to the Bi(110) zigzag direction is limited.There are two contributing factors to this.Firstly, the needle-like shape of the islands, i.e. the small dimension of the islands perpendicular to the zig-zag direction of Bi(110).Secondly, the growth of smaller islands on top of larger ones, creating narrow terraces.Since the island growth is still mostly two-dimensional at 0.6 BL, the streaks at this thickness are mainly caused by the first factor.At higher coverage the second factor becomes increasingly important, finally resulting in a star-shaped pattern at 3.6 BL.

Bi(110) minority islands elongated in the graphene zig-zag direction
When annealing the samples at 410 K3 for 30 min, see figures 3(e)-(h), the streaks at 1.2, 2.4 and 3.6 BL are reduced to an intensity comparable to the one at 0.6 BL.Solely at 0.6 BL the Bi(110) pattern remains almost unchanged.This indicates a strong reduction of the step density on the Bi(110) islands, so that the individual islands are of uniform height after annealing.This observation is confirmed by the STM results shown in figure 4. In particular, the line profiles in (b), taken at the positions indicated in (a), show that the Bi islands are generally of uniform height after annealing at 410 K. Furthermore, the average height of the islands is increased after annealing as shown in the histogram in figure 4(c) as The inset shows epitaxial graphene and the 6 × 6 corrugation of the buffer layer, which was used to determine the crystallographic axes (100 mV, 500 pA).(c) and (d) Histograms of the island heights for average Bi coverages of 0.6 and 2 BL, respectively.The inset shows an atomically resolved STM image of one of the needle-like islands (−100 mV, 1.9 nA), overlayed with a structural model of Bi(110) [21,22].For the majority of Bi(110) islands, their zig-zag direction is aligned with the ⟨1120⟩ direction of SiC (except for a small misalignment, see text), i.e. the armchair direction of graphene.A minority of Bi(110) islands form domain boundaries with an angle of ≈90 • with the majority Bi(110) islands (green arrows).
compared to the histogram in figure 2(d), and consequently the Bi covered area is reduced from 43% to 31%.It should be noted that due to the high steps, the STM image in figure 4(a) had to be measured with a high gain resulting in a comparatively low image quality and as a result possibly misassignments of the island heights, making it impossible to unambiguously determine the existence of 'magic' heights.
The reduction of the Bi covered area due to annealing observed in STM is in line with the increased intensity of the graphene buffer layer spots in LEED after annealing.It is a result of the minimization of the surface energy, and can be viewed as part of the late stage of the dewetting process of thin films [27].The observation of the Volmer-Weber growth mode already established that the surface energy of the Bi(110) plus the interface energy is larger than the surface energy of graphene.The enhanced mobility of the Bi during the annealing process allows the system to further reduce the surface energy by forming higher islands, thus increasing the area of non-covered graphene.The occurrence of the dewetting is not surprising due to the chemical inertness of graphene, i.e. the lack of dangling bonds.The minimization of the total surface energy during this process is in competition with the 'magic' heights related energy minimization discussed above.The annealing process also leads to an increased intensity in LEED of the ring with a radius corresponding to the lattice constant of Bi(111), indicating the formation of rotationally disordered Bi(111).
Moreover, in addition to the three Bi(110) domains discussed above, domains that are rotated by ≈90 • with respect to the first domains become visible after annealing as marked exemplary in figure 3(g) for one sub-domain.In these domains the zig-zag direction of Bi( 110) is (roughly) aligned with the zig-zag direction of graphene instead of the armchair direction.Each of these domains has four sub-domains as marked   in figure 3(h).The zoom-ins marked with the yellow, orange and dark orange boxes show the ( 10), ( 11) and (01) spots of Bi(110), respectively.The spots of the four sub-domains of the ≈90 • rotated domain are marked with arrows in the same color code as the sub-domains in figure 3(h), and the spots of the original two sub-domains are marked with red arrows.The ( 11) spots of two of the four sub-domains overlap with the (11) spots of the original two sub-domains, so that these spots appear brighter.Upon close inspection there are already hints of the ≈90 • rotated domains before annealing (see zoom-ins).Indeed, a minority of ≈90 • rotated domains are observed in STM both before and after annealing (green arrows in figures 2(a), (b) and 4(a)).However, clear LEED spots only appear after annealing, proving that the concentration of these islands strongly increases during the annealing process.In STM we only observed Bi(110) islands, where the zig-zag direction is aligned (roughly) with the zig-zag direction of graphene, that are connected to Bi(110) islands, where the zig-zag direction is aligned (roughly) with the armchair direction of graphene, suggesting that the former type of islands is not stable on its own.LEED images for a deposition temperature of 100 K and a coverage of 1.2 BL before and after annealing at 410 K for 30 min are shown in figures 5(a) and (b), respectively.Before annealing the crystalline order of the Bi islands is very poor.It is improved greatly by the annealing step.However, as compared to the islands grown at 300 K, the rotational disorder of the Bi(110) islands is increased.Interestingly, the concentration of Bi(110) minority islands, that have their zigzag direction (roughly) aligned with the zig-zag direction of graphene, as compared to the majority islands, where the zig-zag direction is (roughly) aligned with the armchair direction of graphene, is also increased (see the (01) spots).This shows again that the formation of the Bi(110) minority domain happens predominantly during the annealing process, while the formation of the Bi(110) majority islands with their zig-zag direction (roughly) in the graphene armchair direction is favored during the deposition.Furthermore, the formation of minority domain islands is easier if the islands are not already aligned with the graphene during the deposition.Thus, the deposition temperature can be used to control the concentration of minority domain islands.

model
In order to precisely measure the lattice constants of the Bi(110) and the misalignment angles between Bi(110) and graphene, we used a LEED image recorded at an electron energy of 127 eV and performed a distortion correction using LEEDCal [28,29].The corrected image is shown in figure 6(a).It was taken at an average Bi coverage of 2.4 BL and after annealing at 410 K for 30 min.An energy of 127 eV was chosen, since the original image is less distorted than that at 90 eV, yet the Bi(110) spots are still clearly visible.Moreover, at 127 eV the graphene buffer layer spots are clearly visible even after adsorption of Bi.These spots were used as the known reference structure in the distortion correction.We first limit ourselves to the Bi(110) majority domains, where the zig-zag direction is aligned (roughly) with the armchair direction of graphene.The measured lattice constants of Bi(110) are (449.9± 2.0) pm and (481.6 ± 2.0) pm and the misalignment angle between Bi(110) and graphene is (1.75 ± 0.10) • .In addition, the same analysis was also performed for the corresponding LEED image before annealing (not shown).In this case, the measured lattice constants of the Bi(110) are (450.8± 2.0) pm and (482.0 ± 2.0) pm, and the misalignment angle is (1.77 ± 0.10) • .Thus, there is no significant change in the lattice constants and the misalignment angle brought about by the annealing process.Compared to the bulk values of 454 pm and 475 pm [21,22] the shorter axis is compressed by approximately 0.8%, while the longer axis is stretched by approximately 1.4%.Two possible models for the alignment of Bi(110) on graphene are presented in figures 6(b) and (c), which show the lattice matching in the armchair and zig-zag directions of graphene, respectively.In model A the misalignment angle is 1.95 • .Assuming the shorter Bi(110) lattice constant to be 454.318pm, the Bi(110) lattice is in registry with the graphene lattice in this direction after every eight Bi(110) unit cells (see figure 6(b)).This represents a stretching of the shorter Bi(110) axis by less than 0.1% with respect to the bulk value.In model B the misalignment angle is 1.74 • .By compressing the shorter Bi(110) lattice constant by about 0.6% with respect to the bulk value to 451.297 pm, the Bi(110) lattice is in registry with the graphene lattice in this direction after every nine Bi(110) unit cells.Out of these models, model B fits the LEED data better, even though it requires a larger deviation from the bulk lattice constants and an additional unit cell to be in registry with the graphene lattice.
In both models no registry in the direction of the longer Bi(110) lattice constant is achieved on a reasonable length scale as shown in figure 6(c).In model A the bulk lattice constant of 475 pm is assumed, while in model B the measured lattice constant of 481.6 pm is used.The variation of the lattice constant in this range, however, has no influence on the lack of registry.This fact explains the tendency of the Bi to form needle-like islands, i.e. islands whose dimension is limited in the direction of the longer Bi(110) axis.
The existence of the four sub-domains of the Bi(110) minority domains, where the zig-zag direction is aligned (roughly) with the zig-zag direction of graphene, i.e. the domains that appear predominantly after annealing, can be explained if it is assumed that the associated islands are aligned with respect to the majority islands.This alignment results in the formation of a mirror twin boundary.Lyu et al have shown that the angle between the two domains at such a boundary is slightly smaller than 90 • .In their case, they measured an angle of 87.6 • [23].This is not surprising considering that the Bi(110) unit cell is rectangular.Aligning the diagonals of two rectangular unit cells at a mirror twin boundary results in an angle of ϑ = 2 • arctan(b 1 /b 2 ) between the domains, where b 1 is the shorter lattice constant and b 2 is the longer lattice constant.Using the bulk lattice constants of Bi(110), 454 pm and 475 pm, results in ϑ ≈ 87.41 • , which is close to the angle measured by Lyu et al [23].Using our measured lattice constants of (449.9 ± 2.0) pm and (481.6 ± 2.0) pm we get ϑ ≈ 86.28 • .
There are two possible alignments of the two Bi(110) domains with respect to each other and two possible alignments of the Bi(110) majority domain with respect to graphene, resulting in four possible alignments of the Bi(110) minority domain.These four alignments are depicted in figures 6(d)-(g).Assuming an angle of 86.28 • between the majority and minority domains, the angles between the zig-zag direction of the Bi(110) minority domain (green) and the zigzag direction of graphene are ±1.98 • and ±5.46 • .These angles agree well with the misalignment angles of the four sub-domains of ±(2.0 ± 0.2) • and ±(5.6 ± 0.2) • measured in LEED (yellow and orange dotted lines in figure 6(a)).The insets in figures 6(d)-(g) show the assignments of the Bi(110) domains to the LEED spots.This shows that the LEED measurements are in line with an increased formation of mirror twin boundaries by annealing.

Summary and conclusions
Bi grows on graphene in a Volmer-Weber growth mode.The majority domain formed during a deposition at 300 K consists of Bi(110) islands that have their zig-zag direction, except for a small misalignment, aligned in the armchair direction of graphene.We proposed a structure model for the exact alignment.A misalignment of ±1.74 • is required in order to achieve lattice matching with the graphene in the Bi(110) zigzag direction.However, no lattice matching is achieved perpendicular to the zig-zag direction.Hence, the Bi(110) islands have a needle-like shape with their dimension perpendicular to the Bi(110) zig-zag direction being limited.Besides this lateral strain effect, the height of the islands are defined by quantum confinement.
An annealing step at 410 K for 30 min leads to the increased formation of Bi(110) mirror twin boundaries, and hence a minority structure that is aligned, again except for a small misalignment, with the zig-zag direction of graphene.This minority structure possesses four sub-domains, due to two possible alignments of the Bi(110) structure with respect to each other and two possible alignments of the Bi(110) majority structure with respect to graphene.The concentration of mirror twin boundaries can be controlled by the deposition temperature.
We showed in this study, that the interface of proximitized 2D materials can be accurately controlled by epitaxy.To what extend these Bi islands will have implications towards the carrier dynamics in graphene will be investigated future transport experiments.

Figure 1 .
Figure 1.(a) and (b) LEED images for an average Bi coverage of 1.2 BL and 0.15 BL, respectively, recorded at an electron energy of 200 eV.In (a) three domains of Bi(110) marked in red, green and blue are clearly visible.In (b) the Bi spots are barely visible.The LEED pattern is essentially that of graphene/SiC.

Figure 2 .
Figure 2. (a) and (b) Large scale STM images for average Bi coverages of 0.6 and 2 BL, respectively (Tunneling parameters: (a) 100 mV, 200 pA; (b) 100 mV, 600 pA).The inset shows epitaxial graphene and the 6 × 6 corrugation of the buffer layer, which was used to determine the crystallographic axes (100 mV, 500 pA).(c) and (d) Histograms of the island heights for average Bi coverages of 0.6 and 2 BL, respectively.The inset shows an atomically resolved STM image of one of the needle-like islands (−100 mV, 1.9 nA), overlayed with a structural model of Bi(110)[21,22].For the majority of Bi(110) islands, their zig-zag direction is aligned with the ⟨1120⟩ direction of SiC (except for a small misalignment, see text), i.e. the armchair direction of graphene.A minority of Bi(110) islands form domain boundaries with an angle of ≈90 • with the majority Bi(110) islands (green arrows).

Figure 3 .
Figure 3. LEED images for average Bi coverages varying from 0.6 to 3.6 BL: (a)-(d) directly after deposition, (e)-(h) after annealing at 410 K for 30 min.The rectangles with dotted lines show different domains of Bi(110) (see text for details).The panels on the right side show zoom-ins of the (01), (11) and (10) spots of Bi(110), respectively, for a Bi coverage of 3.6 BL as marked by the smaller rectangles with dashed lines.The distortions at the edges of the images are due to the mounting clamps.The images were recorded at an electron energy of 90 eV.

Figure 4 .
Figure 4. (a) Large scale STM image for an average Bi coverage of 2 BL after annealing at 410 K for 30 min (Tunneling parameters: 500 mV, 200 pA).(b) Line profiles along the marked positions in (a).Baseline shifted for better visibility.(c) Histogram of the island heights.

Figure 5 .
Figure 5. Variation of the deposition temperature: LEED images for a Bi coverage of 1.2 BL (a) before and (b) after annealing at 410 K for 30 min, recorded at an electron energy of 90 eV.Contrary to all previous experiments the deposition was performed at a substrate temperature of 100 K.

Figure 6 .
Figure 6.Alignment of the Bi(110) islands with respect to graphene: (a) LEED image for a Bi coverage of 2.4 BL after annealing at 410 K for 30 min recorded at 127 eV.The image was corrected for distortions using LEEDCal [28, 29].(b) and (c) Models for the alignment of Bi(110) on graphene in the armchair and zig-zag directions of graphene, respectively.Model A assume a misalignment angle of 1.95 • , while model B assumes a misalignment angle of 1.74 • .Model B fits the LEED data better.The red X mark the intersection of the longer Bi(110) crystal axis with the graphene lattice.(d)-(g) Possible alignments of the two major Bi(110) domains with respect to graphene.Majority: Bi(110) zig-zag direction in graphene armchair direction (blue).Minority: Bi(110) zig-zag direction in graphene zig-zag direction (green).The corresponding LEED spots are marked in the insets.