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Extended α-phase Bi atomic layer on Si(1 1 1) fabricated by thermal desorption
Journal Pre-proofs Full Length Article Extended α-phase Bi atomic layer on Si(111) fabricated by thermal desorption Shin-Ching Hsieh, Chia-Hsiu Hsu, Han-De Chen, Deng-Sung Lin, FengChuan Chuang, Pin-Jui Hsu PII: DOI: Reference:
S0169-4332(19)32919-8 https://doi.org/10.1016/j.apsusc.2019.144103 APSUSC 144103
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Applied Surface Science
Received Date: Revised Date: Accepted Date:
4 July 2019 14 August 2019 18 September 2019
Please cite this article as: S-C. Hsieh, C-H. Hsu, H-D. Chen, D-S. Lin, F-C. Chuang, P-J. Hsu, Extended α-phase Bi atomic layer on Si(111) fabricated by thermal desorption, Applied Surface Science (2019), doi: https://doi.org/ 10.1016/j.apsusc.2019.144103
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Extended α-phase Bi atomic layer on Si(111) fabricated by thermal desorption Shin-Ching Hsieh1,+, Chia-Hsiu Hsu2,+, Han-De Chen1, Deng-Sung Lin1,3, Feng-Chuan Chuang2,* and Pin-Jui Hsu1,3.* 1Department
of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
2Department
of Physics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
3Center + These
for Quantum Technology, National Tsing Hua University, Hsinchu 30013, Taiwan two authors contribute equally to this work.
*Corresponding
authors: [email protected] (F-C Chuang); [email protected] (P.
J. Hsu) Abstract Two-dimensional materials with sizable spin-orbit coupling are not only interesting to fundamental studies, but also useful candidates for technological applications. Here, we report on the fabrication of extended α-phase Bi atomic layer on Si(111) surface by means of thermal desorption. The atomic and electronic structures have been investigated by combining scanning tunneling microscopy (STM) experiments with density functional theory (DFT) calculations. While β-phase Bi trimer with 𝟑 𝐱 𝟑 R30o surface reconstruction can be prepared by room-temperature deposition with subsequent post annealing at 700 K, the α-phase Bi monomer only appears at 800 K due to thermal desorption with the Bi desorption rate of 0.26 ML/min. From our DFT calculations, the α-phase Bi shows Rashba energies ER = 15 meV and 3 meV at high symmetry points of 𝑀 and 𝐾, respectively. Since α-phase Bi monomer represents isotropic lattice symmetry with a dilute Bi density, it may serve as a potential template to tune Rashba effect by incorporating with multiple elements. Keywords: Rashba effect, bismuth, silicon, microscopy, density functional theory
𝟑× 𝟑
R30o surface alloy, scanning tunneling
Introduction: In bulk crystals lacking of inversion symmetry, Dresselhaus discovered that a sizable spin-orbit coupling breaks the Kramers theorem in which electronic bands with opposite spin eigenstates are no longer doubly degenerate1. Similar scenario also applies to the surface or interface with intrinsic inversion asymmetry, Rashba and Bychkov further uncovered the presence of spin splitting on surface electronic band structure driven by spin-orbit interaction in two-dimensional (2D) systems2. Such spin splitting is considerably large due to spin-orbit interaction strength with Landau-Lifshitz Z2 scaling, i.e., Z is atomic number, in heavy elements3,4, and results in spin-momentum locking phenomenon whereas electron backscattering is prohibited by time-reversal symmery5,6. Rashbatype spin splitting has a great potential in technology applications, one well-known example is the development of Datta-Das spin transistor7, which in turn attracts many interests to investigate and realize Rashba effect on semiconductor materials. Furthermore, strong spin-orbit coupling in two dimensional materials, such as surface alloy or graphene-like structure, would also result in two 1
dimensional topological insulator phases (a.k.a quantum spin Hall effect), which has been the focus of numerous studies in recent years8-14. Giant Rashba spin splitting was reported on S1 surface state of β-phase (trimer model) in bismuth (Bi) atomic layer grown on Si(111) substrate15,16, the splitting is located at 𝑀 point along the 𝛤-𝑀-𝛤 direction with a Rashba energy of ER = 140 meV. With high quality sample preparation methods, the splitting of S1 surface state exhibiting a nonvortical feature at 𝑀 point can be observed, which is associated with time reversal symmetry breaking at reciprocal 𝐾 point according to β-phase Bi 3 × 3 R30o surface17. In addition to S1, the other two surface states, S2 and S3 also represent Rashbatype splittings, with ER = 60 meV at 𝑀 point for S2 and ER = 60 meV at 𝛤 point for S317. In contrast to 1 monolayer (ML) β-phase Bi, another α-phase Bi can also be grown but with a lower coverage of 1/3 ML on Si(111) and has a monomer 3 × 3 R30o structure with additional symmetry of two mirror planes15,16. With both σv1 and σv2 of mirror planes, one could expect more isotropic Rashba-type splitting on α-phase Bi monomer as compared to β-phase Bi trimer because of simpler symmetric configuration. Recently, it has been recognized that engineering a single layer of 2D alloy compounds on silicon surface offers a new pathway to tune the Rashba effect18,19. For example, doping β-phase Bi on Si(111) with additional Na rotates 3 × 3 R30o surface reconstruction to form the chained-trimer structure, the electron density of Bi atoms can thus be enhanced to display metallic Rashba surface states18. According to α-phase Bi monomer structure, the distance between Bi atoms is more separated than that of β-phase Bi trimer, it might be used as an interesting template not only capable of incorporating with other materials, but also has higher degrees of freedom to stabilize different surface reconstructions. Although α-phase Bi monomer structure possesses these interesting perspectives from fundamental point of view, there is still no systematic growth study carried out by employing STM approach until so far. In contrast, the spatial averaging techniques, for example, low energy electron diffraction (LEED) combined with LEED I-V, was often the tool used for characterizing α-phase Bi20, which is less straightforward to visualize the detailed features at atomic scale. In this work, we have combined the scanning tunneling microscopy (STM) and density functional theory (DFT) to study the α-phase Bi monomer structure on Si(111). From thickness- and temperature-dependent growth studies, we have demonstrated that single layer of well-defined and extended α-phase Bi monomer can be prepared via thermal desorption from post annealing β-phase Bi trimer monolayer in our STM results. From DFT calculations, the Rashba spin splittings have been observed in α-phase Bi monomer structure at high symmetry points of 𝑀 and 𝐾, respectively The corresponding Rashba energy, momentum offset, and Rashba parameters have been extracted, which are smaller as compared to those values in β-phase Bi trimer monolayer. We also found the magnitude of Rashba parameters is proportional to the surface coverage of Bi atoms. Experimental methods and calculation details: The experiments were performed in an ultrahigh vacuum (UHV) multifunctional chamber with the base pressure p ≤ 2 x 10-10 mbar. The clean Si(111) substrate with 7 × 7 surface reconstruction was prepared by cycles of degassing and flashing up to 1200 K21. The deposition rate of 0.18 monolayer (ML) per minute of Bi was defined from β-phase Bi trimer structure on Si(111) as calibrated from STM measurements directly. The DFT calculations22,23 were carried out within the generalized gradient 2
approximation24 with projector augmented wave (PAW) pseudopotential method25, as implemented in the Vienna Ab-initio Simulation Package (VASP)26,27. The kinetic energy cutoff was set to 400 eV (29.4 Ry), and the gamma-centered 12 × 12 × 1 Monkhorst-Pack grid was used to sample the surface Brillouin zones (SBZ) for the 3 phases. Moreover, for all our surface calculations, the theoretical Si bulk lattice constant of 5.468 Å was adopted. We employed a periodically repeating slab consisting of six Si bilayers, a reconstructed layer, and a vacuum space of ∼20 Å. Hydrogen atoms were used to passivate the Si dangling bonds at the bottom of the slab, and the positions of H atoms were kept fixed. Similarly, the silicon atoms of the bottom bilayer were kept fixed at the bulk crystalline positions. The remaining Bi and Si atoms were relaxed until the residual force was smaller than 0.01 eV/Å. Results and discussions: In Fig. 1, we have carried out the thickness dependent growth studies of Bi on Si(111)-7 × 7 surface at room temperature (RT). Note that the coverage of Bi is calibrated from β-phase trimer structure as described in the section of experimental methods. At the low coverage of 0.25 ML Bi on Si(111) in Fig. 1(a), we still can trace the 7 × 7 surface reconstruction of Si(111) substrate underneath due to only part of the surface is covered by Bi. As the Bi coverage is increased to 0.5 ML in Fig. 1(b), the Si(111) substrate can barely be seen anymore and we did not resolve any ordered structure or reconstruction on Bi covered surface. For higher coverage of 0.75 ML in Fig. 1(c), the surface of Bi film starts to become rough and some Bi clusters even already appear at 1.0 ML as shown in Fig. 1(d). According to these results, we conclude that neither α- nor β-phase Bi structure can be grown when depositing Bi atomic layer onto Si(111)-7 × 7 surface at RT. In order to fabricate highly ordered Bi atomic layer, we did the post annealing procedure after the RT growth aforementioned in Fig. 1. As shown in Fig. 2(a), the STM topography shows the 0.25 ML Bi/Si(111) after post annealing at 700 K for 1 minute. The Si(111)-7 × 7 substrate can remain to be observed at this low Bi coverage, and the bright protrusions with uniform sizes imply for Bi nanodots formation which was intensively reported on several different kinds of materials on Si(111)-7 × 7 surface before28-30. To create long-range ordering of Bi nanodots, the detailed studies with fine tuning of the deposition rate and substrate temperature will be required particularly at such low Bi coverage, which could be an interesting topic for future investigation. In contrast to Bi nanodots at low coverage regime, the β-phase Bi trimer structure starts to form at higher coverage with the same post annealing temperature of 700 K. As seen from Fig. 2(b) to (d), βphase Bi atomic layer gradually covers up the Si(111)-7 × 7 surface and we also found there are always small patches of β-phase Bi islands on top with an apparent height close to 3.1 Å, which is one step height of Si(111)-7 × 7 surface. The atomic resolution image shown in the inset of Fig. 2(c) reveals the β-phase Bi trimer structure with 3 × 3 R30o surface reconstruction. After 1.0 ML of Bi trimer is complete, as seen in Fig. 2(d), further deposition of Bi will result in stabilizing Bi(111) films on top of Si(111) surface31,32. Through subsequent heat treatment, the homogenous β-phase Bi atomic layer can be prepared and we did not observe any indication of α-phase Bi monomer structure when the post annealing temperature is lower than 700 K. Since α-phase Bi monomer has 1/3 the coverage of β-phase Bi trimer, thermal desorption of Bi by means of higher post annealing temperature on β-phase Bi trimer 3
could be one approach leading to the formation of α-phase Bi monomer. As shown in Fig. 3(a), we have first grown a sample with a complete β-phase Bi on Si(111) surface using the same procedures as in Fig. 2(d). Then we further post annealed the sample of Fig. 3(a) with higher temperature at 800 K for 1 minute and the result has been shown in Fig. 3(b) where a mixing of two domains on the sample surface can be observed. According to the atomic scale image of β-phase Bi trimer like the one shown in the inset of Fig. 2(c), we can therefore identify the β-phase Bi domain. Same approach applies to identify the other domain at which the atomic resolution image shows the simulated STM image of α-phase Bi monomer structure with 3 × 3 R30o surface reconstruction as reported before33. While the higher post annealing temperature at 800 K results in desorbing a certain amount of Bi atoms, increasing post annealing time thus indicates that the fabrication of α-phase Bi monomer structure fully covering the Si(111) surface is possible. As shown in Fig. 3(c), we have further demonstrated that the fully extended α-phase Bi monomer structure can be prepared by a longer post annealing time to 3 minutes at 800 K from the sample of Fig. 3(b) and the inset shows the corresponding atomic resolution image of α-phase Bi monomer structure. To quantify the desorption rate, we have counted the percentage of occupied surface area of α- and β-phase Bi as a function of different Bi coverages, and a desorption rate of 0.26 ML/min can be obtained for the post annealing temperature at 800 K from the statistic plot in Fig. 3(d). According to atomic resolution images of α-phase monomer and β-phase trimer are shown in Fig. 4(a) and (b), the energetically favorable structure models have been constructed in Fig. 4(c) and (d), respectively. For the α-phase monomer, Bi atoms adsorb at the top site of bottom layer (T4 site) in the first bilayer of Si substrate, whereas for the β-phase20, the Bi trimer centered over the T4 site formed a milkstool structure. In order to verify experimental observations, we have simulated STM images based on proposed structure models and corresponding results are shown in Fig. 4(e) and (f), showing an agreement for both α- and β-phase Bi surface alloys grown on Si(111). The energy range of simulated STM images are integrals from -2.5 and -3.0 eV to Fermi level for α- and β-phase, respectively. Apart from that, we also examined the Rashba effect from electronic band structures of α-phase monomer in Fig. 5, which has been directly compared with different Rashba parameters of β-phase Bi trimer reported in previous study17. Our analysis shows that the contribution of Bi is mostly at first surface band below Fermi energy in both α-phase and β-phase surfaces, thus we list the Rashba parameters of first surface bands. Fig. 5(a) and 5(b) are the band structures of α-phase monomer along 𝛤-𝑀-𝛤 and 𝛤-𝐾-𝛤, respectively, and both surfaces exhibit Rashba-split bands around 𝑀 and 𝐾 points. In addition, the calculated Rashba-split bands in α-phase are also comparable to those surface localized states reported in previous study of angle-resolved ultraviolet photoelectron spectroscopy near the Fermi level34. The band width along 𝛤- 𝐾 is larger than that along 𝛤-𝑀. Furthermore, due the bonding characters of two surfaces, our band structures showed that, in αphase, Rashba-split band has the major orbital contribution from pz orbital, since sp2 hybrid orbitals of Bi atom bond to three underneath Si atoms, leaving the pz orbital of Bi unbonded on the surface. On the other hand, in β-phase, the Rashba-split band has the major contribution from the px and py orbitals. Since each Bi atom bonds to Si atom nearly perpendicularly via pz orbital, this leaves both px and py unbonded on the surface. Rashba parameter (𝛼𝑅) is a characteristic parameter quantifying the strength of the spin splitting which is obtained from the momentum offset (𝑘0) and Rashba energy (𝐸𝑅)15. In Fig. 5(c) and 5(d), the 4
band structures are zoomed in both 𝑀 and 𝐾 points. From the band dispersions, we extracted the momentum offset 𝑘0 = 0.043 Å ―1, Rashba energy 𝐸𝑅 = 0.015 𝑒𝑉 around 𝑀 point, and obtained the Rashba parameter 𝛼𝑅 = 0.69 𝑒𝑉Å. In addition, the values of 𝑘0 = 0.018 Å ―1, 𝐸𝑅 = 0.003 𝑒𝑉 and 𝛼𝑅 = 0.39 𝑒𝑉Å are acquired around 𝐾 point. We have also calculated the band structures and Rashba parameter of β-phase trimer the same way as Ref. [17] using the highest occupied surface band (corresponding to the S1 band reported in Ref[17]) along 𝛤-𝑀-𝛤 and 𝛤-𝐾-𝛤, which is in fairly good agreement with previous results17. The calculated 𝛼𝑅 of β-phase trimer around 𝑀 and 𝐾 points are 2.22 and 1.40 𝑒𝑉Å, respectively. All these values are summarized in Fig. 5(e). We found that the 𝛼𝑅 of α-phase monomer are almost one third of that of β-phase trimer. This result seems to be associated with the concentration of Bi atoms in these two phases. Conclusions: A monolayer β-phase Bi film can be prepared by depositing Bi on Si(111)-7 × 7 surface at RT and subsequent post annealing at 700 K, and has been characterized from atomic resolution of 3 × 3 R30o trimer structure in STM studies. With an increase of post annealing temperature to 800 K, αphase Bi monomer appears with the same 3 × 3 R30o surface structure, but one-third of β-phase Bi coverage due to thermal desorption of Bi. By counting the surface area ratios of α- and β-phase Bi, the Bi desorption rate of 0.26 ML/min has been extracted at post annealing temperature of 800 K. In combination with DFT calculations, α-phase Bi monomer exhibits Rashba-type spin splitting with momentum offset 𝑘0 = 0.043Å ―1, Rashba parameter 𝛼𝑅 = 0.69 𝑒𝑉Å, and Rashba energy 𝐸𝑅 = 0.015 𝑒𝑉 for the 𝑀 point and 𝑘0 = 0.018 Å ―1, 𝛼𝑅 = 0.39 𝑒𝑉Å, and 𝐸𝑅 = 0.003 𝑒𝑉 for the 𝐾 point, respectively. With these results, we refer the absence of lattice symmetry reduction and dilute Bi density to the weaker Rashba splitting on α-phase Bi monomer as compared to β-phase trimer on one hand, and expect the α-phase Bi monomer a more interesting template to engineer Rashba effect due to higher structural flexibility on the other hand. Acknowledgements: SCH, HDC, DSL and PJH acknowledge support from the competitive research funding from National Tsing Hua University, Ministry of Science and Technology of Taiwan under Grants No. MOST-1082636-M-007-002 and MOST-107-2112-M-007-001-MY3, and center for quantum technology from the featured areas research center program within the framework of the higher education sprout project by the Ministry of Education (MOE) in Taiwan. CHH and FCC acknowledge support from the National Center for Theoretical Sciences and the Ministry of Science and Technology of Taiwan under Grants No. MOST-107-2628-M-110-001-MY3. CHH and FCC are also grateful to the National Center for HighPerformance Computing for computer time and facilities. References 1. G. Dresselhaus, Spin-oribit coupling effects in zincblend structures, Phys. Rev. 100, 580-586 (1995) 2. Y. A. Bychkov and E. I. Rashba, Properties of a 2D electron gas with lifted spectral degeneracy, JETP Lett. 39, 78-81 (1984) 3. A.R. Mackintosh, O.K. Andersen, in: M. Springford (Ed.), Electrons at the Fermi Surface, Cambridge University Press, London, p. 149 (1980) 4. K. V. Shanavas, Z. S. Popović, and S. Satpathy, Phys. Rev. B 90, 165108 (2014) 5
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Fig. 1. STM topography images of different coverages of Bi grown on Si(111) at RT. a) 0.25 ML, b) 0.5 ML, c) 0.75 ML, and d) 1.0 ML. From 0.25 ML Bi coverage in a), the atomic structure of Si(111) 7 × 7 substrate can still be observed. Above 0.25 ML, we did not resolve periodic ordering and the surface roughness keeps increasing up to 1.0 ML for the RT growth. Measurement parameters: U = -2.0 V; I = 0.2 nA; T = 300 K.
8
Fig. 2. STM topography images of different coverages of Bi grown on Si(111) at RT with post annealing at 700K. After post annealing for 1 minute at this temperature, the atomic flat Bi monolayer with small patches of the 2nd layer can be obtained. Only β-phase 3 × 3 R30o trimer forms at the surface after this post annealing treatment. Measurement parameters: U = -2.0 V; I = 0.2 nA; T = 300 K.
9
Fig. 3. STM topography images of different post annealing temperatures and times of Bi grown on Si(111). a) 1.0 ML Bi coverage with post annealing at 700 K for 1 min. b) 1.0 ML Bi coverage with post annealing at 800 K for 1 min. The α-phase monomer with 1/3 ML Bi coverage appears due to thermal desorption of Bi at higher annealing temperature. c) Extended α-phase Bi monomer over the whole surface can be prepared by post annealing at 800 K for 3 mins. d) Areas of α and β-phase as a function of different coverages after post annealing at 800 K for 1 min. The desorption rate of Bi determined from these statistics is about 0.26 ML/min. Measurement parameters: U = -2.0 V; I = 0.2 nA; T = 300 K.
10
Fig. 4. STM topography image and structure model of single-layer Bi on Si(111). The atomic resolution images for α and β-phases are shown in a) and b), respectively. The top and bottom atoms of first layer of Si(111) substrate are denoted by blue and light blue, respectively. The underlying Si layers are denoted by yellow. c) Monomer structure (α-phase) with 1/3 ML Bi coverage. d) Trimer structure (β-phase) with 1 ML Bi coverage. The black rhombus indicates the 3 × 3 R30o unit cell in the inset. e) and f) are the simulated STM images based on structure models in c) and d). Measurement parameters: U = -2.5 V for a); U = -3.0 V for b); I = 1 nA; T = 77 K.
11
Fig. 5. Band structures of the DFT calculation for α-phase Bi/Si(111) along a) 𝛤-𝑀-𝛤 and b) 𝛤-𝐾-𝛤.The blue solid circles and red circles indicate the spin orientations along ― 𝑦 and + 𝑦 axis, respectively. The surface Brillouin zones are inserted in a). The red lines represent the SBZ for 1x1 phase and black lines represent that for 3 × 3 phase. c) and d) are the zoom-in band structures around the 𝑀 and 𝐾 point, respectively. Momentum offset (𝑘0), Rashba energy (𝐸𝑅), and Rashba parameter (𝛼𝑅) of bands contributed from the Bi atoms are summarized in Table e) and comparison between α- and βphase Bi/Si(111).
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S0169-4332(19)32919-8 https://doi.org/10.1016/j.apsusc.2019.144103 APSUSC 144103
To appear in:
Applied Surface Science
Received Date: Revised Date: Accepted Date:
4 July 2019 14 August 2019 18 September 2019
Please cite this article as: S-C. Hsieh, C-H. Hsu, H-D. Chen, D-S. Lin, F-C. Chuang, P-J. Hsu, Extended α-phase Bi atomic layer on Si(111) fabricated by thermal desorption, Applied Surface Science (2019), doi: https://doi.org/ 10.1016/j.apsusc.2019.144103
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Extended α-phase Bi atomic layer on Si(111) fabricated by thermal desorption Shin-Ching Hsieh1,+, Chia-Hsiu Hsu2,+, Han-De Chen1, Deng-Sung Lin1,3, Feng-Chuan Chuang2,* and Pin-Jui Hsu1,3.* 1Department
of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
2Department
of Physics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
3Center + These
for Quantum Technology, National Tsing Hua University, Hsinchu 30013, Taiwan two authors contribute equally to this work.
*Corresponding
authors: [email protected] (F-C Chuang); [email protected] (P.
J. Hsu) Abstract Two-dimensional materials with sizable spin-orbit coupling are not only interesting to fundamental studies, but also useful candidates for technological applications. Here, we report on the fabrication of extended α-phase Bi atomic layer on Si(111) surface by means of thermal desorption. The atomic and electronic structures have been investigated by combining scanning tunneling microscopy (STM) experiments with density functional theory (DFT) calculations. While β-phase Bi trimer with 𝟑 𝐱 𝟑 R30o surface reconstruction can be prepared by room-temperature deposition with subsequent post annealing at 700 K, the α-phase Bi monomer only appears at 800 K due to thermal desorption with the Bi desorption rate of 0.26 ML/min. From our DFT calculations, the α-phase Bi shows Rashba energies ER = 15 meV and 3 meV at high symmetry points of 𝑀 and 𝐾, respectively. Since α-phase Bi monomer represents isotropic lattice symmetry with a dilute Bi density, it may serve as a potential template to tune Rashba effect by incorporating with multiple elements. Keywords: Rashba effect, bismuth, silicon, microscopy, density functional theory
𝟑× 𝟑
R30o surface alloy, scanning tunneling
Introduction: In bulk crystals lacking of inversion symmetry, Dresselhaus discovered that a sizable spin-orbit coupling breaks the Kramers theorem in which electronic bands with opposite spin eigenstates are no longer doubly degenerate1. Similar scenario also applies to the surface or interface with intrinsic inversion asymmetry, Rashba and Bychkov further uncovered the presence of spin splitting on surface electronic band structure driven by spin-orbit interaction in two-dimensional (2D) systems2. Such spin splitting is considerably large due to spin-orbit interaction strength with Landau-Lifshitz Z2 scaling, i.e., Z is atomic number, in heavy elements3,4, and results in spin-momentum locking phenomenon whereas electron backscattering is prohibited by time-reversal symmery5,6. Rashbatype spin splitting has a great potential in technology applications, one well-known example is the development of Datta-Das spin transistor7, which in turn attracts many interests to investigate and realize Rashba effect on semiconductor materials. Furthermore, strong spin-orbit coupling in two dimensional materials, such as surface alloy or graphene-like structure, would also result in two 1
dimensional topological insulator phases (a.k.a quantum spin Hall effect), which has been the focus of numerous studies in recent years8-14. Giant Rashba spin splitting was reported on S1 surface state of β-phase (trimer model) in bismuth (Bi) atomic layer grown on Si(111) substrate15,16, the splitting is located at 𝑀 point along the 𝛤-𝑀-𝛤 direction with a Rashba energy of ER = 140 meV. With high quality sample preparation methods, the splitting of S1 surface state exhibiting a nonvortical feature at 𝑀 point can be observed, which is associated with time reversal symmetry breaking at reciprocal 𝐾 point according to β-phase Bi 3 × 3 R30o surface17. In addition to S1, the other two surface states, S2 and S3 also represent Rashbatype splittings, with ER = 60 meV at 𝑀 point for S2 and ER = 60 meV at 𝛤 point for S317. In contrast to 1 monolayer (ML) β-phase Bi, another α-phase Bi can also be grown but with a lower coverage of 1/3 ML on Si(111) and has a monomer 3 × 3 R30o structure with additional symmetry of two mirror planes15,16. With both σv1 and σv2 of mirror planes, one could expect more isotropic Rashba-type splitting on α-phase Bi monomer as compared to β-phase Bi trimer because of simpler symmetric configuration. Recently, it has been recognized that engineering a single layer of 2D alloy compounds on silicon surface offers a new pathway to tune the Rashba effect18,19. For example, doping β-phase Bi on Si(111) with additional Na rotates 3 × 3 R30o surface reconstruction to form the chained-trimer structure, the electron density of Bi atoms can thus be enhanced to display metallic Rashba surface states18. According to α-phase Bi monomer structure, the distance between Bi atoms is more separated than that of β-phase Bi trimer, it might be used as an interesting template not only capable of incorporating with other materials, but also has higher degrees of freedom to stabilize different surface reconstructions. Although α-phase Bi monomer structure possesses these interesting perspectives from fundamental point of view, there is still no systematic growth study carried out by employing STM approach until so far. In contrast, the spatial averaging techniques, for example, low energy electron diffraction (LEED) combined with LEED I-V, was often the tool used for characterizing α-phase Bi20, which is less straightforward to visualize the detailed features at atomic scale. In this work, we have combined the scanning tunneling microscopy (STM) and density functional theory (DFT) to study the α-phase Bi monomer structure on Si(111). From thickness- and temperature-dependent growth studies, we have demonstrated that single layer of well-defined and extended α-phase Bi monomer can be prepared via thermal desorption from post annealing β-phase Bi trimer monolayer in our STM results. From DFT calculations, the Rashba spin splittings have been observed in α-phase Bi monomer structure at high symmetry points of 𝑀 and 𝐾, respectively The corresponding Rashba energy, momentum offset, and Rashba parameters have been extracted, which are smaller as compared to those values in β-phase Bi trimer monolayer. We also found the magnitude of Rashba parameters is proportional to the surface coverage of Bi atoms. Experimental methods and calculation details: The experiments were performed in an ultrahigh vacuum (UHV) multifunctional chamber with the base pressure p ≤ 2 x 10-10 mbar. The clean Si(111) substrate with 7 × 7 surface reconstruction was prepared by cycles of degassing and flashing up to 1200 K21. The deposition rate of 0.18 monolayer (ML) per minute of Bi was defined from β-phase Bi trimer structure on Si(111) as calibrated from STM measurements directly. The DFT calculations22,23 were carried out within the generalized gradient 2
approximation24 with projector augmented wave (PAW) pseudopotential method25, as implemented in the Vienna Ab-initio Simulation Package (VASP)26,27. The kinetic energy cutoff was set to 400 eV (29.4 Ry), and the gamma-centered 12 × 12 × 1 Monkhorst-Pack grid was used to sample the surface Brillouin zones (SBZ) for the 3 phases. Moreover, for all our surface calculations, the theoretical Si bulk lattice constant of 5.468 Å was adopted. We employed a periodically repeating slab consisting of six Si bilayers, a reconstructed layer, and a vacuum space of ∼20 Å. Hydrogen atoms were used to passivate the Si dangling bonds at the bottom of the slab, and the positions of H atoms were kept fixed. Similarly, the silicon atoms of the bottom bilayer were kept fixed at the bulk crystalline positions. The remaining Bi and Si atoms were relaxed until the residual force was smaller than 0.01 eV/Å. Results and discussions: In Fig. 1, we have carried out the thickness dependent growth studies of Bi on Si(111)-7 × 7 surface at room temperature (RT). Note that the coverage of Bi is calibrated from β-phase trimer structure as described in the section of experimental methods. At the low coverage of 0.25 ML Bi on Si(111) in Fig. 1(a), we still can trace the 7 × 7 surface reconstruction of Si(111) substrate underneath due to only part of the surface is covered by Bi. As the Bi coverage is increased to 0.5 ML in Fig. 1(b), the Si(111) substrate can barely be seen anymore and we did not resolve any ordered structure or reconstruction on Bi covered surface. For higher coverage of 0.75 ML in Fig. 1(c), the surface of Bi film starts to become rough and some Bi clusters even already appear at 1.0 ML as shown in Fig. 1(d). According to these results, we conclude that neither α- nor β-phase Bi structure can be grown when depositing Bi atomic layer onto Si(111)-7 × 7 surface at RT. In order to fabricate highly ordered Bi atomic layer, we did the post annealing procedure after the RT growth aforementioned in Fig. 1. As shown in Fig. 2(a), the STM topography shows the 0.25 ML Bi/Si(111) after post annealing at 700 K for 1 minute. The Si(111)-7 × 7 substrate can remain to be observed at this low Bi coverage, and the bright protrusions with uniform sizes imply for Bi nanodots formation which was intensively reported on several different kinds of materials on Si(111)-7 × 7 surface before28-30. To create long-range ordering of Bi nanodots, the detailed studies with fine tuning of the deposition rate and substrate temperature will be required particularly at such low Bi coverage, which could be an interesting topic for future investigation. In contrast to Bi nanodots at low coverage regime, the β-phase Bi trimer structure starts to form at higher coverage with the same post annealing temperature of 700 K. As seen from Fig. 2(b) to (d), βphase Bi atomic layer gradually covers up the Si(111)-7 × 7 surface and we also found there are always small patches of β-phase Bi islands on top with an apparent height close to 3.1 Å, which is one step height of Si(111)-7 × 7 surface. The atomic resolution image shown in the inset of Fig. 2(c) reveals the β-phase Bi trimer structure with 3 × 3 R30o surface reconstruction. After 1.0 ML of Bi trimer is complete, as seen in Fig. 2(d), further deposition of Bi will result in stabilizing Bi(111) films on top of Si(111) surface31,32. Through subsequent heat treatment, the homogenous β-phase Bi atomic layer can be prepared and we did not observe any indication of α-phase Bi monomer structure when the post annealing temperature is lower than 700 K. Since α-phase Bi monomer has 1/3 the coverage of β-phase Bi trimer, thermal desorption of Bi by means of higher post annealing temperature on β-phase Bi trimer 3
could be one approach leading to the formation of α-phase Bi monomer. As shown in Fig. 3(a), we have first grown a sample with a complete β-phase Bi on Si(111) surface using the same procedures as in Fig. 2(d). Then we further post annealed the sample of Fig. 3(a) with higher temperature at 800 K for 1 minute and the result has been shown in Fig. 3(b) where a mixing of two domains on the sample surface can be observed. According to the atomic scale image of β-phase Bi trimer like the one shown in the inset of Fig. 2(c), we can therefore identify the β-phase Bi domain. Same approach applies to identify the other domain at which the atomic resolution image shows the simulated STM image of α-phase Bi monomer structure with 3 × 3 R30o surface reconstruction as reported before33. While the higher post annealing temperature at 800 K results in desorbing a certain amount of Bi atoms, increasing post annealing time thus indicates that the fabrication of α-phase Bi monomer structure fully covering the Si(111) surface is possible. As shown in Fig. 3(c), we have further demonstrated that the fully extended α-phase Bi monomer structure can be prepared by a longer post annealing time to 3 minutes at 800 K from the sample of Fig. 3(b) and the inset shows the corresponding atomic resolution image of α-phase Bi monomer structure. To quantify the desorption rate, we have counted the percentage of occupied surface area of α- and β-phase Bi as a function of different Bi coverages, and a desorption rate of 0.26 ML/min can be obtained for the post annealing temperature at 800 K from the statistic plot in Fig. 3(d). According to atomic resolution images of α-phase monomer and β-phase trimer are shown in Fig. 4(a) and (b), the energetically favorable structure models have been constructed in Fig. 4(c) and (d), respectively. For the α-phase monomer, Bi atoms adsorb at the top site of bottom layer (T4 site) in the first bilayer of Si substrate, whereas for the β-phase20, the Bi trimer centered over the T4 site formed a milkstool structure. In order to verify experimental observations, we have simulated STM images based on proposed structure models and corresponding results are shown in Fig. 4(e) and (f), showing an agreement for both α- and β-phase Bi surface alloys grown on Si(111). The energy range of simulated STM images are integrals from -2.5 and -3.0 eV to Fermi level for α- and β-phase, respectively. Apart from that, we also examined the Rashba effect from electronic band structures of α-phase monomer in Fig. 5, which has been directly compared with different Rashba parameters of β-phase Bi trimer reported in previous study17. Our analysis shows that the contribution of Bi is mostly at first surface band below Fermi energy in both α-phase and β-phase surfaces, thus we list the Rashba parameters of first surface bands. Fig. 5(a) and 5(b) are the band structures of α-phase monomer along 𝛤-𝑀-𝛤 and 𝛤-𝐾-𝛤, respectively, and both surfaces exhibit Rashba-split bands around 𝑀 and 𝐾 points. In addition, the calculated Rashba-split bands in α-phase are also comparable to those surface localized states reported in previous study of angle-resolved ultraviolet photoelectron spectroscopy near the Fermi level34. The band width along 𝛤- 𝐾 is larger than that along 𝛤-𝑀. Furthermore, due the bonding characters of two surfaces, our band structures showed that, in αphase, Rashba-split band has the major orbital contribution from pz orbital, since sp2 hybrid orbitals of Bi atom bond to three underneath Si atoms, leaving the pz orbital of Bi unbonded on the surface. On the other hand, in β-phase, the Rashba-split band has the major contribution from the px and py orbitals. Since each Bi atom bonds to Si atom nearly perpendicularly via pz orbital, this leaves both px and py unbonded on the surface. Rashba parameter (𝛼𝑅) is a characteristic parameter quantifying the strength of the spin splitting which is obtained from the momentum offset (𝑘0) and Rashba energy (𝐸𝑅)15. In Fig. 5(c) and 5(d), the 4
band structures are zoomed in both 𝑀 and 𝐾 points. From the band dispersions, we extracted the momentum offset 𝑘0 = 0.043 Å ―1, Rashba energy 𝐸𝑅 = 0.015 𝑒𝑉 around 𝑀 point, and obtained the Rashba parameter 𝛼𝑅 = 0.69 𝑒𝑉Å. In addition, the values of 𝑘0 = 0.018 Å ―1, 𝐸𝑅 = 0.003 𝑒𝑉 and 𝛼𝑅 = 0.39 𝑒𝑉Å are acquired around 𝐾 point. We have also calculated the band structures and Rashba parameter of β-phase trimer the same way as Ref. [17] using the highest occupied surface band (corresponding to the S1 band reported in Ref[17]) along 𝛤-𝑀-𝛤 and 𝛤-𝐾-𝛤, which is in fairly good agreement with previous results17. The calculated 𝛼𝑅 of β-phase trimer around 𝑀 and 𝐾 points are 2.22 and 1.40 𝑒𝑉Å, respectively. All these values are summarized in Fig. 5(e). We found that the 𝛼𝑅 of α-phase monomer are almost one third of that of β-phase trimer. This result seems to be associated with the concentration of Bi atoms in these two phases. Conclusions: A monolayer β-phase Bi film can be prepared by depositing Bi on Si(111)-7 × 7 surface at RT and subsequent post annealing at 700 K, and has been characterized from atomic resolution of 3 × 3 R30o trimer structure in STM studies. With an increase of post annealing temperature to 800 K, αphase Bi monomer appears with the same 3 × 3 R30o surface structure, but one-third of β-phase Bi coverage due to thermal desorption of Bi. By counting the surface area ratios of α- and β-phase Bi, the Bi desorption rate of 0.26 ML/min has been extracted at post annealing temperature of 800 K. In combination with DFT calculations, α-phase Bi monomer exhibits Rashba-type spin splitting with momentum offset 𝑘0 = 0.043Å ―1, Rashba parameter 𝛼𝑅 = 0.69 𝑒𝑉Å, and Rashba energy 𝐸𝑅 = 0.015 𝑒𝑉 for the 𝑀 point and 𝑘0 = 0.018 Å ―1, 𝛼𝑅 = 0.39 𝑒𝑉Å, and 𝐸𝑅 = 0.003 𝑒𝑉 for the 𝐾 point, respectively. With these results, we refer the absence of lattice symmetry reduction and dilute Bi density to the weaker Rashba splitting on α-phase Bi monomer as compared to β-phase trimer on one hand, and expect the α-phase Bi monomer a more interesting template to engineer Rashba effect due to higher structural flexibility on the other hand. Acknowledgements: SCH, HDC, DSL and PJH acknowledge support from the competitive research funding from National Tsing Hua University, Ministry of Science and Technology of Taiwan under Grants No. MOST-1082636-M-007-002 and MOST-107-2112-M-007-001-MY3, and center for quantum technology from the featured areas research center program within the framework of the higher education sprout project by the Ministry of Education (MOE) in Taiwan. CHH and FCC acknowledge support from the National Center for Theoretical Sciences and the Ministry of Science and Technology of Taiwan under Grants No. MOST-107-2628-M-110-001-MY3. CHH and FCC are also grateful to the National Center for HighPerformance Computing for computer time and facilities. References 1. G. Dresselhaus, Spin-oribit coupling effects in zincblend structures, Phys. Rev. 100, 580-586 (1995) 2. Y. A. Bychkov and E. I. Rashba, Properties of a 2D electron gas with lifted spectral degeneracy, JETP Lett. 39, 78-81 (1984) 3. A.R. Mackintosh, O.K. Andersen, in: M. Springford (Ed.), Electrons at the Fermi Surface, Cambridge University Press, London, p. 149 (1980) 4. K. V. Shanavas, Z. S. Popović, and S. Satpathy, Phys. Rev. B 90, 165108 (2014) 5
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Fig. 1. STM topography images of different coverages of Bi grown on Si(111) at RT. a) 0.25 ML, b) 0.5 ML, c) 0.75 ML, and d) 1.0 ML. From 0.25 ML Bi coverage in a), the atomic structure of Si(111) 7 × 7 substrate can still be observed. Above 0.25 ML, we did not resolve periodic ordering and the surface roughness keeps increasing up to 1.0 ML for the RT growth. Measurement parameters: U = -2.0 V; I = 0.2 nA; T = 300 K.
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Fig. 2. STM topography images of different coverages of Bi grown on Si(111) at RT with post annealing at 700K. After post annealing for 1 minute at this temperature, the atomic flat Bi monolayer with small patches of the 2nd layer can be obtained. Only β-phase 3 × 3 R30o trimer forms at the surface after this post annealing treatment. Measurement parameters: U = -2.0 V; I = 0.2 nA; T = 300 K.
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Fig. 3. STM topography images of different post annealing temperatures and times of Bi grown on Si(111). a) 1.0 ML Bi coverage with post annealing at 700 K for 1 min. b) 1.0 ML Bi coverage with post annealing at 800 K for 1 min. The α-phase monomer with 1/3 ML Bi coverage appears due to thermal desorption of Bi at higher annealing temperature. c) Extended α-phase Bi monomer over the whole surface can be prepared by post annealing at 800 K for 3 mins. d) Areas of α and β-phase as a function of different coverages after post annealing at 800 K for 1 min. The desorption rate of Bi determined from these statistics is about 0.26 ML/min. Measurement parameters: U = -2.0 V; I = 0.2 nA; T = 300 K.
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Fig. 4. STM topography image and structure model of single-layer Bi on Si(111). The atomic resolution images for α and β-phases are shown in a) and b), respectively. The top and bottom atoms of first layer of Si(111) substrate are denoted by blue and light blue, respectively. The underlying Si layers are denoted by yellow. c) Monomer structure (α-phase) with 1/3 ML Bi coverage. d) Trimer structure (β-phase) with 1 ML Bi coverage. The black rhombus indicates the 3 × 3 R30o unit cell in the inset. e) and f) are the simulated STM images based on structure models in c) and d). Measurement parameters: U = -2.5 V for a); U = -3.0 V for b); I = 1 nA; T = 77 K.
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Fig. 5. Band structures of the DFT calculation for α-phase Bi/Si(111) along a) 𝛤-𝑀-𝛤 and b) 𝛤-𝐾-𝛤.The blue solid circles and red circles indicate the spin orientations along ― 𝑦 and + 𝑦 axis, respectively. The surface Brillouin zones are inserted in a). The red lines represent the SBZ for 1x1 phase and black lines represent that for 3 × 3 phase. c) and d) are the zoom-in band structures around the 𝑀 and 𝐾 point, respectively. Momentum offset (𝑘0), Rashba energy (𝐸𝑅), and Rashba parameter (𝛼𝑅) of bands contributed from the Bi atoms are summarized in Table e) and comparison between α- and βphase Bi/Si(111).
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