Tunable electronic properties in stanene and two dimensional silicon-carbide heterobilayer : A first principles investigation

A novel two-dimensional heterobilayer, stanene-silicon carbide (Sn/SiC) is predicted using first principles calculations. Three representational stacking configurations are considered to study the structure and electronic properties of Sn/SiC heterobilayer in detail. All the stacking patterns of the heterobilayer manifest a wide band gap of ∼160meV at the K point with the Dirac cone well preserved, exhibiting the largest energy band gap among all stanene-based two dimensional heterostructures. Moreover, the energy gap can be efficiently varied through changing the interlayer distance between stanene and SiC layer as well as applying biaxial strain. Our computed small effective mass (∼0.0145mo) and the characteristic of nearly linear band dispersion relation of the heterobilayer also suggest high mobility of the carriers. The space charge distribution of the valence and conduction bands and the density of states (DOS) of the heterostructure unravel that SiC monolayer retains the various excellent electrical properties of stanene in a great extent and allows the carriers to move through the stanene layer only. This implies the potentiality of 2D SiC as a good substrate for stanene to adopt the heterobilayer. Our results reveal that Sn/SiC heterobilayer would be a promising platform for future Sn-based high speed nanoelectronic and spintronic devices. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5066029


I. INTRODUCTION
After the successful exfoliation of graphene in 2004, 1 research in two dimensional (2D) nanostructures has experienced an enormous attention. 2,3In recent times, group-IV elements including germanene, silicene, plumbene and stanene have attracted especial consideration owing to their exotic electronic feature and potential applications in nanodevices. 4In this arena of 2D materials, stanene has been remarkably known as a material for topological insulator due to its strong spin orbit coupling (SOC) in room temperature. 5,6tanene film functionalized with ethynyl 7 is reported as an excellent candidate to show Quantum spin Hall (QSH) effect with a bulk gap of ∼0.22eV, which is much higher than the recently reported light weight arsenene oxide QSH insulator (89 meV) 8 or heavier WSe 2 QSH insulator (116meV). 9If the coupling between spin and orbital degrees of freedom is allowed, asymmetry-functionalized stanene turns into quantum anomalous Hall (QAH) insulator with a sizable nontrivial band gap of 0.31 eV. 10 This is also greatly larger than the recently predicted band gaps of 75meV and 20 meV in hexagonal Nb 2 O 3 11 and kagome Cs 2 Mn 3 F 12 lattice, 12 respectively.Other intriguing features of stanene such as topological superconductivity, 13 enhanced thermoelectricity: 14 all these have drawn immense interest in the research of this prospective material.In addition, Zhu et al. 15 successfully fabricated low buckled stable form of stanene 16 on Bi 2 Te 3 (111) surface using molecular beam epitaxy.Of late, Yuhara et al. 17 have synthesized 2D stanene epitaxially on a Ag(111) single crystal template and analyzed its crystalline structure synergetically.
However, likewise graphene possesses zero band gap semi-metallic feature which limits its application in high performance nanoelectronic devices, although ∼0.1 eV band gap is found with the inclusion of SOC. 5,18In this regard, recently Khan et al. 19 studied heterobilayer consisting of stanene and hexagonal boron nitride (h-BN) taking various stacking configurations and reported an energy band gap of ∼30 meV at the K point with the linear dispersion relation well preserved.Besides, Chen et al. 20 investigated stanene/graphene bilayer hybrid structure considering various stacking patterns with the aid of density functional theory (DFT) and found 77meV energy gap for their 20 relatively stable stacking pattern, although the Dirac cone of stanene 16 was not maintained in the heterostructure.Unlike stanene, 2D SiC possesses a huge direct band gap of ∼2.5 eV 21,22 and is a material of interest. 23,24Recent investigation 25 suggests that SiC is an excellent substrate to grow graphene epitaxially together.The chemical stability, significant band gap of 2D SiC along with similar hexagonal structure as that of stanene make SiC very promising to apply it with stanene in the form of heterobilayer with a view to enlarging the band gap and modulating other electronic features of stanene while preserving its Dirac cone feature. 16n the present article, we report an Ab initio DFT study on the structure and electronic characteristics of the Sn/SiC heterobilayer.Three representative atomistic models are considered so as to examine the influence of various stacking methods on the important properties of Sn/SiC heterobilayer.A considerable band gap is induced with Fermi level of the heterostructure located at the gap accompanied by the presence of almost linear energy dispersion relation around the K point.All the models are studied regarding their stability, electronic properties including electronic band diagram, total and partial density of states (PDOS), effective carrier mass, charge density distribution of the valence and conduction bands, charge transfer between the stanene and SiC monolayers accompanied by the tuning of energy band gap upon varying the interlayer spacing as well as applying tensile strain.Due to the coupling of a considerable large band gap and high mobility of the carriers, Sn/SiC heterobilayer would be an excellent platform for the realization of future Sn-based high-speed spintronic and nanoelectronic devices.

II. METHODS
We accomplished first principles calculations in the framework of DFT by a plane-wave basis set as implemented in the Quantum Espresso 26,27 PWSCF suite to examine the structure and electronic characteristics of the Sn/SiC heterobilayer.The generalized gradient approximation (GGA) 28 with Perdew-Burke-Ernzerhof (PBE) exchange correlation functional is employed to define the electron exchange correlation energy.Norm conserving Troullier Martin pseudo-potentials 29 are used to represent the electron-ion interactions.To include the Vander Waals (vdW) inter-molecular attractive forces, Semi-empirical Grimme's DFT-D2 30,31 is implemented throughout the calculation.Cutoff for plane-wave energy is taken as 400 eV.For the structural optimization, threshold for maximum force was taken as 10 −3 Ry/a.u.The convergence of the k points is checked and a 6 × 6 × 1 Monkhorst-Pack k-mesh scheme 32 is adopted for the Brillouin zone integrations.We utilized a necessary vacuum of 20 Å towards the direction normal to the heterobilayer interface to avoid the interactions between two immediate bilayers.Besides, Heyd-Scuseria-Ernzerhof (HSE) 33,34 screened exchange hybrid functional is introduced to compare the electronic band structures.
To evaluate the structural stability of three stacking patterns quantitatively, binding energies (E b ) per Sn atom were calculated as where, E Sn/SiC is the overall energy of the Sn/SiC heterobilayer, E Sn and E SiC are the energies of the free standing stanene and SiC single layer with the same structure as they were in the respective heterobilayer, N is the total number of the stanene atoms.For all the considered structures, we estimated the effective mass of electrons (m e * ) from the curvature of the conduction band minimum whereas the effective mass of holes (m h * ) from the curvature of the valence band maximum at the K point using the expression: where, m * is the particle effective mass, h is the reduced Planck constant, k is the wave vector and E(k) is the energy dispersion relation.

III. RESULTS AND DISCUSSIONS
As a benchmark test, we first calculated the optimized lattice parameters of free standing stanene and monolayer SiC.In our study, we found the lattice constant of SiC as 3.095 Å after optimization which is consistent with the earlier theoretical investigations. 21,22This value also corresponds well with the experiment by Lin et al. 35 For the low buckled stanene, the lattice constant, buckling height and Sn-Sn bond length after optimization are computed as 4.595 Å, 0.8838 Å and 2.7963 Å, respectively which also corresponds well with earlier experimental 15,36 and theoretical 16,19,20,37,38 studies.To model the bilayer heterostructure, since the lattice constant of Sn is about 33% more than the lattice constant of SiC, we constructed the Sn/SiC heterobilayer taking a lateral periodicity of 2 × 2 for stanene and a lateral periodicity of 3 × 3 for SiC, as shown in Fig. 1.Consequently, the lattice constant of the heterostructure is set as a Sn/SiC =3a SiC =9.285 Å with only ∼1% tensile strain being caused on stanene monolayer to confirm the commensurability criterion of the heterobilayer supercell.
Thus, our supercell for the Sn/SiC bilayer heterostructure comprises eight Sn atoms, nine C atoms and nine Si atoms.Our proposed model can be compared to the Sn/h-BN heterobilayer structures studied by Khan et al. 19 The difference between the lattice constant of stanene and h-BN was ∼47%, therefore they 19 implemented the heterostructure taking a lateral periodicity of 4 × 4 for h-BN and a lateral periodicity of 2 × 2 for stanene where stanene monolayer was subjected to ∼7% tensile strain to ensure the commensurability.Electrical and optical properties of graphene/stanene bilayer hybrid structures were studied by Chen et al. 20 where they 20 considered a supercell comprising 4× 4 graphene and 2× 2 stanene supercell owing to ∼ 46% lattice difference between graphene and stanene.Further, 4.7% strain was applied to stanene layer to satisfy the commensurability condition.In addition, to investigate the change in electronic behavior of graphene/MoS 2 heterobilayer 39 under external strain and electric field, a lateral periodicity of 5× 5 for graphene along with a lateral periodicity of 4 × 4 for MoS 2 was implemented owing to ∼23% lattice variation where graphene was subjected to ∼3.8% tensile strain.Three representational high-symmetry bilayer configurations are taken into consideration in this investigation with three non-identical lateral rearrangements of the two layers as illustrated respectively in Fig. 1(a), 1(b) and 1(c).Pattern-A displays the bilayer heterostructure with the armchair edge of Sn is placed directly above that of SiC with one C atom being located below one Sn atom.In case of pattern-B, as like as pattern-A the armchair edge of Sn is placed directly above that of SiC, but here, one Si atom being positioned below one Sn atom.Pattern-C is obtained by placing the center of a hexagon in the SiC layer directly below that of the stanene layer.Cai et al. 40 and Ren et al. 41 considered similar stacking patterns to study the silicene/h-BN and stanene/MoS 2 heterobilayer structures, respectively.
In order to find the equilibrium interlayer spacing between the Sn and SiC layer, we calculated the interface binding energies at interlayer distances within the range 2.   I).Obtained result is in near proximity to the interlayer distance of SiGe/h-BN heterostructure studied by Chen et al. 42 Using PBE in the scheme of GGA, they 42 obtained an equilibrium interlayer distance of 3.26 Å for their 42 relatively stable stacking pattern.Our result is also comparable to that of graphene/h-BN heterobilayer studied by Fan et al. 43 For AB stacking pattern (the most stable configuration), their DFT simulation yielded an equilibrium interlayer spacing of 3.2 Å with local density approximation (LDA).In addition, for the stanene/MoS 2 heterostructure studied by Ren et al., 41 their simulation study gave an equilibrium interlayer spacing of 3.2 Å for their 36 most stable stacking pattern.Accordingly, ∼3.3 Å interlayer distance is reported in literature for all patterns of graphene/BC 3 44 and graphene/stanene 20 heterobilayers.The three configurations exhibit almost similar binding energies while structure-A showing the lowest one.Our calculated binding energies per stanene atom at equilibrium are -223.89meV, -223.67 meV, -223.75 meV for structure A, B and C, respectively.Similar binding energies give a prior implication that the character of the present heterobilayer system will be insensitive to the stacking configurations.This phenomenon will be verified later while calculating the energy band diagram and density of states (DOS) for all three configurations.Besides, binding energy characterizes the inter-layer interaction strength quantitatively.Greater negative value of the binding energy suggests that the heterobilayer structures are energetically stable and might be uncomplicated for experimental realization. 42It also confirms the electronic stability of all three configurations.As an aside, the binding energies per Sn atom at equilibrium for three configurations exceed 220meV.This value is greater than 20 the regular binding energies of vdW interactions 45 indicating rather than weak vdW interaction, stanene is bound to monolayer SiC by some other method, such as orbital hybridization or electrostatic interaction. 46The binding energies of the heterobilayers like silicene/h-BN, 40 stanene/MoS 2 41 as well as SiGe/h-BN 42 are less than 100meV reflecting weak vdW interactive forces between the two different layers of these heterobilayer systems.On the contrary, in Sn/h-BN heterostructure, 19 stanene monolayer and the h-BN substrate are bound to each other with binding energies exceeding 250 meV per unit cell.Our obtained result for binding energy at optimum spacing also corresponds well with graphene/stanene heterobilayer 20 where stanene is firmly bound to graphene through binding energy higher than 180 meV per stanene atom as well as the system where graphene adsorbed on HfO 2 (111) with 110meV binding energy. 46esides, the optimized interlayer spacings of the stacking patterns of the Sn/SiC heterobilayer are in the range from in nanoelectronic devices.Again, there is an optical gap at the Γ point.These results are consistent with the DFT simulation studies by Broek et al. 16 as well as Lu et al. 38 In addition, the energy bands of the stanene at the Dirac point are made up of 5Pz unsaturated hybrid orbitals which form π-bonding, assuring the stability of the stanene.Unlike stanene, monolayer SiC exhibits semiconducting property whose electronic band diagram is depicted in Fig 3(b).In our study, we found a direct band gap of 2.5192 eV at the K point, agrees well with the previous studies. 21,22The gap stretches over the Dirac cone region of stanene.These results confirm the validity of our simulation.Our intension is to induce a band gap and modulate other electronic features of stanene even though maintaining its Dirac cone. 16Due to several fascinating properties, 2D SiC is predicted to be an excellent material to achieve this goal with introducing no further carrier transport route around the Fermi surface.Next, we concentrate our investigation on the band structures of the three configurations to see the influence of SiC monolayer on the electronic behavior of stanene.The band diagrams along DOS of the Sn/SiC heterobilayer for the three optimized configurations are presented in Fig. 4. The Fermi level is made 0. For all the configurations, the shapes of the band structure are almost identical verifying that the character of the present heterobilayer is quite irresponsive to the stacking pattern.Comparing to the band diagram of pristine stanene shown in Fig. 3(a), the linear band structure near Fermi level is interrupted, resulting in a metal to semiconductor transition.Therefore, Sn/SiC heterobilayer is a semiconductor with band gap of 162.2 meV, 154.7 meV, 159.8 meV respectively for structure A, B and C at the K-point (Dirac point) as enrolled in Table I.Opening a band gap in the heterobilayer is further supported by the corresponding DOS of each structure.Like other 2D honeycomb structures, stanene also exhibits lattice symmetry which is broken in the Sn/SiC heterostructure owing to strong interlayer interaction and thereby inducing a bang gap.This kind of behavior is also reported in graphene based heterostructures. 43,44,49o the best of our knowledge, the band gap induced in the present heterobilayer is larger than that of other approaches of opening a band gap in stanene.For instance, Garg et al. 50onsidered four patterns for the co-doping of boron-nitride in stanene and reported a maximum band gap of 80 meV.Khan et al. 19 showed a gap opening of ∼30meV in stanene by adopting Sn/h-BN heterobilayer.Xiong and co-workers 51 found a band gap of 105meV for the MoS 2 /stanene bilayer heterostructure.Furthermore, the Dirac feature of freestanding stanene, π bands, is well preserved near the Fermi level in the energy gaps of the proposed heterostructures (Fig. 4).Opening a direct band gap while maintaining the Dirac cone of stanene indicates its potential application in nanoelectronics.
Since PBE functional tends to underestimate the energy gap of the semiconductor, we also checked the electronic band structure of the Sn/SiC heterobilayer using HSE hybrid functional which is proven to provide the energy band gap close to the experiments.The HSE computed band gaps of the heterobilayer are 598.4meVfor structure-A, 581.2meV for structure-B and 591.7meV for structure-C.Although the HSE enhances the band gap of the heterobilayer, similar electronic band structure near Fermi level with a direct band gap at the K-point is observed.Comparably, for 2D octagon-nitrogene 52 the PBE yielded a band gap of 2.9 eV which was enhanced to 4.7 eV using HSE functional with identical band structure as that of PBE near Fermi level.A large increase of the band gap with HSE functional is also noticed in h-BN 53 (4.56 eV to 5.56 eV), arsenene oxide 8 (from 89 meV to 232 meV) as well as Nb 2 O 3 11 (from 75 meV to 110 meV).Therefore, it is expected that upon experimental realization we might have a wider band gap of the Sn/SiC heterobilayer rather than the gap obtained from PBE.
Moreover, to see the result of SOC on the Sn/SiC heterobilayer, we have computed the band diagrams of all three configurations incorporating SOC effect.Fig. 5 presents the band structures of the three patterns incorporating the effect of SOC.The observed band gaps are 91.78meV for structure-A, 84.72meV for structure-B and 91meV for structure-C.Although the gaps are found at the K point and at the Fermi level, the inclusion of SOC decreases the band gap.Remarkable energy splitting is induced in the conduction bands and valence bands of the bilayer system due to SOC effects.Band splitting in the conduction and valence bands accompanied by the reduction of band gap due to SOC effects is also observed in the investigation of Ren et al. 41 for stanene/MoS 2 heterobilayer system.Using PBE their 41 hollow pattern of stanene/MoS 2 heterobilayer yielded a band gap 76.5meV without SOC.However, when they 41 included SOC, the energy gap decreased to a value of 11.9 meV.Correspondingly, energy band splitting in the conduction bands and also in the valence bands is noticed in the investigation of Xiong et al. 51 for MoS 2 /stanene heterobilayer system.
Linear band dispersion near Dirac point indicates high mobility of the carriers which is an important aspect for the application in high speed FET devices.To examine this feature, the effective mass of holes (m h * ) and electrons (m e * ) at the K point is computed for all the configurations of the Sn/SiC bilayer system.As we can see from Table I, the effective mass of electrons ranges within 0.0136-0.015m0 whereas the effective mass of holes ranges between 0.0149-0.0153m0 for the three configurations.Similar values of the effective mass for electrons and holes were reported in graphene/g-C 3 N 4 bilayer. 54These values are very small as well as more superior to others stanene-based nanoelectronics.Furthermore, we have estimated the carrier mobility (µ) using the expression µ = eτ m ; here τ is the scattering time.Taking the scattering time of stanene as same as that of graphene or silicene (∼10 -13 s), 41,55 our calculation yielded the carrier mobility of the present heterobilayer on the order ∼10 5 cm 2 V -1 s -1 .The scattering time of silicene is also in this order (∼10 5 cm 2 V -1 s -1 ). 56s a comparison, carrier mobility of stanene calculated with the deformation potential approximation (DPA) 57 is 3-4 × 10 6 cm 2 V -1 s -1 .
With a view to studying the interlayer interaction in conjunction with the electronic behavior of the Sn/SiC heterobilayer to a greater extent, the total and atom projected density of states of structure A and B are shown in Fig. 6.For the valence band within a range from −2 to 0 eV and also for the conduction band within a range from 0 to 2 eV, the dominating nature of stanene in the electronic conditions in the characteristic peaks can be easily observed from Fig. 6(a) and (c).Again, the atom projected density of states structure A and B presented respectively in Fig. 6(b) and (d) reflect that the contribution of stanene P orbital (Sn-P) is the most prominent one in the valence and conduction bands.This characteristics is as same as the behavior of pristine stanene (Dominating role of unsaturated π orbital near Fermi level). 16Moreover, stanene orbitals are not hybridized with SiC orbitals around the Fermi energy level indicating the interactions between the two different layers are not intensive.Therefore, carriers will move through the stanene layer only.For further verification, we have calculated the real-space charge distribution of the valence and conduction bands for the three configurations.
All the configurations yielded similar results, therefore the charge density distribution of structure A is shown in Fig. 7.
The valence band and conduction band are confined within the stanene, indicating the dominating nature of stanene to determine the electronic behavior of the Sn/SiC heterobilayer.Hence, SiC will be a good substrate with introducing no extra transport route around the Fermi surface.
We next examine the transfer of charge between the stanene and SiC layer in order to observe the charge redistribution after the development of the heterobilayer.SiC layer in the corresponding heterobilayer.As the CDDs of the three configurations gave similar results, we have plotted the CDD of structure-A (Fig. 8) as a representative of the Sn/SiC bilayer.From Fig. 8 we can see that the SiC layer gives of electrons which are received by the stanene layer.Significant localization of the electron rearrangement at the Sn/SiC interface is also observed.Again, there is the evidence of intralayer charge redistribution within buckled honeycomb stanene: a certain amount of electrons are reduced in the Sn-Sn bonds as well as in the lower Sn atoms while majority of the electrons are piled up in the upper Sn atoms.This transfer of charge within the sublattices of stanene leads to the breaking of symmetry.The localization of charge reorganization in the interlayer section is due to orbital overlap, 20 or the polarization and potential gradient fields from neighboring layers. 40ext to these, we concentrate our investigation to modulate the band gap of Sn/SiC heterobilayer for its potential application in high speed nanoelectronic devices.At first, we examined the effect of varying the interlayer distance of the Sn and SiC monolayer on the electronic structure of Sn/SiC heterobilayer for all three stacking configurations.The change of the energy band gap upon changing the interlayer distance is shown in Fig. 9.When the interlayer spacing is increased, the band gap decreases.This is because of the fact that with the increasing of the interlayer spacing, the influence of the SiC substrate on stanene layer reduces, thereby stanene tends to recover it original symmetry. 58,59As a consequence, the energy band gap reduces.When the interlayer spacing is decreased from the optimized value, the gap size increases firstly due to the increased interaction between the stanene and SiC monolayers which leads to destroy the lattice symmetry of stanene.If the interlayer spacing is further decreased, the stronger interlayer coupling causes the destruction of the band structures of the heterobilayer struc-  heterobilayer 51 where the band gap increases at first upon reducing the interlayer distance, but decreases after that if the reduction of the interlayer spacing is further continued from the optimized value.
In this section, we investigate the homogeneous external strain to modulate the band gap of Sn/SiC heterostructure.We applied biaxial strain on the heterobilayer system using the expression ε = a−a 0 a 0 × 100%, where a 0 is the intrinsic lattice constant and a is the strained lattice constant.The band gap variation of structure-A when tensile biaxial strain of variable percentage applied to the system is shown in Fig. 10(a).When the structure was subjected to tensile strain, a minor rise in the energy gap at an expense of increased effective mass up to 4% tensile strain can be observed.At 6% biaxial strain, a relatively large decrease of band gap as well as huge increase of electron effective mass is noticed reflecting strain limitation of the structure.The magnification of the band structure around the Fermi level nearby K point under 4% and 6% biaxial strain subjected to the structure-A is shown in Fig. 10(b).Upon applying 8% tensile stress, the destruction of the Dirac feature of stanene is observed implying the destruction of the structure under strain.However, the strain causes self-hole doping characteristics with the downward shifting of the Fermi level noticeably as depicted in Fig. 10(b).
Finally, the feasibility of the experimental realization of the Sn/SiC heterobilayer is discussed based on the obtained theoretical results.Negligible lattice mismatch (∼1%) between stanene and SiC supercells together with the higher binding energy (>223meV per Sn atom) suggests that the bilayer is feasible in experiments. 60This fact is further supported by the absence of covalent bonding between Sn and SiC layer (∼3.2 Å interlayer distance). 8,60Previously, h-BN 19 and MoS 2 41 were proposed as substrate to support the stanene film where the lattice mismatches were 7% and ∼1.28% respectively indicating that Sn/SiC heterobilayer having the lowest lattice mismatch.As to discuss the effect of h-BN and MoS 2 substrate on stanene, identical to SiC layer, h-BN and MoS 2 substrates open an energy gap in stanene with the dominance of the stanene near the Fermi level is observed implying that stanene plays the key role in the electronic behavior of stanene/h-BN 19 and stanene/MoS 2 41 heterobilayers.However, for the stanene/MoS 2 41 heterobilayer linear Dirac dispersion was preserved a little bit away for the K point.Comparing to h-BN and MoS 2 , the highest opened band gap, the lowest lattice mismatch accompanied by the emergence of the Dirac cone make SiC as a potential substrate to realize stanenebased heterostructures for application in experiments and nanoelectronic devices.

IV. CONCLUSIONS
In summary, a novel 2D Sn/SiC heterobilayer is proposed by means of first principles DFT calculation.The structure and electronic properties of Sn/SiC heterobilayer are systemically examined taking vdW interaction between Sn and SiC layers into consideration.We have studied three representational stacking patterns and their binding energies more than that of weak vdW interaction suggest improved stability of the heterostructure.The band gaps for all three stacking patterns are found to be ∼160meV owing to symmetry breaking of the two sublattices in stanene with the Dirac cone well preserved.Thus, Sn/SiC heterobilayer might excel the main barrier of stanene to apply it in the nanoelectronic devices, the absence of energy band gap.The space charge density distribution and PDOS analysis reveal that the Sn/SiC heterobilayer will retain various excellent electrical properties of stanene in a great extent.Therefore, SiC monolayer can be a perfect substrate for stanene letting the carriers to transport through the stanene layer only.Moreover, our computed small effective mass coupled with the nearly linear band dispersion relation of stanene indicates high carrier mobility.What's more, the change of the interlayer spacing between the Sn and SiC layer can tune the band gap efficiently.A minor increase in band gap is also noticed under tensile biaxial strain.These exceptional and excellent properties of the Sn/SiC heterobilayer would further promote its experimental realization with a decent band gap and applying in novel Sn-based integrated functional nanodevices and spintronic devices.

FIG. 1 .
FIG. 1.Three representational stacking configurations of Sn/SiC heterobilayer at equilibrium (a) Pattern-A (b) Pattern-B (c) Pattern-C (d) Side view of the heterobilayer.'D' denotes the inter-layer distance between Sn and SiC monolayer and 'h' is the buckling height of the stanene.

FIG. 2 .
FIG. 2. The variation of binding energy per stanene atom as a function of interlayer distance for three stacking configurations of Sn/SiC heterobilayer.Down arrows indicate the optimized interlayer distances.

FIG. 6 .FIG. 7 .FIG. 8 .
FIG. 6. Atom projected density of states for structure-A and structure-B of the Sn/SiC heterobilayer.The Fermi level is made 0. Overall contribution from Sn, Si and C atoms of (a) structure-A and (c) structure-B.Individual contribution of each orbital of the atoms in the range -2 to 2 eV for (b) structure-A and (d) structure-B.

FIG. 9 .
FIG. 9.The energy band gap of Sn/SiC heterobilayer with the variation of interlayer distance for all the three different stacking arrangements.

FIG. 10 .
FIG. 10. (a)The variation of band gap and electron effective mass with the increase of biaxial strain up to 6% applied to structure-A of the heterobilayer.(b) Magnification of the band structure nearby K point around Fermi level under 4% and 6% biaxial strain.

TABLE I .
Structural and electronic properties of Sn/SiC heterobilayer for the three configurations, comprising binding energies per Sn atoms (E b ), band gap at K point (E g ) using PBE and HSE functional, optimized interlayer distance (D), and the effective masses of electrons (m e * ) and holes (m h * ) at Dirac point, here m o is the free electron mass.
3.20 Å for structure-C (listed in Table