Chemical Physics Letters 766 (2021) 138318
Contents lists available at ScienceDirect 
Chemical Physics Letters 
journal homepage: www.elsevier.com/locate/cplett 
Research paper 
The stability of 3C-SiC(111) on Si(111) thin films: 
First-principles calculation 
Eric K.K. Abavare a,*, Bright Kwakye-Awuah a, Oswald A. Nunoo a, Peter Amoako-Yirenkyire b, 
G. Gebreyesus d, Abu Yaya c, Keshaw Singh a 
a Department of Physics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana 
b Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana 
c Department of Materials Science and Engineering, University of Ghana, Legon, Ghana 
d Department of Physics, University of Ghana, Legon, Ghana  
A B S T R A C T   
We report total energy calculation to elucidate the interface structures between SiC(111) and Si(111) with unequal atom densities due to apparent lattice matching 
between them. The result shows one stable and three metastable structures for a particular interfacial system with energy differences ranging from 10–52 meV per Å2 
for both Si-C and Si-Si interfaces respectively. It was observed that, there is atomic undulation near the Si-C interface pinched at Si substrate. The interface formation 
energies indicates Si-Si is more favourable compared with Si-C. The electronic structure reveals metallic character due to electron transfer from SiC to Si due to 
relative electronegativity differences between Si and C atoms.   
1. Background SiC can be employed to grow high quality graphene sheet[6,7] by 
thermal evaporation of Si atoms from the surfaces of either 4H-SiC 
Silicon carbide (SiC) is a semiconductor material with several [8–12] or 6H-SiC[13–15] respectively because of similarities in struc-
stacking sequence of carbon and silicon often referred to as polytypism tural symmetry towards mass production of graphene,[16] selective 
[1] in a long-periodicity. There are several known identifiable polytypic graphitisation of Si atoms from SiC substrates offers natural way to grow 
structures with the first six (6) set being the most ”basic” and structurally few graphene layers on wafer-size pseudosubstrates.[17] Graphene 
fundamental while the rest, long ranged-periodic[1,2]. The sequential science and graphene technology[18,19] of SiC is an envisaged de − facto 
labelling and symmetry are either cubic or hexagonal such as 2H next generation technology material for device applications.[20,21] The 
(wurtzite), 3C(zincblende), 4H, 6H with the nearest atoms being sp3 intension of this boom is related to the formation of potential wide area 
hybridisation. The compounds show rather wide band gap of 2.40, 3.26 graphene sheets on SiC substrate, a more plausible alternative to the 
and 3.02 eV for 3C-, 4H- and 6H-SiC[3] respectively and their break- fabrication of large graphene. Nevertheless, the challenge to this ex-
down dielectric strength ten times higher compared with that of Si. pected explosive growth of graphene technology is prevented by the 
These characteristics have received considerable attention as a potential small wafer size of SiC. Therefore, any application usage of this impor-
new compound semiconductor materials whose applications in power tant semiconductor material requires large wafer size. In other to 
electronic devices includes but not limited to: Schottky barrier diodes in overcome the SiC smallness wafer problem, researchers grow large SiC 
hostile environment, resistance to radiation damage, chemical stability, thin films on Si substrate.[22–25] The epitaxial growth is achieved using 
biotransducers in biosensors,[4] electro-optical properties of photovol- chemical vapour deposition which intuitively accommodates the post 
taics[5] in the visible light region. These applications are plausible silicon technology and offer more robust throughput SiC-related device 
because of the material’s numerous structural modifications possibil- production and application. Notwithstanding, this approach is expected 
ities. In spite of these advantages and impressive volumes of research to offer an alternative potential route for large scale synthesis of uniform 
papers on it in the last 30 years, the realisation of any meaningful wafer-size graphene layers for technological application. 
technological device application is still a challenge because of lack of It should be noted that SiC on Si substrates growth is only possible for 
reproducibility of high quality large crystal epilayers by sublimation 3C-SiC owning to their inherent intrinsic natural symmetry relationship. 
process. But, there is large lattice mismatch that exist between 3C- and Si of 
* Corresponding author. 
E-mail address: eabavare@yahoo.com (E.K.K. Abavare).  
https://doi.org/10.1016/j.cplett.2021.138318 
Received 9 November 2020; Received in revised form 9 December 2020; Accepted 2 January 2021   
Available online 7 January 2021
0009-2614/© 2021 Elsevier B.V. All rights reserved.
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
about 20 % with bond lengths being 1.88 Å and 2.35 Å, respectively. The 
growth of 3C-SiC(111) films on Si(110) surface by chemical vapor 
deposition has been reported by Nishiguchi and collaborators in which 
the near interface is smooth.[26] It was observed that there exist 
geometrical relationship between Si(110) and 3C-SiC(111) hetero-
structure which is parallel in the lateral plane, similarly Si[110] is 
parallel to 3C-SiC[110]. It has been confirmed by other studies that 
epitaxial growth of 3C-SiC(111) films on Si can lead to the generation of 
graphene and often referred to as graphene on silicon (GOS).[27–30] 
Recently, several groups have employed experimental techniques to 
investigate the epitaxial graphene growth of 3C-SiC(111) on Si(111) 
substrates[17,31–33] leading to the growth of pseudomorphic SiC thin 
films in several orders of nanometers on Si. 
Nishiguchi group observed that Si lattice constant aSi [001] matches 
half of the SiC lattice constant aSiC[112] with reduced mismatch of 
1.66%. Similarly doubling the lattice constant of Si along aSi[110] di-
rection matches two and half of the lattice constant of SiC along the 
direction aSiC[110] with mismatch of about 0.26 % between Si(110) and 
3C-SiC(111) surface. Now the reduced mismatch is similar when 
extended to SiC(111) on Si(111) interface where the smallest hexago-
nal cell size of 4 × 4 of Si(111) almost matches 5 × 5 of SiC(111) 
respectively leading to a mismatch of 0.21% which we assumed to be 
matched. However, the unusual matching can cause epitaxial growth on 
each of the (111) faces even though the faces do not meet exactly with 
each other in terms of facial atomic density. For this reason, the Si(111) 
on 3C-SiC(111) surface with a particular alignment as indicated in Fig. 1 
is associated with different interfacial atom densities leading to bond 
strains and twisting of dangling bonds mainly because of atoms 
inequality on the two materials surfaces. The matching interface is un-
usual and can therefore lead to faceting of small surface of different 
Miller-indeces.[34] As a consequence, whenever a crystal is cut normal 
to any selected direction randomly, spontaneous polarisation near the 
interface would results and accelerate the faceting process. If the surface 
is terminated, it would become unstable and ultimately determines the 
physical and chemical properties of the structure.[35] Thin film of SiC 
grown experimentally on Si(110) and Si(111) terminated surfaces 
suggest clearly planar interfacial surfaces[26,30] following graphene Fig. 1. Schematic illustration of the hexagonal 5x5 of 3C-SiC(111) surface (a) 
sublimation on the heterostructure.[31] Clearly, it is scientifically and and 4x4 of Si (111) surface (b); (c) and (d) are C-rich and Si-rich terminated 
technologically interesting to examine why the denser SiC(111) surface surfaces with H passivation respectively for the heterostructures, and are 
grows on sparser Si(111). The atomistic understanding of clarifying slightly pushed down to show the top terminated surfaces. Solid and open balls 
why it is unusual for such lattice matched interfacial morphology to exist shows the first- and second-layer of atoms at the 3C-Si(111) on Si(111) interface supercell. The parallelogram cell shown in (a) is same in (b) indicating 
is totally unknown and theoretical understanding is required. The the matching of the lattice sides of the supercell. 
motivation of this present work is to employ first-principles calculations 
in the framework of density functional theory to investigate the atomic 
structures and electronic states of the interface as well as the structural Zunger[39] fitted to the Quantum Monte Carlo results for the electron 
stability of the heterostructure. The calculation revealed that, near gas.[40] Nuclei and core electrons are simulated by norm-conserving 
perfect interface exist between the dense 3C-SiC(111) and relatively pseudopotentials generated in a recipe proposed by Troullier and Mar-
sparsed Si(111) surfaces, indicating an epitaxial growth unlike the sit- tins.[41] We treat the non-local part of the pseudopotentials following 
uation of the Si(110) on Si(111) calculation where the interface expe- the scheme by Kleinman and Bylander.[42] We regard 2s and 2p of C as 
riences an undulation[36]. well as 3s and 3p of Si as valence orbitals. We have examined the 
The organisation of the paper is as follows: In Section 2, we describe transferability of the pseudopotentials by generating various core radii 
method of calculation in density functional theory in the framework of and computing structural parameters of 3C-SiC. We found that using 
real space formalism. Section 3, presents the energetics and construction core radii of 1.50 a0 and 1.54 a0 for 2s and 2p, respectively, and 2.25 a0 
mechanism of 3C-Si(111) on Si(111) interfacial heterostructure, elec- for both 3s and 3p (a0 = 1 bohr = 0.529 Å) yield equilibrium parameters 
tron states at the interfaces as well as electronic band structures. We such as lattice constant and bulk modulus of 3C-SiC, which are repro-
summarise our results and give our conclusion in Section 4. duced within 1 % and 9 % respectively in calculation errors when compared with experimental values accordingly with other LDA calcu-
2. Method of calculations lations[43–45]. In real space formalism (RS), wave function, electron density, po-
2.1. The density functional theory scheme in real space tential field and other important related quantities are calculated discretely on three dimensional physical coordinates as lattice grid 
The total-energy electronic structure calculations in the framework points. The Hamiltonian matrix in RS is sparce, so computation is effi-
of density-functional theory has been performed in real space scheme. cient when traversing global communication nodes on all parallel 
[37,38] The exchange–correlation effects are treated within the local computers. In this formalism,[46–48] the kinetic-energy operator is 
density approximation (LDA) with parameterized form by Perdew and replaced by a finite-difference operation with sixth-order difference formula, which is sufficient for most applications. Systematic 
2
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
improvements in the accuracy of calculations are achieved by reducing adopted approach is too simplistic and limited in scope because there 
the grid spacing H. In this work, treatment of Si and C element required exist a large number of spatial degrees of freedom for obtaining realistic 
the use of H = 0.21 Å, corresponding to about 62 Ry in the plane-wave- structures. One key issue is the separation between the 3C-SiC(111) face 
basis-set. This cutoff energy is sufficient to assure the required accuracy from the surface of the substrates Si(111) along the perpendicular di-
of 26 meV per atom in total-energy difference among geometries. Atoms rection for individual atomic relaxation. Secondly, the relative lateral 
are fully relaxed until forces acting on each atom is smaller than 50 arrangements of atoms must be overcome since this poses serious 
meV/Å. The numerical calculations are performed in this newly devel- computational challenges for treatment of realistic heterostructure. 
oped code, RSDFT, which is designed for large scale calculations on We have overcome these difficulties and obtained stable structures of 
multi-core massively parallel computers.[49,50] The key benefits of the sparse Si on dense SiC using thin interface slabs which are feasible and 
scheme is that, it is essentially free from Fast Fourier Transform (FFT) then manually explored all multi-dimensional space degrees of freedom 
which is heavy burden in communications on massively parallel archi- for stable structural geometries. For completeness, we used 2 SiC bi-
tecture. The above calculation procedure could reproduce the formation layers (4-layers) and 4-layers of Si to create the 4L/4L interfacial 
energy[51] of 3C-SiC at 0.58 eV in good agreement with experiment at structure (as shown in Fig. 2) with the other two surfaces facing the 
0.68 eV [52]. opposite direction, sufficient vacuum thickness of about 12Å was 
created. The (111) surfaces of SiC and Si dangling bonds were termi-
nated with hydrogen atoms[53]. On Si(111) surface, we examine 
2.2. Slab model calculation several different lateral arrangements and optimised the geometries 
using calculated forces. Stable geometries were reached from the slab 
We define interface as an imperfection of a perfect crystalline ma- model after which we considered lateral primitive cell [the dashed 
terial. For the present system of 3C-SiC(111) on Si(111) hetero- parallelogram in Fig. 1(a)] and define twelve positions on the Si (111) 
structure, there are only two possible interfaces. The surface plane of C surface, the twelve dots are indicated and separated from each other by 
in SiC which meets Si, is the Si-C interface (this creates a surface of Si 
referred to as Si-rich surface) whereas the interface of Si-Si, is where the 1Å along [111]and [100] directions of the SiC side. A given trial ge-ometry which represents a dot is defined as (ix jy) where (i, j = 0, 1, 2, 
Si in SiC meets the Si (again this creates a surface of C called C-rich −
surface). We employ the repeating slab model with atomic slab peri- 3) representing the structures in x-y search space. The interface structure can then be visualised as AxA/BxB (where A and B nearly matched 
odically arranged along perpendicular direction to the surface and 
leaving sufficiently thick vacuum layer which creates the intended lattices) as lateral cell size of SiC and Si respectively shown in Fig. 1 supercell. 
interface. We obtained stable geometries having used slab model with 
fixed atomic layers that are far from the interface. By systematically Now, we put reference points each for the twelve positions on the lateral cell of the Si side and perform structural optimisation for all the 
increasing the atomic layers, we examined the convergence of the 
interface structure and corresponding interface energy. However, this atoms in the slab. This ensure that lateral rearrangements of the indi-
Fig. 2. The side view from Si[100] direction of the Si substrate or the 3C-Si [111]direction of the SiC side geometries: (a) the most stable (S); (b), (c) and (d) 
Metastable (MS) geometries of Si-Si interface of the 3C-SiC(111) on Si(111) heterostructure. The large (blue) and small (purple) balls indicate Si and C atoms 
respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 
3
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
vidual atom positions and interfacing spacings are all optimised. This 3C-SiC(111) on Si(110)[36] system. We found that the calculated 
systematic procedure is repeated for all the trial structures. The 3C-SiC interface energies per unit area of the two models were nearly compa-
(111) face and Si(111) faces commensurate to each other in their rable. We found that the interface energy per unit area of the present 
primitive periodicities, as a consequence, these twelve trials of the model with that obtained from 8L/8L of 3C-SiC(111) on Si(110)[36] 
structural optimisation inherently includes all the other inequivalent interface were comparable. All the performed calculations were done 
trials in which the reference points in the SiC side is put on somewhere using 2x1x1, k-sampling points in the lateral plane of the Brillouin zone 
between the twelve selected positions. In this, the search space for the (BZ) region, and this assured the required accuracy of the investigation. 
structural optimisation is now expanded. For clarity in the optimization 
procedure, two stage steps were performed. First, all the atoms in the 3. Results of calculation and discussion 
supercell were allowed to move freely without any constraint including 
the passivated hydrogen atoms for all the twelve possible structures. 3.1. Interface relaxation structure 
Following that exercise, we again repeated the procedure but this time 
with the hydrogen atoms as well as the first layers of both Si and SiC We performed extensive interface geometry calculations of 3C-Si 
sides were fixed to mimic the semi-infinite bulk structure of both Si and (111) thin films on Si(111) substrate, to search for stable structures of 
SiC. After extensive optimisation procedure and calculations, we arrived either Si-Si or Si-C heterostructure as discussed in Section 2. We found 
at four stable structures for Si-C and Si-Si interface each respectively for several interface geometries (i.e. four optimised geometries for Si-S and 
both two steps approaches which were not dissimilar. Following that, Si-C interfaces respectively). The most stable geometry (S) is the ground 
the atomic layers prepared were increased consisting of either 3 or 4 SiC state structure while three other metastable geometries(MS) exist. Th 
bilayers and 6 or 8 Si layers slabs (8L/8L) successively with terminating atomic arrangements of these stable and metastable structures are 
H atoms on each geometry. By starting from the optimised structures shown in Figs. 2 and 3 respectively, with some of the Si-C interfacial 
earlier obtained at the 4L/4L slab model, we relaxed all the atoms in the atoms showing three- and fivefold coordinated arrangements. Even 
8L/8L model slab and those of larger layers were found to be unstable. though 4L/4L interface layers are considered ultra-thin, the interfacial 
As a consequence, the rest of the calculations were done using the 4L/4L morphology are observed within this regime from previous experience. 
model heterostructure and the results obtained were not significantly However, an interesting observation during the investigation is that, 
different when compared with the 8L/8L model of earlier calculation of beyond the 4L/4L interfacial layers, any additional layer to the 
Fig. 3. The side view from Si[100] direction of the Si substrate or the 3C-Si C[111]direction of the SiC side geometries: (b) the most stable (S); (a), (c) and (d) 
Metastable (MS) geometries of Si-Si interface of the 3C-SiC(111) on Si(111) heterostructure. The large (blue) and small (purple) balls indicate Si and C atoms 
respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 
4
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
heterostructure rendered the superstructure nearly unstable. We find compounds in the heterostructure region retains their natural atomic 
this situation to be intuitive because, when one ordinarily puts two bulk morphology without loss in character. 
systems together, it would be clearly unstable and so the interface 
structures can be thought of in the same way. Therefore, we think of this 3.2. Interface energy and band structure calculations 
emergence as a threshold of instability in the geometry beyond which 
stability breaks-down. The energy differences between MS geometries 
2 In this section, the interface structural stability is discussed for the and S geometry are as follows: 40.94, 6.38 and 51.52 meV/Å respec- calculated systems under consideration. The energy of the interface EI is tively as indicated in Fig. 2 for Si-Si interface. Similarly with Si-C such an important quantity that we defined it as the cost of energy 
interface, we have the MS energies differences being: 2.25, 9.43 and 
2 needed to form the interface heterostructure of 3C-SiC on Si using the 3.73 meV/Å as referenced in Fig. 3 thereof. various chemical potentials of the components. The interface energy of 
Fig. 4 indicates localised electron charge distribution calculated near the slab model is thus defined as: 
the Fermi level for S Si-Si and Si-C interfaces respectively. The charge 
distributions are floating bonds in character. We find in Fig. 3 that, the EI = Eopt − μSiNSi − μCNC − μHNH (1)  
Si-C interface has peculiar threefold atomic coordination (dangling 
bonds) which persist even after the geometry optimisation. The analysis where Eopt is a calculated slab total energy of a model. The NSi,NC and 
also reveals detailed fivefold coordinated (the floating bonds[54]) NH are the numbers for Si, C and H atoms respectively in the slab model 
appearance of some C atoms at the interface. These under- and over- where μSi, μC as well as μH as the corresponding chemical potentials of 
coordinated atoms creates defects along the Si[001] or equivalently the individual chemical element. With sufficiently thick Si substrate, the 
the SiC[111] interface direction. interface would be in equilibrium with SiC films as a result, it is proper 
In Fig. 4, it is evident that, the semblance of combination of these to assume that 
threefold and fivefold coordination bonding mechanism is related to the μSi = μbulk Si, μC = μbulk SiC − μbulk Si, (2)  
interface formation stability. This is because there are excess dangling 
bonds from the SiC side compared with the Si side, which is not one-to- where μbulk Si and μbulk SiC are calculated for each of the crystalline ma-
one rebonding hence leading to complex interfacial bonding mechanism terials per atom as the cohesive energy namely for Si and 3C-SiC 
as a consequence of atomic mismatch. The revealed fivefold coordinated respectively, corresponds to the stoichiometric condition of the SiC 
atoms with floating bonds[54] persisting near the interfaces is uniquely thin film. For simplicity, stoichiometric condition(SCM, here after) is 
observed in the present situation. As a results, when carefully observed used to represent such situations as Si-rich or C-poor. Similarly, when 
there is an atoms-scale undulation[36] feature appearing near the Si-C there is precipitate of diamond in SiC films as a consequence of limited Si 
interface, making the first interface layer atoms in that region of Si- or excess of C, we refer to such condition as Si-poor or C-rich and so we 
side to pinched with the SiC and this is not observed at the Si-Si inter- again define the following expressions for the cohesive energies. 
face. The observed atomic bond distances between the Si and C atoms of 
the SiC-side are in the range of 1.80–2.08 Å, similarly between the μC = μbulk diamond, μSi = μbulk SiC − μbulk diamond, (3)  
neighbours of Si in the Si-side are 2.29–2.38 Å. When these values are 
compared with the corresponding bulk bond lengths of 1.89 Å for Si-C where μbulk diamond is the cohesive energy of crystalline C per atom. Now, we need to be extremely careful defining the hydrogen 
and 2.35 Å for Si-Si are very much consistent. Even though, there are chemical potential μH in the model system. This is because, in a situation no observable bond breaking near the interface of Si-Si (sparse), that is where we simulate Si-C interface, we attache H atoms to Si surface atoms 
not what is seen at the SiC-side, as there is severe localised stress at the at both sides in the supercell. This means, we must removed all the 
dense SiC-side. This atomic rearrangement may help in the stabilisation interface energy contributions originating from H-Si bonding. There-
of the heterostructure. The general observation is that, the individual fore, it is appropriate to write the following equation: 
Fig. 4. (Color online) The calculated localised electron distribution near the Fermi level are shown in the Si[001] or the SiC[111] direction of the stable structures 
of Si-Si (a) and Si-C (b) interfaces respectively. The localised density is indicated by isovalue surface of 35% of the maximum isovalue. The large (blue) and (small) 
purple balls depicts atoms of Si and C. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 
5
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
μH = μH(Si) ≡ (μSilane − μSi)/4. (4) Table 2 
Calculated interface energies EI of the most stable (S) and metastable (MS) ge-
Similarly when Si-Si interface is simulated, we encounter two types ometries of Si-C and Si-Si interfaces in the Si-poor condition. Similarly, when 
of H that needs to be treated differently. That is, those hydrogen atoms different hydrogen chemical potentials were used, the E′I and E′′I interfaces were 
attached to the Si surface (top layer) and the others that are with the C also calculated and indicated (see text).  
surface (bottom layer), their contributions to the interface energy must Geometry  S geometry  
equally be removed. When hydrogen is attached to Si, we employ Eq. (4) Si-C Si-Si 
to determine the corresponding chemical potential. The contribution of 
E
interface energy coming from C-H bonding and therefore, the corre- I 
[eV/cell]  96.19 98.34 
2
sponding chemical potential of H is defined by the equation below: γ [eV/Å ]  0.48 0.49 
E′I [eV/cell]  102.74 94.70 
μH = μH(C) ≡ (μMethane − μC)/4. (5) E′′I [eV/cell]  108.71 97.26  
The number NH in Eq. (1) is modified depending on which interface Geometry  MS geometry  
system is being considered. For clarity and consistency, LDA was 1x_1y 1x_1y 
employed to calculate all the chemical potentials used in the model slab. EI [eV/cell]  98.07 99.61 
2
Having obtained all the relevant chemical potentials, the interface en- γ [eV/Å ]  0.49 0.50 
′
ergy per unit area is given as EI [eV/cell]  104.63 95.98 
E′′I [eV/cell]  110.59 98.54   E
γ I= , (6)  
A 0x_0y 0x_1y 
EI [eV/cell]  96.65 96.64 
with A being the interface area of the slab model. γ [eV/Å2]  0.48 0.53 
The interface energy as defined in Eq. (6) is limited in meaning with E′I [eV/cell]  103.20 102.89 
respect to the calculated absolute value. This is the cost of energy to E′′I [eV/cell]  109.16 105.44   
create the interface from both the bulk SiC and Si in Si-rich stoichio-
metric condition (SCM), or in Si-poor condition of SiC bulk diamond 0x_2y 2x_1y E [eV/cell]  96.932 108.64 
with attached H at the boundaries. It is clear now that, the stability of the I 
γ [eV/Å2]  0.48 0.54 
interface can properly be discussed and that assessment of the interface ′ 103.49 105.00 
energy EI is acceptable. Table 1 and Table 2 provide the interface en-
EI [eV/cell]  
′′
ergies calculated for the stable and metastable structures in the SCM or EI [eV/cell]  109.45 107.56  
the Si-poor conditions respectively for the initial trial geometry posi-
tions. The results shows unambiguously that Si-Si interfaces is energet- the structures in question and also the growth medium. In an extreme 
ically favoured compared with Si-C interface in the S geometry of the Si- case of the Si-poor condition, interface energy EI is influenced by the 
rich but not Si-poor conditions. However, the situation is different as the deficiency of Si atoms as a result, the stability appear to favour the Si-C 
MS geometries appear to have indeterminate interface stability. interface of the MS geometry and that also depends on the surface of the 
Nevertheless, the stability might depend on the initial trial geometry of substrate. The chemical potentials of hydrogen μH(Si) in Eq. (4) and μH(C)
in Eq. (5) have different values: in the stoichiometric condition μH(C) is 
Table 1 − 15.46 eV similarly in the Si-poor condition it is − 15.61 eV in the 
Calculated interface energies E of the most stable (S) and metastable (MS) ge- calculation. Since there is uncertainty in the choice of the hydrogen I 
′
ometries of Si-C and Si-Si interfaces in the stoichiometric Si-rich condition. chemical potential, the interface energies should be considered for: EI 
Similarly, when different hydrogen chemical potentials were used, the E′ and E′′ and E′′I I I , with μH = μH(Si) and μH = μH(C) respectively and similarly in the 
interfaces were also calculated and indicated (see text).  Si-poor condition as well. This means, the whole spectrum of μH limit has 
Geometry  S geometry  reasonably been covered. In Tables 1 and 2, we showed the calculated E′I 
Si-C Si-Si and E′′I of the extreme ends of the spectrum of the interface energy base 
EI [eV/cell]  27.69 22.57 on the different hydrogen chemical potentials. Clearly, the values ob-
γ [eV/Å2]  0.14 0.22 tained from the interface calculation, one can conclude that with the 
E′I [eV/cell]  21.73 20.24 exception of the extreme conditions in which SiC films are of low quality 
E′′I [eV/cell]  28.29 23.87  because of diamond precipitates, which of course depends on the initial 
growth environment, the interface of Si-Si is energetically favourable 
Geometry  MS geometry  compared with the interface of Si-C. 
1x_1y 1x_1y 
EI [eV/cell]  29.58 30.76 The calculated energy bands of 4L/4L geometry is shown in Figs. 5 
γ [eV/Å2]  0.15 0.12 and 6 for Si-C and Si-Si interfaces respectively for the stable and meta-
E′I [eV/cell]  23.61 21.52 
stable geometries after complete atomic geometry optimisation. Topo-
E′′ [eV/cell]  30.17 25.15   graphically, the two different sets of interfaces dispersions are strikingly I different but all show metallic behaviour even though the exchange 
0x_0y 0x_1y correlation employed in the calculation is LDA. Figs. 5(b) and 6(a) in-
EI [eV/cell]  28.14 30.76 dicates band structure of the ground state Si-Si and Si-C interfaces 
γ [eV/Å2]  0.14 0.15 respectively, while the remaining figures represents the corresponding 
E′I [eV/cell]  22.18 28.43 metastable bands. The fermi energy level is set to zero of energy in all 
E′′I [eV/cell]  28.74 32.06   the figures. The slight differences in the band structure topology for all 
0x_2y 2x_1y the structures probably relates to the initial trial geometry. The calcu-
EI [eV/cell]  28.44 32.870 lation reveals an intuitive understanding that, excess dangling bonds 
γ [eV/Å2]  0.14 0.16 still persist at the heterojunction and mainly comes from the dense SiC- 
E′ [eV/cell]  22.47 30.54 side. Therefore, there is net dangling bonds from SiC side after I 
E′′ [eV/cell]  29.03 34.18  rebonding with those coming from the sparsed Si-side. One can conclude I 
6
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
Fig. 5. Calculated optimized band structures of the stable and metastable ge-
ometries of Si-C interface (b) stable interface while (a), (c) and (d) indicates Fig. 6. Calculated optimized band structures of the stable and metastable ge-
metastable interface structures of 3C-SiC(111) on Si(111) using the 4L/4L slab ometries of Si-Si interface (a) stable interface while (b), (c) and (d) indicates 
model. Fermi level is set as the origin of the energy scale. metastable interface structures of 3C-SiC(111) on Si(111) using the 4L/4L slab 
model. Fermi level is set as the origin of the energy scale. 
that, the effective unrebonded dangling bonds are the ones giving rise to 
the metallic behaviour of the interface and this is the consequence of the respectively with complex electronic bonding mechanism as a results of 
mismatching atoms of the different compounds forming the interface localised interface states. We find that stable and metastable structures 
through twisting and bending bonds. It must be noted that, simple of Si-Si interface are generally epitaxial without any observable bond 
rebonding of the dangling bonds is not possible as relaxation mechanism breaking but bonding strain exist near the heterojunction. However, the 
in the interface is associated with atom-scale undulation especially so for Si-C interface is associated with atomic-undulation resulting in over- 
the Si-C interface leading to fivefold coordinated floating bonds. The coordinated atomic bonds which leads to un-expitaxy at the interface 
remaining dangling bonds(under-coordinated atoms) give rise to the and pinched at the Si-region of the Si-C heterojunction. The Si-Si 
metallic character of the interface structures. The electronic distribution interface energy calculated indicates that, it is energetically favour-
relates electron transfer from the SiC side to the Si because of relative able compared with that of the Si-C. The electronic band structure 
differences in electronegativities between Si and C atoms. calculation of all the interfaces exhibits metallic character for the stable and metastable structures. The origin of metallicity of the hetero-
4. Conclusion structure is due to un-rebonded dangling bonds near the heterojunction because of unequal dangling bonds distribution coming from the denser 
We report total-energy electronic structure calculations based on SiC-region as a result of interfacial atomic mismatch. 
density functional theory in the framework of real space formalism. We 
employed local density approximation and investigated the interface CRediT authorship contribution statement 
and electronic structures of Si(111) on 3C-SiC(111) thin films. The 
calculations revealed peculia atom scale electronic structure morphol- Eric K.K. Abavare: Conceptualization, Data curation, Formal anal-
ogies at the heterojunction as a result of significantly reduced lattice ysis, Investigation, Methodology, Software, Visualization, Supervision, 
mismatch between the compounds. The differences in atom densities of Writing - original draft, Writing - review & editing. Bright Kwakye- 
the two compounds’ (111) surfaces might account for these peculiar- Awuah: Data curation, Validation, Writing - review & editing. Oswald 
ities. We have found one stable interface and three other metastable A. Nunoo: Data curation, Resources, Software. Peter Amoako-Yir-
structures each for the investigated interfaces after manually searching enkyire: Resources, Validation, Visualization, Writing - review & edit-
all space. The total energy difference between the structures of Si-C and ing. G. Gebreyesus: Validation. Abu Yaya: Formal analysis, 
Si-Si interfaces are in the range of 2.25–9.5 meV Å2 and 6–52 meV Å2 Investigation, Methodology, Resources, Supervision, Writing - review & 
editing. Keshaw Singh: Validation, Supervision, Writing - review & 
7
E.K.K. Abavare et al.                                                                                                                                                                                       C  h  e  m  i c  a l  P  h  y  s i c s   L e  t t e r  s  766 (2021) 138318
editing. [23] S. Nishino, Y. Hazuki, H. Matsunami, T. Tanaka, Chemical vapor deposition of 
single crystalline -sic films on silicon substrate with sputtered SiC intermediate 
layer, J. Electrochem. Soc. 127 (12) (1983) 2674–2680. 
Declaration of Competing Interest [24] Q. Wahab, R. Glass, I. Ivanov, J. Birch, J.-E. Sundgren, M. Willander, Growth of 
epitaxial 3C-SiC films on (111) silicon substrates at 850◦C by reactive magnetron 
sputtering, J. Appl. Phys. 74 (3) (1993) 1663–1669. 
The authors declare that they have no known competing financial [25] T. Perova, J. Wasyluk, S. Kukushkin, A. Osipov, N. Feoktistov, S. Grudinkin, Micro- 
interests or personal relationships that could have appeared to influence Raman mapping of 3C-SiC thin films grown by solid–gas phase epitaxy on Si (111), 
Nanoscale Res. Lett. 5 (9) (2010) 1507. 
the work reported in this paper. [26] T. Nishiguchi, M. Nakamura, K. Nishio, T. Isshiki, S. Nishino, Heteroepitaxial 
growth of (111) 3C–SiC on well-lattice-matched (110) Si substrates by chemical 
Acknowledgments vapor deposition, Appl. Phys. Lett. 84 (16) (2004) 3082–3084. [27] M. Suemitsu, Y. Miyamoto, H. Handa, A. Konno, Graphene formation on a 3C-SiC 
(111) thin film grown on Si (110) substrate, e-journal of Surf, Sci. Nanotech. 7 (9) 
One of us, Eric acknowledges material and logistical support from (2009) 311–313. 
TWAS under Grant No. 18–027 RG/PHYS/AF/AC I for scientific [28] M. Suemitsu, H. Fukidome, Epitaxial graphene on silicon substrates, J. Phys. D: − Appl. Phys. 43 (37) (2010) 374012. 
research and Kwame Nkrumah University of Science and Technology [29] A. Severino, C. Bongiornor, N. Piluso, M. Italia, M. Camarda, M. Mauceri, 
(KNUST). The authors acknowledge the Centre for High Performance G. Condorelli, M. Di Stefano, B. Cafra, A. La Magna, et al., High-quality 6 inch 
Computing (CHPC), South Africa, for providing computational resources (111) 3C-SiC films grown on off-axis (111) Si substrates, Thin Solid Films 518 (6) 
to carry out this scientific research and Prof. Jun-Ich Iwata for the use of (2010) S165–S169. [30] H. Fukidome, S. Abe, R. Takahashi, K. Imaizumi, S. Inomata, H. Handa, E. Saito, Y. 
RSDFT code. Enta, A. Yoshigoe, Y. Teraoka, et al. Controls over structural and electronic 
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(111)/Si, Appl. Phys. Exp. 4 (11) (2011) 115104. 
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