Jakub Sołtys 1 , Jacek Piechota 1 , and Stanisław Krukowski 1, 2
1 Interdisciplinary Centre for Mathematical and Computational Modelling, University of
Warsaw, Pawińskiego 5a, 02-106 Warsaw, Poland
2 Institute of High Pressure Physics, Polish Academy of Sciences, Sokołowska 29/37, 01-142
Warsaw, Poland
Physical properties of SiC(0001) surface under various coverage by Si adatoms was studied using density functional theory (DFT) calculations. The clean SiC(0001) surface has the Fermi level pinned by Si broken bond state located 0.8 eV below CBM. The most stable position of single Si atom adsorbed at SiC(0001) surface is H3 site bonded to three neighboring Si atoms, saturating their broken bonds. The adsorption energy is about 7.1 eV that leads to creation of 2 3

2 3 stable surface reconstruction. For more atoms up to 0.25
ML coverage the energy gain is smaller by 0.4 eV. The stability of the adatoms at H3 position is related to electronic properties of the system so that Si accepts four electrons from Si broken bonds states. That creates energy effect of about 1.5 eV, thus the adsorption energy in this range is about 6.7 eV. According to EECR further increase exhausts Si broken bond electron source at about 0.25 ML coverage that lowers the adsorption energy down to about 5 eV. Further adsorption of Si atoms occupied H3 sites that have common Si top atoms with other Si adatoms that lower the adsorption energy gain to 4.2 eV at the coverage exceeding
0.4 ML in which H3 and on top configurations have roughly the same energy so the transition to SiC lattice position by subsequent Si adatoms is possible. The reduction of the adsorption energy leads to drastic decrease of the equilibrium pressure of silicon by 3 orders of magnitude in the region between 0.25 ML and 0.40 ML coverage. Generally it is expected that for typical conditions for SiC growth from the vapor, the coverage of SiC(0001) surface
1

is close to 0.3 ML.
2

1. Introduction
Properties of silicon carbide such as high breakdown voltage (~10
6
V/cm), high charge mobility, high temperature stability and thermal conductivity, excellent chemical resistance and easy p- and n-type doping predetermine this compound as primary candidate for applications in many branches of future electronic technologies [1-4]. Among these applications high power and high temperature electronics are the most prominent future options. Yet possible applications are hampered be the presence of the nanopipes, i.e. empty core linear defects that are difficult to remove from the growing SiC crystal [5-6].
Accordingly, high quality SiC substrates are very expensive that hampers effective development of SiC based electronic technologies, such as nanpopipes, etc. [7,8]. Therefore understanding mechanisms of creation nanopipes in silicon carbide is an important issue in the growth of bulk SiC [9-11]. One possible way to deal with the problem is the identification of the molecular mechanism leading to local termination of the growth, which may be related to the molecular mechanism controlling adsorption of the growth species during growth from the vapor. Therefore investigation of adsorption of silicon and carbon at principal faces of SiC is of high potential importance. Such investigations are intensively conducted by large number of researchers.
Among all possible surfaces of hexagonal 4H-SiC, the polar Si- and C-terminated, denoted as SiC(0001) and SiC(0001) were investigated most intensively. The bare, direct cut surface is extremely difficult to achieve. This is related to high chemical activity of such semiconductor surface due to presence of high density of broken bond that leads to attachment of active species, such as oxygen, hydrogen, water etc. that are extremely difficult to remove from the surface [12]. Therefore the experimental data on clean SiC(0001) and
SiC(0001) are not reliable.
On the other hand, the clean SiC(0001) surface is convenient starting point for ab initio simulations of such important issues of surface physics as reconstruction and adsorption
[12]. Therefore the clean SiC(0001) surface was investigated by Sabisch et al. [13]. They found that Si-terminated surface does not undergo any reconstruction, but the strong relaxation by strong inward motion of the two outermost atoms takes place. The electronic structure calculations showed existence of half-filled state in the bandgap about 1 eV below conduction band minimum (CBM), related to Si broken bonds [13]. These conclusions were confirmed by later simulations by Soltys et al. who found strong relaxation of the topmost layers in the surface for all three basic hexagonal structures [14]. It was also confirmed that
3

the Si-broken bond related state is in the bandgap for all structures. Additionally it was shown that the field in the slab could drastically change the energy of the surface state with respect to band state due to field related projection of the spatially extended band states.
Experimental investigations of SiC(0001) under various coverage were intense that brought a number of interesting results [15-24]. It was shown that several surface reconstructions exists, that are related to nonstoichiometry of the surface layers. Among the most prominent were those related to excess of silicon, such as 3

3 R 30

, 3

3 [14,15],
2 3

31 R 30

[17], 4

4 and also disordered 1

1 structure [18]. The structures emerging due to surplus of carbon were identified as 6 3

6 31 [15], 3

3 [16], 6

6 [19,20], and finally 1

1 graphite [15, 16, 18, 20]. These structures were classified according to surplus or shortage of silicon and the temperature [18]. Generally, the increase of the temperature leads to Si escape and carbonization of the surface, so the deposition of silicon is needed to sustain the Si-rich reconstructions. It was shown that after chemical cleaning the annealing in 800-
1300°C leads to emergence of 3

3 R 30

[16], which is associated with Si 1/4 monolayer
(ML) coverage. The structure remains after cooling down to room temperature. An increase of
Si coverage to above 1 ML leads to transition to 3

3 structure which is associated with the high silicon surplus [18,19]. Further increase of Si coverage leads to emergence of
2 3

31 R 30

and 4

4 and also disordered 1

1 structures [16,17]. On the contrary, annealing to above 1000°C without additional Si flux leads to carbonization of the SiC surface and emergence of 6 3

6 31 structure which was also identified as graphite layer
[20]. Further depletion of Si leads to development of 6

6 and finally 1

1 disordered structure [15,18,20,21]. The structure was identified first by Bommel et al. which is considered now as the first evidence of emergence of graphene layer on SiC(0001) surface
[21].
The identification of molecular structure of these reconstructions was painfully difficult job which is still not finalized. The two basic models were proposed for
2 3

31 R 30

reconstruction: the ordered array of Si adatoms, proposed by Kaplan [12] and later by Owmann and Martensson [22] and ordered array arrangement of Si surface vacancies, proposed by Bermudez [16] and later on by Li et al. [23] . These structures were intensively investigated, that led to prevalence of adatom model [19, 24, 25]. These investigations additionally provided data for identification of the adsorption site. Out of the possible candidates, on-top, H3 and T4, the accumulated evidence indicates the latter as the most likely
4

candidate [25-27]. Electronic properties of the surface were also investigated. Angle resolved photoelectron spectroscopy (ARPES) provided an evidence of filled states located 1.0 eV above valence band maximum (VBM), having limited dispersion of about 0.2 eV [27].
Semiconducting surface was also obtained in k-resolved photoelectron spectroscopy
(KRIPES) measurement which confirmed existence of dangling bond state 1.1 eV above
VBM which was found to be empty [28]. Scanning Tunneling Spectroscopy confirmed existence of pair of the states in the bandgap of Mott-Hubbard type one filled and one empty.
[24]. Thus the number and position of these states are not finally resolved.
The other Si reconstructions were less investigated. Kaplan proposed a structural model [15] fully analogous to well known dimer-adatom-stacking fault model of 7 x 7 reconstruction of Si(111) surface designed by Takanayagi et al. [30]. Li and Tsong proposed tetrahedron model in which the surface coverage is 4/9 ML [19]. Amy et al. proposed Si rich model consisting of Si adlayer, Si trimer and Si adatom, which gives 13/9ML combined [31].
Further increase of Si coverage leads to the structure typical for Si surfaces [18].
The structures of C-rich surface were attributed to transition to graphite or graphene structures, characterized by six-fold symmetry [18]. Annealing of 3

3 R 30

SiC(0001) surface 1300°C leads to emergence of 6 3

6 31 graphene structure, which is now basis of synthesis of graphene by Si evaporation from SiC surfaces [32, 33].
Ab intio simulations were also used in the investigations of properties of Si- and Crich SiC(0001) surfaces [34-38,18]. Northrup and Neugebauer used local density approximation (LDA) ab initio calculations proving that 3

3 R 30

structure is related to
Si-adatom configurations. They argued that in the whole allowed range of chemical potential
Si adatom in T4 site is thermodynamically stable configuration. They identified broken bond state in the bandgap which is half filled. Thus the surface should behave as metallic which is in disagreement with the existing ARPES and KRIPES data. These finding were confirmed by later ab initio LDA calculations by Sabisch et al. who confirmed Si adatom in T4 site as stable structure and identified Si broken bond, half-filled in the bandgap [35]. Similar results concerning both structure and electronic states were obtained by Furthmuller et al. who obtained metallic state of the surface [36]. They argued that Hubbard-Mott splitting of the states could explain discrepancy between ARPES data and the results of ab initio calculations.
The ab initio calculations were used to explain the transition from 3

3 R 30

to 3

3 structures and related to that drastic decrease of Si adsorption energy [18]. The authors argued that drastic decrease of Si adsorption energy from 4.5 eV to 1.6 eV corresponds to shift from
5

attachment at adatom vacancy to the position on top of Si capping atom for the latter case
[18]. Starke et al. proposed 3 Si layer model consisting of Si adlayer, Si-trimer and Si adatom as the candidate for 3

3 reconstruction [37]. They argued that the twist of Si atoms facilitate reduction of dangling bonds [38]. A different model of 3

3 reconstruction was proposed by
Li et al. [38]. They suggested that this model better explained the observed photoelectron spectroscopy (PES) and electron energy loss spectroscopy (EELS) data.
In this work we use recently developed methods of controlling the level of Fermi energy and the electric field at the surface to simulate their influence on the properties of
SiC(0001) surface [39-40]. The projection of band states on the atomic states of the row of atoms will be used to present the bands and surface states and to identify states related to presence of additional Si adatoms at the surface [41].
2. The method
Vienna ab initio simulation package (VASP), based on a plane wave basis set [42-45] was used for an ab initio simulation of the energy barrier for the diffusional motion of carbon and silicon atoms at polar SiC(0001) surface. The projector augmented wave (PAW) approach
[46] was used in its variant available in the VASP package [45]. For the exchange-correlation functional, the Generalized gradient approximations (GGA) was applied. The plane wave cutoff energy was set to 500 eV. The Monkhorst-Pack k-point mesh was set to 3×3×1 [1647 The
4H-SiC(0001) super lattice was constructed using 4 bilayers of Si-C. Two top SiC layers were relaxed using the conjugate gradient algorithm. Atomic relaxation consisted of several stages: in the first instance, all atoms were allowed to move freely in a simulation cell. The atoms from the two topmost layers of the slab were allowed to relax to optimal energy positions. The cell size was not relaxed. The vacuum space between slab replicas was set to 19.68 Å that assured their quantum isolation. Optimization of ionic positions was performed using
Generalized Gradient Approximation (GGA) energy functional in order to obtain properly relaxed structures. In the first instance, a standard plane wave functional basis set, as implemented in VASP with the energy cutoff of 29.40 Ry (400.0 eV), was adopted. The
Monkhorst-Pack grid: (5x5x1), was used for k-space integration [47]. For Ga and N atoms, the Projector-Augmented Wave (PAW) potentials for Perdew, Burke and Ernzerhof (PBE) exchange-correlation functional, was used in Generalized Gradient Approximation (GGA) calculations [48]. Gallium 3d electrons were accounted in a valence band explicitly. The energy error for the termination of electronic self-consistent (SCF) loop was set equal to 10 -6 .
6

These parameters recover basic structural and energetic properties of 2H SiC with good accuracy.[18] The lattice parameters of 2H SiC obtained from the DFT calculations were: a =
3.092 Å and c = 5.074, compared well to the experimental data a = 3.079 Å and c = 5.053 Å
[49-51].
3. The results
The results presented will include position of bands and surface states, obtained for the clean SiC(0001) surface first, then the description of the adsorption of single silicon and carbon atoms at flat SiC(0001) surface. These results allow to identify quantum states of the clean surface, position of Fermi level and the structure of the surface. Subsequently, the extended electron counting rule will be applied to the adsorption of single silicon atom at
SiC(0001) surface which allow us to predict Si coverage of the surface at which the depinning of Fermi level occurs and pinning at newly created Si states. In the following the a. Electronic properties of clean SiC(0001) surface
Investigation of electronic properties of SiC(0001) were conducted using traditional methods by several authors. Most advanced study was reported in our work where the influence of electric field in the slab demonstrated. As it turned out, the electric field, related to charged surface states may locally shift the band states at the surface leading to Surface
States Stark Effect (SSSE). As it is shown in Figure 1 the projection of the band states on the common energy axis causes the decrease or even disappearance of the bandgap. Naturally, the position of the surface states with respect of so defined band is shifted, leading to errors in their determination. As shown in Figure 1, the surface donor state (SDS) is located in the middle of the bandgap. Nevertheless the position of the SDS with respect of conduction band minimum (CBM) is preserved, while with respect of the valence band maximum is totally misrepresented. Using k-space diagram only one may conclude, mistakenly, that the SDS is degenerate with valence band (VB). Similarly the energy position of surface acceptor state
(SAS) is properly represented with respect of VBM while it is misrepresented with respect of
CBM. Again k-space diagram suggests that SAS is degenerate with conduction band (CB) while in reality, it is located in the midgap. As it is shown also, the surface neutral state (SNS) is represented with respect to VB and CB. These diagrams indicate that proper assessment of the surface states could be achieved either by attaining electric neutrality of the surface state by manipulation of slab termination atoms or by representation of the states in real and momentum space. The electric neutrality is technically difficult to attain, therefore
7

simultaneous presentation of the k-space and real space bands is optimal reliable and clear way to present the surface states in presence of the fields. Thus the dual space presentation of the results will be used in the following.
Figure 1. Electronic properties of clean SiC(0001) surface and the surface state showing band diagram in real and momentum space, in presence of: a) surface donor state (SDS), b) surface neutral state (SNS), c) surface acceptor state (SDS). Red, blue and green colors denote
8

conduction, valence and surface states, respectively. Black and yellow arrows represent real and skewed bandgap respectively.
As it is demonstrated in Figure 2, at the clean SiC(0001) surface, the surface state, associated with the Si-broken bond is located about 0.8 eV below conduction band minimum
(CBM). It is partially occupied, thus the Fermi level is pinned by the state. Naturally, the surface state occupation, i.e. its charge depends crucially on the doping in the bulk. For p-type material the state becomes donor, i.e. it is positively charged bending the band downward at the surface. In the case of n-type bulk, the state behaves as surface acceptor with the band profiles bend upward. These both cases are presented in Fig. 2.
Figure 2. Electronic properties of clean SiC(0001) surface for p-type (a) and n-type (b) bulk silicon carbide: band diagram in momentum and real (along direction perpendicular to the
9

surface) space and total density of states (DOS). The color code represents the density of states in real space.
Therefore it was demonstrated that the simulation procedure may recover different charge of the surface state, i.e. donor and acceptor by simulation of n- and p-type doping in the bulk. The procedures are capable to determine the position of surface states, their occupation, related to Fermi level at the surface. These data are used in determination of basic features of adsorption of silicon and carbon atoms at the surface. b. Electronic properties of silicon covered SiC(0001) surface using
Determination of adsorption sites of silicon atoms at SiC(0001) surface was made
2 3

2 3 supercell, as 3

3 reconstruction was reported in investigations of this system. The number of Si-C double atomic layers (DALs) was set to 10, as this number is sufficient to avoid influence of quantum overlap of real and termination surface states. The possible adsorption sites include H3, T4 and on-top. The slab used for calculations and the position of Si adatom is presented in Fig. 3.
Figure 3. The 2 3

2 3 slab used for simulations of Si-terminated SiC(0001) surface. By different colors various position of Si adatoms are denoted: red - H3, blue - T4 and green - on top.
10

The total energies of the system consisting of Si adatom and the 3

3 slab were ...... for
H3, T4, and on-top position, respectively. In order to verify whether the results may depend on the interaction with the images in the neighboring cells, the comparative calculations were made for 2 3

2 3 supercell. The results were , respectively. Comparing the difference we have shown that the image contribution does not affect these results and the most stable site for single Si adatom is H3. The present results is not compatible with the results reported in
Ref. 24-26 where T4 site was suggested as the most stable site.
The investigation of the states associated with the presence of Si adatom was systematically conducted, starting form the system of Si atom located far away from the surface. The selected distance include 4.67 Å where the overlap is small with some splitting of Sip y
state, at 3.37 Å distance - increased overlap at leading to splitting of Sip states and some dispersion of Sis state, at 2.87 Å and equilibrium position at 1.77 Å from the surface.
As shown in Fig. 4, the largest distance (4.67 Å) panel presents standard behavior of such system, very strong splitting of s and p states of separated single silicon atom of which the Sis states are located deep in the valence band (VB). These states are typical molecular states, characterized by zero dispersion in k-space. Naturally both Sis states are fully occupied. The Sip x
and Sip y
states are pinned to Fermi level of the slab. The Sip z
states are split with the higher energy state empty and the lower fully occupied. The effect is an artifact of DFT simulation procedure which fills the states consecutively, independent of their location in space. Thus nonlocal effects are introduced into the model due to the calculation procedures used. These p states are degenerate which confirm that the distance is sufficient to treat Si atoms as independent.
Reduction of the Si-SiC distance to 3.37 Å changed this simple overall picture. All Sip states are split into bonding and antibonding states with bonding states fully occupied and the antibonding - empty. They attain some dispersion, both bonding and antibonding. The splitting due to overlap with the surface states is considerable, exceeding 1.0 eV. The Sis states become more dispersive, with dispersion of order of 3 eV. They are located in the VB, and therefore they are fully occupied.
Further reduction of the distance to 2.17 Å brings further changes. The splitting of pstates becomes more pronounced with the bonding states of molecular type and the antibonding becoming dispersive surface states.
The termination position, i.e. equilibrium location at 1.77 Å enhances these changes.
The Si s-related state increases its dispersion still preserving its energy. The Si p-related states
11

increase their splitting, preserving other features. The upper, empty states are dispersive and the lower occupied are molecular like.
Figure 4. Band diagrams in momentum and real space of the slab representing SiC(0001) surface and projected density of states (PDOS) on s (magenta), p x
(blue), p z
(yellow) and p y
12

(brown line) states of the Si atom located at the distance of: (a) 4.67 Å; (b) 3.37 Å; (c) 2.17 Å;
(d) 1.77 Å. Additionally the PDOS of surface topmost Si atom without saturation is shown
(blue line).
The above scenario may be additionally verified by the constant energy surface plots of the real wavefunctions of the above states. As it is shown in Fig. 5, these wavefunctions confirm the identification made above. The two Sip x
, Siy related states create overlap with the neighboring Si surface topmost atoms while Sip z
related states correspond to bonding and antibonding to Si surface atoms. Note that the latter states are directed perpendicular to the surface. Thus each Si adatom saturates three Si topmost atom sp
3
broken bond states.
Figure 5. Energy surface plots of the wavefunction density of several Si-related states at
SiC(0001) surface: (a) and (b) - Sip x
, Sip x
related states, (c) and (d) - Sip z
related states.
Denote by α the concentration of Si adatoms (i.e. Si adatom to Si topmost surface atoms ratio)
13

and by β - the fraction of the nonsaturated Si topmost atoms, the normalization condition gives:
3
   
1 (2)
The above behavior may be supplemented by the following scheme of the states occupation.
The energy scale in the Figure 4 is not adequate to identify occupation of these states.
Therefore in Figure 6 the more detailed presentation of the properties of surface states emerging due to attachment of Si adatom are given. For the comparison the clean SiC(0001) is also presented. As determined from Figure 4, the bonding Sis related states located deep in
VB are not shown in the diagram. These two states are occupied.
Figure 6. Band diagrams in momentum and real space of the slab representing clean
SiC(0001) surface (a) and SiC(0001) surface with Si atom located at the distance of 1.77 Å
(b). On the right diagrams PDOS of Sis (magenta), Sip x
(blue), Sip z
(yellow) and Sip y
(brown) states of the Si adatom and also of the topmost surface Si atom without saturation (blue line) are shown.
The two bonding Sip x
and Sip y
related (surface parallel) states create overlap with sp
3 orbitals
14

of topmost surface Si atom. They both are fully occupied. The two Sip z
, surface perpendicular states are also identified in the diagram the lower is fully occupied while the upper is half occupied half empty. Thus the Fermi level is pinned by the latter state. It is shown also that in the considered slab out of twelve, nine surface topmost Si atoms have no saturation; therefore their states are partially filled. These states should have their energies approximately equal to the upper Sip z
states, i.e. they also pin Fermi level. This is confirmed by the PDOS diagrams in Figure 6. The two low energy states are those having overlap with Sip x
and Sip y
and lower
Sip z
related states. The state at 4 eV is present both in clean and the Si attached surface in
Figure 6. The state is partially filled, also pinning Fermi level. Thus the obtained ab initio results are consistent with the predictions.
The extended electron counting rule (EECR) charge conservation equation is constructed in such a way that the number of donated electrons calculated on the left side is equal to the absorbed electron given on the right side. The EECR equation describes the charge free surface where the states are fully occupied or completely empty, without pinning
Fermi level at the surface. In the presently analyzed case the EECR state may be attained by increase of surface coverage. In such case each Si uncovered surface atom broken bonds donate single electron to attached Si adatoms. Thus on the left side the term β is present. The
Si adatom donate four electrons and three neighboring Si topmost surface atoms donate three electron. Thus the term proportional to α has the appropriate coefficient on the left hand side
(4 + 3). On the acceptor side, due to two spin orientations every adatom Sis states absorb two electrons and also six electrons occupy Sip x
and Sip z
and lower Sip y
related states. Therefore each Si adatom potentially absorbs 8 electrons. The electron balance is:

4

3
    
8

(2)
The solution of the above equations is
   
1
4
. Therefore the ECR states should be observed for the coverage

Si
  
1
4
, corresponding to the Fermi level located between the lower and upper Sip z
related states. The verification of this prediction was made by simulation of the 2 3

2 3 slab, i.e. the slab with the 12 surface sites. Results of the simulation of this system with 2, 3 and 4 Si adatoms are presented in Figure 7.
15

Figure 7. Band diagrams in momentum and real space of the slab representing SiC(0001) surface with the following number of Si atoms located at the distance of 1.77 Å: two (a); three
(b) and four (c). Additionally PDOS of Sis (magenta), Sip x
(blue), Sip z
(yellow) and Sip y
(brown) states of the Si adatom and also PDOS of surface of the topmost Si atom without saturation (blue line) are shown.
The results presented in Figures 6 and 7 present the evolution of the electronic properties of the surface states. The Fermi level is pinned to upper Sip z
broken bond state for the single and two adatoms attached. For the three adatoms present, i.e. for EECR state the
Fermi level is located between the upper Sip z related state and Sip x
and Sip y
related state. The upper Siz related state is empty while the lower is occupied. Thus the ab initio results fully confirm prediction based on EECR calculations.
The latter diagram presents the system with no uncovered Si topmost states. The band
16

diagrams presents the Sip z related surface state in the bandgap and the two Sip x
and Sip y related surface states degenerate with the valence band. The Fermi level is pinned to the Sip z related bonding state which is partially occupied. Again the agreement with EECR is perfect.
For the higher coverage the position of Si adatom has to be changed as, the number of neighbors without saturated bonds is insufficient. Therefore the calculations were made comparing the energy for different of Si adatoms positions on top of the 2 3

2 3 slab. The initial coverage was 4 or 5 adatoms in H3 positions, the positions of the additional atom was changed (H3, T4 and on top).
Figure 8. The positions of the additional Si adatoms on top of the 2 3

2 3 slab representing SiC(0001) surface .
As it is shown, the adsoprtio of fifth atom is different with respect of the number of broken
17

bonds that could be saturated. In case of H3, position, the Si topmost atom has already saturated broken bond state, thus the bonding is different due to geometric constraints. Also the T4 and on top position have different bonding with the surface. Therefore it is of interest how these changed bonding affect the electronic states on the surface which is presented in
Figure 9.
Figure 9. Band diagrams in momentum and real space of the slab representing SiC(0001) surface with the fifth Si atom located at the distance of 1.77 Å in: H3 (a); T4 (b) and on top
(c) positions. PDOS of Sis (magenta), Sip x
(blue), Sip z
(yellow) and Sip y
(brown) states of the
Si adatom and also PDOS of surface of the topmost Si atom without saturation (blue line) are shown.
Thus different bonding affects electronic states of these three configurations: c. Adsorption of Si atom at SiC(0001) surface
The energy effect associated with the adsorption of single Si atom may by calculated according to the following formula:
E ads

E
DFT
 slab

Si



E
DFT
 slab


E
DFT
  
(3) where the DFT energies are obtained from slab calculations with identical geometry. The energies are plotted on Figure 10 for three different termination sites, in function of coverage by Si atoms located in H3 sites.
18

-3
-4
-5
-6
-7
H3
T4
on-top
0.4
0.0
0.1
0.2
0.3
Figure 10. Adsorption energy of Si atom on the three different sites of SiC(0001) surface covered by Si adatoms located in H3 sites only: H3 - black full squares, T4 - red empty circles, on-top - empty blue stars. The coverage is defined as the ration of Si adatoms before adsorption (i.e. number of Si adaoms in H3 sites) to the number of Si topmost atoms in SiC lattice.
The data presented in Figure 10 indicate that there exist two different regimes for adsorption of Si adatom at stable H3 site. For low coverage regime, up to 0.25 ML, the adsorption energy is about 6.65 eV. The lowest value, lower by about 0.4 eV is related to stable 2 3

2 3 surface reconstruction. For higher coverage the energy is subsequently reduced to 5 eV first, i.e. by about 1.6 eV and next to 4.2 eV, i.e. by additional 0.8 eV. Altogether this reduction is by about 2.4 eV.
This complex behavior indicates on the presence of two different factors governing the process. The difference between the first three points and the fourth is caused by electronic transfer only. As shown in Figure 7, the Femi level for the three adatoms is pinned by Si broken bond and by the attached Si bonding state. Thus for the adsorption at low coverage, the electrons are transferred for Si-broken bond site states to the states associated with the adsorbed atoms. As it was shown the states associated wi Si adatoms are occupied by 9 electrons, 2 at Sis states, 4 at bonding Sip x
and Sip y
states, 2 at bonding Sip z and 1 at
19

antibonding Sip z
state. Five electrons occupy the states intact before adsorption. The antibonding state has approximately the same energy as Si broken bond state, thus transition of this electron brings negligible energetic effect. Therefore the lowering of the Fermi level to the nonpinned position observed in Figure 7c does not affect this balance. Thus the transfer of three electrons creates the adsorption energy jump of order of 1.5 eV. As it is shown in Figure
6, the energy difference between Sip x
and Sip z
bonding states and the Fermi level is about 1.2 eV and 0.3 eV, respectively. Thus the transition of single electron to Sip x
state contributes about 1. eV while two electrons to Sip z
bonding states aadditional 0.5 eV. Thus the total contribution of electron transfer creates about 1.5 eV approximately the difference between the low and high coverage adsorption energies at H3 sites. Naturally, some contribution arises from interaction with the neighbors, but these are smaller contributions.
For the subsequent adatoms, the bonding is different which reduced the adsorption energy by 0.8 eV down to 4.2 eV. This energy is approximately equal for both H3 and on top positions which indicates how the adsorption is shifted from off-lattice to the lattice sites for higher coverage. This is interesting as it may contribute to better understanding of the growth of Sic from the vapor. Further investigations, including carbon adatoms at this surface are in progress. d. Thermodynamics of silicon covered SiC(0001) surface and silicon vapor.
According to Refs 39-41 different regimes of adsorption may be observed, characterized by different pinning of Fermi level at the surface and related different electron transfer. This observation is confirmed here for the case of Si adsoprtion at SiC(0001) surface.
In order to obtain equilibrium pressure of silicon vapor over SiC(0001) surface the chemical potential equality has to be invoked:

Si
 
 
Si
 
(4) where the adsorbed chemical potential is um of energetic (enthalpy) and thermal, configurational entropy term, dependent on the Si coverage θ
Si
:

Si
 
 h
Si
 

Ts
Si
 h
Si
 k
B
T ln


1


Si

Si

 (5)
20

The chemical potential of Si in the vapor may be expressed as:

Si
   h
Si
    
Si

T , p
Si

(6) where pressure-temperature dependent contribution, frequently used in representation of ab initio stability, denoted as chemical potential of silicon

Si
, is given by:
 
Si

T , p
Si

 
1 .
57 x

0 .
26 x
2 
0 .
034 x
3  k
B
T ln
 
Si
(7) and x = T/1000, where temperature is expressed in kelvins and pressure in bars [52,53].
Combining Eqs 4-7 we arrive at the following expression for the equilibrium pressure of silicon: k
B
T ln
 
Si

1 .
57 x

0 .
26 x
2 
0 .
034 x
3  k
B
T ln



1

Si

Si


 h
Si
 
 h
Si
 
(8) in which the enthalpy difference at 0K is equal to Si adsorption energy, i.e. h
Si
 
 h
Si
 

E ads
 
(10) given by Eq. 3 and plotted in Figure 9. These data are sufficient to obtain the equilibrium pressure of silicon, which is plotted in Figure 10 for several selected temperatures.
21

1x10
3
1x10
0
1x10
-3
1x10
-6
1x10
-9
10
-12
0.0
0.1
0.2

Si
0.3
0.4
0.5
Figure 11. Equilibrium pressure of Si above SiC(0001) surface for several, technically important temperatures: blue open stars - 1687 K (Si melting temperature), red open circles -
2000K, green full squares - 2500K.
As it is shown, the equilibrium pressure of silicon depends on the temperature. It is also worth to note in the region between 0.25 ML and 0.40 ML coverage drastic increase of the pressure by three orders of magnitude is observed. For 2500 K the Si pressure is of order of 0.001 bar for low coverage, increases to about 100 bar for coverage above 0.4 ML. Similar changes from 10 -7 bar to 0.1 bar and from 10 -10 bar to 10 -3 bar are observed for 2000 K and
1687 K, respectively. Generally it is expected that for typical growth conditions, the coverage of SiC(0001) surface is close to 0.3 ML.
4. Conclusions
Ab initio simulations the clean SiC(0001) surface has the Fermi level pinned by Si broken bond state located 0.8 eV below CBM. They also indicate that the most stable position of single Si atom adsorbed at SiC(0001) surface is H3 site at 1.87 Å from the topmost Si atoms in SiC lattice. Si adatom is bonded to three neighboring Si atoms, saturating their broken bonds. The adsorption energy is about 7.1 eV that leads to creation of 2 3

2 3 surface reconstruction.
Adsorption of the subsequent atoms leads to energy gain of 6.7 eV, smaller by 0.4 eV
22

indicating that 2 3

2 3 is energetically most stable. These subsequent adatoms are also located at H3 sites up to 0.25 ML coverage.
The stability of the adatoms at H3 position is related to electronic properties of the system. The Si adatom in all three positions: H3, T4 and on top create Sis state deep in VB, which is always occupied. The difference stems from Sip states. The Si adatom creates two doubly occupied resonating Sip surface parallel bonds saturating three Si broken bond states.
In addition the two Sip states perpendicular to the surface emerge. The lower energy bonding is double occupied while the upper, antibonding is occupied by single electron. This states has its energy approximately equal to Si broken bond states, thus both are pinning Fermi level at the surface. The configuration accepts four electrons from Si broken bonds states. That creates energy effect of about 1.5 eV, thus the adsorption energy in this range is about 6.7 eV.
According to EECR further increase exhausts Si broken bond electron source at about
0.25 ML coverage. Therefore Fermi level is lowered from the antibonding state to bonding which lowers the adsorption energy down to about 5 eV.
Further adsorption of Si atoms occupied H3 sites that have common Si top atoms with other Si adatoms. Thus the broken bond states are saturated that lower the adsorption energy gain to 4.2 eV at the coverage exceeding 0.4 ML. In this coverage range the H3 and on top configurations have roughly the same energy indicating the possible transition from the off lattice to SiC lattice position by subsequent Si adatoms.
The reduction of the adsorption leads to drastic decrease of the equilibrium pressure of silicon by 3 orders of magnitude is observed in the region between 0.25 ML and 0.40 ML coverage. For 2500 K the Si pressure is of order of 0.001 bars for coverage below 0.25 ML and increases to about 100 bar for coverage above 0.4 ML. Similar changes from 10
-7
bar to
0.1 bar and from 10
-10
bar to 10
-3
bar are observed for 2000 K and 1687 K, respectively.
Generally it is expected that for typical conditions for SiC growth from the vapor, the coverage of SiC(0001) surface is close to 0.3 ML.
ACKNOWLEDGMENTS
This work has been supported by the SICMAT Project financed under the European Founds for Regional Development (Contract No. UDA-POIG.01.03.01-14-155/09).
23

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