The constant adsorption energy surfaces for hydrogen adsorbed on Si-and C-terminated hexagonal 4H-SiC{0001} surfaces have been calculated within density functional theory framework. The two unreconstructed and one reconstructed √ 3 × √ 3 surfaces were taken into account. We show that on all surfaces there is a global energy minimum indicating the most favourable adsorption site corresponding to H atom adsorption on-top of the topmost substrate layer atom. In case of reconstructed surface, there is another small and shallow local minimum. Moreover, the diusion barrier is much higher at reconstructed surface than at unreconstructed ones

A Kiejna

E Wachowicz

CiteSeerX

Vol. 124 (2013) ACTA PHYSICA POLONICA A No. 5
Proceedings of the 42th Jaszowiec International School and Conference on the Physics of Semiconductors, Wisªa 2013
Potential Energy Surfaces for H
Adsorbed at 4H-SiC{0001} Surfaces
E. Wachowicza,b and A. Kiejnaa
aInstitute of Experimental Physics, University of Wrocªaw, Pl. M. Borna 9, PL-50-204 Wrocªaw, Poland
bInterdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw
A. Pawi«skiego 5a, PL-02-106 Warsaw, Poland
The constant adsorption energy surfaces for hydrogen adsorbed on Si- and C-terminated hexagonal
4H-SiC{0001} surfaces have been calculated within density functional theory framework. The two unreconstructed
and one reconstructed
√
3 ×
√
3 surfaces were taken into account. We show that on all surfaces there is a global
energy minimum indicating the most favourable adsorption site corresponding to H atom adsorption on-top of the
topmost substrate layer atom. In case of reconstructed surface, there is another small and shallow local minimum.
Moreover, the diusion barrier is much higher at reconstructed surface than at unreconstructed ones.
DOI: 10.12693/APhysPolA.124.765
PACS: 68.35.bg, 68.35.bj, 68.43.−h, 71.15.Mb
1. Introduction
The wide band-gap semiconductor silicon carbide has
attracted a great interest during the past decades [111]
because of number of properties which make it very at-
tractive for many applications in electronic devices. SiC
may crystallize in many polytypes. For electronic ap-
plications purposes hexagonal 4H-SiC is the preferred
polytype. The (0001) surfaces of the hexagonal polytype
4H-SiC are structurally equivalent to the Si(111) surface
for which hydrogenation has proved to be the method to
produce unreconstructed, extremely at, H-terminated
surfaces [1]. The hydrogen atoms attach to semiconduc-
tor dangling bonds thus providing the surface chemically
and electronically passivated. Moreover, hydrogen is
present in reactor chambers during SiC crystal growth so
it can inuence both the process and the quality of grown
crystals. Several theoretical papers presented research on
the electronic and atomic structure of hydrogen adsorbed
on Si-rich cubic SiC(001)3× 2 surface [10, 1215].
Our previous paper [16] presented results of our studies
of the eect of on-surface and sub-surface adsorption of H
atoms on structural and energetic properties of this sur-
face on unreconstructed SiC{0001}. Another important
issue is to understand H atoms movements on the sur-
face. Therefore, we calculated the potential energy sur-
face and, consequently, barriers for diusion for hydro-
gen atom on at SiC{0001} surfaces. Polar SiC{0001}
surfaces are known to experience many reconstructions
either Si- or C-rich. To compare H behaviour on at and
reconstructed surface we carried out similar calculations
for H on Si-terminated 4H-SiC(0001)
√
3×
√
3 reconstruc-
tion.
2. Methods
Our calculations have been performed using density
functional theory (DFT) as implemented in Siesta pro-
gram package [17]. The electron exchange-correlation
eects were treated within the generalized gradient ap-
proximation (GGA) using the PerdewBurkeErnzerhof
(PBE) form of the exchange-correlation functional [18].
The electron ion-core interactions were represented by
pseudopotentials of the TroullierMartins type [19] and
the electron wave-functions were expanded into the
atomic-orbital basis set using the double-ζ polarized set.
The cuto of 120 Ry was used for the real space mesh.
The Brillouin zone integrations were performed apply-
ing (4, 4, 1) k-points meshes for 2 × 2 surface supercell
calculations.
According to the tests reported in our previous pa-
per [16], we constructed slabs of 12 Si-C double-layers
representing the (0001) and (0001̄) surfaces of the 4H-SiC
crystal, terminated respectively with Si and C atoms. For
brevity, in the following these surfaces will be referred to
as Si(0001) and C(0001̄). The dangling bonds on the bot-
tom layer atoms of the slabs were saturated by hydrogen
atoms. The slabs of such thickness which were separated
from their periodic replicas in neighbouring cells by a
vacuum region of ≈ 20 Å proved to be sucient for re-
producing surface properties [20]. The atomic positions
of the four topmost double Si-C layers of the slab, and
of the terminating H atoms on the backside were relaxed
until forces on atoms converged to less than 0.02 eV/Å.
The positions of atoms of the remaining double Si-C lay-
ers have been held xed. Calculations of potential energy
surface were performed in 2 × 2 supercell for unrecon-
structed surface and in 1× 1 supercell for
√
3×
√
3 one.
3. Results
In order to obtain constant potential energy surface H
atom was placed in various sites on the surface. Hy-
drogen's x and y-coordinates were kept frozen while
z-coordinate and the substrate were allowed to relax.
There were used 25 evenly distributed sites in 1/4 of
2× 2 supercell on unreconstructed surfaces and 100 sites
(765)
766 E. Wachowicz, A. Kiejna
on reconstructed
√
3 ×
√
3 surface. For each point the
adsorption energy Eads was calculated. The adsorption
energy is dened as follows: Eads = EH/SiC−ESiC−EH,
where EH/SiC, ESiC, and EH are total energies of surface
with adsorbed hydrogen, clean surface, and free H atom,
respectively. This denition yields the lower adsorption
energy for the more favourable energetically adsorption
site.
Results of such calculations are given in Fig. 1. Our
previous calculations [16] showed that hydrogen atoms
are attached on top of the surface atoms saturating either
Si or C dangling bonds. The minima observed at all
plots correspond to the same case, i.e. H on top of the
topmost substrate layer atom. The lowest adsorption
energy (the strongest bond) equal to−4.81 eV is observed
for hydrogen on C(0001̄) surface. On Si(0001), H atom is
less strongly bound with Eads = −4.10 eV [16]. In both
cases constant energy surfaces reveal threefold symmetry
characteristic for hexagonal surfaces.
Fig. 1. Constant adsorption energy Eads surfaces√
3 ×
√
3 or hydrogen adsorbed at Si-terminated (a),
C-terminated (b) and Si-terminated
√
3 ×
√
3 (c) sur-
faces.
Fig. 2. High-symmetry adsorption sites on
4H-SiC{0001} surfaces. Top view of the surface
with 1× 1 supercell indicated in red. Blue/yellow balls
represent Si or C atoms depending on the termination
considered.
The observed maxima are related to the high-
-symmetry adsorption sites H3 and T4 on hexagonal
semiconductor surfaces (Fig. 2). At the Si(0001) surface
the main energy maximum is for hydrogen adsorbed in T4
site, where C atom from the second layer is just below H
atom. There, the adsorption energy equals to −2.65 eV.
In the second maximum, when H is at the H3 site (over
the C atom from the third layer) Eads = −3.19 eV. On
the C(0001̄) opposite situation is observed: main maxi-
mum exists for hydrogen at H3 site with adsorption en-
ergy equal to −3.47 eV. There is the second maximum
when H atom is placed at T4 site and Eads = −3.9 eV.
The energy barrier that H atom should overcome pass-
ing from one minimum to the other is higher on Si(0001)
and equals to 0.7 eV. At C(0001̄) surface the barrier for
diusion is lower and amounts to 0.5 eV.
Dierent hydrogen atom behaviour is observed on re-
constructed Si-terminated
√
3 ×
√
3 surface (Fig. 1c).
Similarly to unreconstructed surfaces, the constant en-
ergy surface experiences a deep minimum related to the
H atom bound on top of the topmost Si atom which is
indicated by letter A at the plot. In this case, the ad-
sorption energy equals to −3.40 eV.
Fig. 3. Final atomic conguration for clean recon-
structed surface (a), hydrogen adsorbed in the main
minimum (b), and the second minimum (c) on recon-
structed 4H-SiC(0001)
√
3 ×
√
3 surface. Yellow, cyan,
and white balls represent Si, C, and H atoms, respec-
tively.
Another type of minimum indicated by letter B at the
plot is much smaller and shallower with Eads = −2.54 eV.
Looking at the atomic positions corresponding to the
minima (Fig. 3) it can be easily noticed that in both cases
hydrogen atom is bound to the topmost surface silicon.
In the most favourable situation, topmost silicon remains
in the same T4 position as on the clean surface with the
bond length to the nearest Si atom equal to 2.44 Å. The
H-Si bond length is 1.53 Å. It is similar to that on un-
reconstructed Si(0001) surface where it ranges from 1.52
to 1.55 Å depending on the H coverage. In the second
minimum the topmost Si atom with H attached on is
shifted to the H3 site. At clean surface, the H3 site for
Si atom is less favourable energetically by ≈ 0.5 eV. The
energy dierence for hydrogen adsorption at these two
positions is even bigger and amounts to 0.84 eV. Nev-
ertheless, the local geometry remains almost unchanged:
the bond length between Si atoms is 2.45 Å and between
Potential Energy Surfaces for H . . . 767
the H atom and underlying Si atom 1.54 Å. In the path
of the lowest energy for H atom passing from site A to B
the barrier of 1.16 eV should be overcome. Then, there is
another barrier for H going from B to another A of 0.6 eV.
4. Summary
In this work, the ab initio method was applied to calcu-
late constant energy surfaces for hydrogen atom adsorbed
on 4H-SiC{0001}. Two unreconstructed and one recon-
structed surfaces were taken into account. In general,
hydrogen is bound more strongly to the unreconstructed
surfaces but there is higher barrier for diusion on recon-
structed
√
3 ×
√
3 surface. Our calculations show deep
and wide minima on all surfaces corresponding to H atom
adsorbed on-top of the topmost substrate layer atom.
Hydrogen is bound more strongly to the C-terminated
surface with adsorption energy equal to −4.81 eV. On the
Si-terminated surface Eads is higher by about 0.7 eV. On
both surfaces, the dierences between maximal and min-
imal values of adsorption energy are similar and amount
to about 1.4 eV. The barriers for diusion are 0.7 eV and
0.5 eV on the Si(0001) and C(0001̄) surface, respectively.
In case of reconstructed Si-terminated
√
3×
√
3 surface,
there are two types of minima of adsorption energy. Both
of them correspond to H adsorption on top of the same
topmost Si atom but in deeper minimum Si is placed at
the T4 site while in the other at the H3 site. The adsorp-
tion energies in those minima are −3.40 and −2.54 eV.
The barrier for diusion is much higher at reconstructed
surface and equals 1.16 eV.
Acknowledgments
This research was carried out within the SICMAT
Project nanced under the European Funds for Regional
Development (contract No. UDA-POIG.01.03.01-14-
-155/09). We acknowledge computer time granted by
the Interdisciplinary Centre for Mathematical and Com-
putational Modelling (ICM) of the Warsaw University
within the project No. G44-23.
References
[1] Th. Seyller, Appl. Phys. A, Mater. Sci. Proc. 85,
371 (2006).
[2] G.P. Brandino, G. Cicero, B. Bonferroni, A. Fer-
retti, A. Calzolari, C.M. Bertoni, A. Catellani, Phys.
Rev. B 76, 085322 (2007).
[3] Th. Seyller, J. Phys., Condens. Matter 16, S1755
(2004).
[4] Th. Seyller, R. Graupner, N. Sieber, K.V. Emtsev,
L. Ley, A. Tadich, J.D. Riley, R.C.G. Leckey, Phys.
Rev. B 71, 245333 (2005).
[5] G.V. Soares, I.J.R. Baumvol, C. Radtke, F.C. Stedile,
Appl. Phys. Lett. 90, 081906 (2007).
[6] Y. Aoki, H. Hirayama, Appl. Phys. Lett. 95, 094103
(2009).
[7] S. Nannarone, M. Pedio, Surf. Sci. Rep. 51, 1
(2003).
[8] K.C. Pandey, Phys. Rev. Lett. 49, 223 (1982).
[9] K. Heinz, J. Bernhardt, J. Schardt, U. Starke,
J. Phys., Condens. Matter 16, S1705 (2004).
[10] D.G. Trabada, F. Flores, J. Ortega, Phys. Rev. B
80, 075307 (2009).
[11] P. Deák, B. Aradi, J.M. Knaup, Th. Frauenheim,
Phys. Rev. B 79, 085314 (2009).
[12] R. Di Felice, C.M. Bertoni, C.A. Pignedoli, A. Catel-
lani, Phys. Rev. Lett. 94, 116103 (2005).
[13] X. Peng, P. Krüger, J. Pollmann, Phys. Rev. B 72,
245320 (2005).
[14] H. Chang, J. Wu, B.-L. Gu, F. Liu, W. Duan, Phys.
Rev. Lett. 95, 196803 (2005).
[15] R. Rurali, E. Wachowicz, P. Hyldgaard, P. Ordejón,
Phys. Status Solidi (RRL) 2, 218 (2008).
[16] E. Wachowicz, A. Kiejna, J. Phys., Condens. Matter
24, 385801 (2012).
[17] J. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Jun-
quera, P. Ordejón, D. Sanchez-Portal, J. Phys., Con-
dens. Matter 14, 2745 (2002).
[18] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev.
Lett. 77, 3865 (1996).
[19] N. Troullier, J.L. Martins, Phys. Rev. B 43, 1993
(1991).
[20] J. Soªtys, J. Piechota, M. opuszy«ski, S. Krukowski,
New J. Phys. 12, 043024 (2010).


Potential Energy Surfaces for H Adsorbed at 4H-SiC{0001} Surfaces

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=DE2A4F4C1064476517B23E3C9B71629D?doi=10.1.1.1037.1583&rep=rep1&type=pdf

Potential Energy Surfaces for H Adsorbed at 4H-SiC{0001} Surfaces

Abstract

Similar works

Full text

Available Versions

CiteSeerX