VOLUME 79, NUMBER 20 PHYSICAL REVIEW LETTERS 17NOVEMBER 1997
Reconstructions of the GaNsss0001ddd Surface
A. R. Smith,
1
R. M. Feenstra,
1
D. W. Greve,
2
J. Neugebauer,
3
and J. E. Northrup
4
1
Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
2
Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
3
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
4
Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, California 94304
(
Received 20 June 1997)
Reconstructions of the GaNs0001
¢
surface are studied for the first time. Using scanning tunneling
microscopy and reflection high-energy electron diffraction, four primary structures are observed:
1 3 1, 3 3 3, 6 3 6, and cs6 3 12d. On the basis of first-principles calculations, the 1 3 1 structure
is shown to consist of a Ga monolayer bonded to a N-terminated GaN bilayer. From a combination of
experiment and theory, it is argued that the 3 3 3 structure is an adatom-on-adlayer structure with one
additional Ga atom per 3 3 3 unit cell. [S0031-9007(97)04507-9]
PACS numbers: 68.35.Bs, 61.16.Ch, 68.55.Jk
Gallium nitride and other III nitrides have attracted
considerable interest recently because of their application
for blue light-emitting diodes and lasers [1]. These
materials have several unique properties compared to
the more conventional III-V semiconductors (GaAs, InP,
etc.): they exist in both cubic (zinc blende) and hexagonal
(wurtzite) form, they are refractory, and some of the
materials have large band gaps. The relatively small size
of nitrogen, compared to Ga or In, in these compounds
leads to a number of unique surface structures, which
have begun to be explored both experimentally and
theoretically for the (001) growth surface of cubic GaN
[2,3]. However, for the technologically more relevant
(0001) growth surface of hexagonal GaN, very little is
known concerning its structure aside from several reports
of 2 3 2 and other reconstructions based on reflection
high-energy electron diffraction (RHEED) [4]. It is
important to understand the surface structures of these
materials, since this knowledge will impact our ability to
achieve high quality epitaxial growth of the materials as
required for optoelectronic applications.
In this Letter we report the first observations of recon-
structions on the GaNs000
1
d
surface. The reconstructions
are studied using scanning tunneling microscopy (STM),
RHEED, and ab initio calculations. We find four domi-
nant reconstructions, which in order of increasing sur-
face GayN ratio are given by 1 3 1, 3 3 3, 6 3 6, and
cs6 3 12d. From among a number of candidate struc-
tures, the 1 3 1 reconstruction is found to consist of a
monolayer (ML) of Ga atoms, located in atop sites above
the N atoms of a N-terminated bilayer. This is a novel
structure, with no known analog among other semicon-
ductor surfaces. It is energetically feasible because of the
much larger size of the Ga atoms compared to N atoms.
For the 3 3 3 reconstruction, we find experimentally that
it consists of a single additional Ga atom per 3 3 3 unit
cell. Theoretically, the most plausible model for such a
structure consists of the additional Ga atom in a threefold
coordinated site just above the adlayer. Substantial in-
ward relaxation of the Ga adatoms is found, accompanied
by large lateral relaxation of the Ga adlayer.
It is important to note that the (0001) and s000
1d sur-
faces of GaN are inequivalent (by convention, the [0001]
direction is given by a vector pointing from a Ga atom
to a nearest-neighbor N atom). Thin films having either
surface polarity have been grown [5], although for growth
by molecular beam epitaxy (MBE) the conditions which
determine the surface polarity are not well understood [6].
The reconstructions studied in the present Letter are pre-
pared on the s000
1d surface, with this assignment being
made on the basis of (1) the observed reconstructions,
which differ from those seen by both other workers [4]
and ourselves [6] on surfaces believed to be (0001), (2)
the theoretical studies presented here, which do not yield
any acceptable models for a 1 3 1 structure on the (0001)
face, and (3) convergent beam electron diffraction studies
on our samples, which compared with theoretical simula-
tions favor the assignment of s000
1d polarity [7].
The experiments are performed in an MBE system
equipped with STM. Growth is performed on solvent-
cleaned sapphire(0001) substrates, heated first to 1000
±
C
under a nitrogen plasma for 30 min. The substrate
temperature is then reduced to 685
±
C, and the growth
is initiated. During the first few hundred angstroms of
growth, the substrate temperature is gradually increased
to about 775
±
C. After growing a 2000 Å thick film, the
growth is stopped and the sample is annealed at 800
±
C for
15 min. The resulting film surface consists of atomically
flat terraces up to a micron in width and exhibits a
1 3 1 structure. Depositing additional Ga atoms onto
this surface results in the 3 3 3, 6 3 6, and cs6 3 12d
reconstructions. Ga flux rates were calibrated using an
in situ water-cooled crystal thickness monitor, at 20
±
C.
STM images of our GaN surfaces are displayed in
Fig. 1. Figure 1(a) displays a large-scale view of the sur-
face, prepared in this case with Ga coverage intermediate
between the 3 3 3 and 6 3 6 reconstructions. Coexisting
with those structures we also occasionally observe small
3934 0031-9007y97y79(20)y3934(4)$10.00 © 1997 The American Physical Society
VOLUME 79, NUMBER 20 PHYSICAL REVIEW LETTERS 17NOVEMBER 1997
FIG. 1. STM images of the GaNs0001
¢
surface displaying
(a) mixed reconstructions, with dislocation near center of
image, (b) 1 3 1, (c) 3 3 3,(d)636, and (e) cs6 3
12d reconstructions. Sample bias voltages are 11.0, 20.75,
20.1, 11.5, and 11.0 V, respectively. Tunnel currents are in
the range 0.03
0.11 nA. Gray scale ranges are 4.2, 0.17, 0.88,
1.33, and 1.11 Å, respectively. Unit cells are indicated with
edges along k11
20l directions.
areas of a somewhat disordered s4
p
3 3 4
p
3 d-R30
±
struc-
ture, as indicated in the image. The atomic steps seen in
Fig. 1(a) all have height of about 2.6 Å. A screw dislo-
cation is seen emerging near the center of the image, with
component of the Burgers vector in the [0001] direction
of c 5.19 Å. Such dislocations are commonly imaged
on our surfaces. We point out that all the reconstructions
observed in this study are stable only to temperatures up
to 100
300
±
C, at which point a reversible phase transition
occurs to a 1 3 1 structure as seen by RHEED. We asso-
ciate this transition with an order-disorder transition of the
Ga adatoms atop the 1 3 1 structure, evidence for which is
seen even at room temperature by characteristic “glitchy”
behavior in the images near certain domain boundaries in-
dicative of adatom motion [8].
Detailed STM images for the 1 3 1, 3 3 3, 6 3 6,
and cs6 3 12d reconstructions are shown in Figs. 1(b)–
1(e), along with unit cells for each. The 1 3 1 appears
as a hexagonal array of corrugation maxima, with a lat-
eral spacing equal to the c-plane lattice constant of GaN,
3.19 Å. The 3 3 3 is similar in appearance but displays
an asymmetry within the unit cell as well as additional
structure at lower biases. The asymmetry of the unit cell
reflects the fact that each GaN bilayer has only threefold
symmetry. STM images confirm that this asymmetry re-
verses upon descending a single bilayer-high step on the
surface. The 6 3 6 is made up of ring-shaped structures.
Each ring has threefold symmetry with lobes from three
neighboring rings coming close together. This results in
two different kinds of “holes” around the rings, one appear-
ing deeper than the other. The cs6 3 12d reconstruction
is qualitatively different in appearance from the previous
three. Rowlike structures are observed running parallel
to k1100l directions of the crystal. Circular corrugation
maxima appear in pairs along the rows; there are two pos-
sible angular orientations of these pairs of maxima with
respect to the row directions in addition to the three possi-
ble row directions. Voltage dependence of the STM im-
ages for each reconstruction has been studied; no strong
dependence is observed, except for the cs6 3 12d struc-
ture where the appearance of the rowlike features differs
between empty and filled states.
For determining structural models of the observed re-
constructions, an important constraint is the number of Ga
(and N) atoms involved in each structure. These quanti-
ties have been studied by observing the dependence of the
surface reconstructions on the amount of Ga deposited.
Initial experiments were performed at a sample tempera-
ture of 630
±
C. Results are shown in Fig. 2(a), where
we plot the fractional coverage of each major reconstruc-
tion, as determined by STM. Also shown are represen-
tative RHEED patterns for each of the reconstructions.
While the amount of Ga deposited is known for Fig. 2(a)
(Ga flux of 0.058 MLys), the sticking coefficient at that
sample temperature was found to be much less than unity
so that an absolute determination of surface Ga cover-
age was not possible. Further experiments were per-
formed with a sample temperature of 60
±
C, as shown in
Fig. 2(b). In this case, the RHEED intensities were used
for determining the fractional coverage of a particular re-
construction. Focusing on the formation of the 3 3 3,we
find from Fig. 2(b) that this structure is formed at a cov-
erage of 0.145 6 0.025 ML, corresponding to 1.3 6 0.2
atoms per 3 3 3 unit cell. Since the number of atoms
per unit cell must be an integer, we conclude that the
3 3 3 structure contains one additional atom per 3 3 3
cell compared with the 1 3 1. (The observed value is
slightly greater than 1, probably because the sticking co-
efficient at 60
±
C is slightly less than that for the thickness
monitor used to calibrate the flux.)
Total energy calculations have been performed within
the local density functional theory using first-principles
pseudopotential methods similar to those employed in
previous studies of GaN and AlN [3]. Reconstructions
for both the (0001) and s000
1d polarities have been
examined, and for each polarity the relative stabilities
of possible structures have been determined within the
thermodynamically allowed range of the Ga chemical
3935
VOLUME 79, NUMBER 20 PHYSICAL REVIEW LETTERS 17NOVEMBER 1997
FIG. 2. (a) Fractional coverage of 1 3 1, 3 3 3, 6 3 6, and
cs6 3 12d reconstructions vs Ga deposition time, determined
by STM imaging of the surfaces. Sample temperature during
deposition was 630
±
C. RHEED patterns corresponding to
the different reconstructions are shown in the upper part
of the figure. RHEED beam direction is along f11
20g.
(b) Ratio of RHEED intensities of the s
2
3
0d and s10dstreaks
vs amount of Ga deposited in monolayers s1 ML 1.14 3
10
15
atomsycm
2
d. Sample temperature during deposition was
60
±
C. All curves between data points are drawn as guides to
the eye.
potential: m
Gasbulkd
2DH,m
Ga
,m
Gasbulkd
. Our cal-
culations indicate that DH, the heat of formation of GaN,
is equal to 0.9 eV, in good agreement with the experimen-
tal value, 1.1 eV. The calculations have been performed
with a plane wave cutoff of 60 Ry and with the Ga 3d
states included in the valence band.
During the initial stages of the investigation we fo-
cused on the (0001) surface, but discovered that each of
the 1 3 1 structures examined could be shown to be en-
ergetically unfavorable with respect to various structures
having 2 3 2 periodicity. The relative formation energies
calculated for the most relevant structures are shown in
Fig. 3(a). Under N-rich conditions we find a s2 3 2d-H3
N-adatom model to be most stable, and under Ga-rich con-
ditions we find a s2 3 2d-T4 Ga-adatom model is favored.
Both the ideal topology 1 3 1 surface (consisting of a
Ga-terminated bilayer) and the 1 3 1 Ga adlayer (com-
prised of a monolayer of Ga above the Ga-terminated bi-
layer) are energetically unfavorable. The 1 3 1 N adlayer
is highly unstable. On the basis of these results we surmise
that there is no stable 1 3 1 structure for the GaN(0001)
surface. We emphasize, however, that the 2 3 2 Ga- and
N-adatom models are each good candidates to explain the
2 3 2 structure observed in RHEED studies of the (0001)
surface [4].
Not finding a stable 1 3 1 structure for the (0001)
polarity, we turned our attention to the s000
1d surface.
As shown in Fig. 3(b) we find the 1 3 1 Ga adlayer
structure to be stable under Ga-rich conditions. Other
structures, including the s2 3 2d-H3 Ga adatom, are
FIG. 3. (a) The relative energies calculated for possible
models of the GaN(0001) surface are shown as a function of
the Ga chemical potential. (b) Relative energies for GaNs000
1
¢
surfaces. The zeros of energy in (a) and (b) are not related.
predicted to be more stable under N-rich conditions, but
there is a substantial range where the 1 3 1 Ga adlayer
is the preferred structure. In the stable 1 3 1 model
a full monolayer of Ga atoms sit directly atop the N
atoms, with the Ga-N bond length equal to 1.99 Å. The
Ga-Ga separation in the adlayer, 3.19 Å, is considerably
larger than a typical Ga-Ga separation of 2.7 Å in bulk
Ga. However, we find that the structure is stabilized by
metallic bonding within the adlayer: a large overlap of
the p
x
and p
y
orbitals of the Ga adlayer atoms gives
rise to an energy dispersion of the surface states derived
from these orbitals which is much greater than the bulk
band gap. Consequently, the Fermi energy is located near
the bottom of the band gap and there is no occupation
of high energy Ga dangling bond states. We have also
found that the 1 3 1 adlayer is stable with respect to
adding Ga adatoms in threefold coordinated sites to create
either a 2 3 2 adatom-on-adlayer (AOA) structure or a
p
3 3
p
3 AOA structure. On the basis of energetics,
the GaNs000
1
d
1 3 1 Ga adlayer is the best candidate to
explain the 1 3 1 structure observed here; this structure
is illustrated in Fig. 4(a).
Calculations have also been performed for several
possible models of the 3 3 3 surface. Because of the
large size of the 3 3 3 unit cell these calculations were
performed with the Ga 3d electrons treated as part of
the core using the nonlinear core correction (nlcc) [9].
Structural models having one, two, or three additional
3936
VOLUME 79, NUMBER 20 PHYSICAL REVIEW LETTERS 17NOVEMBER 1997
FIG. 4. Schematic view of structures determined for the
(a) 1 3 1 Ga adlayer and (b) 3 3 3 adatom-on-adlayer recon-
structions of GaNs000
1
¢
. For the 3 3 3 structure, the lateral
(in-plane) displacement of the adlayer atoms bonded to the Ga
adatom is 0.51 Å away from the adatom. All other lateral or
vertical displacements of the adlayer atoms are less than 0.1 Å.
Ga adatoms on (or in) the Ga adlayer were considered.
These nlcc calculations indicate that a structure containing
one additional Ga atom in each 3 3 3 cell is the best
model for the observed 3 3 3 reconstruction. One may
construct a class of such adatom-on-adlayer structures
by adding threefold coordinated Ga atoms to the 1 3 1
adlayer. This addition lowers the symmetry from 1 3 1
to n 3 n where 1ysn 3 nd is the fraction of added Ga
atoms. We have determined that such structures with
n
p
3 and n 2 are each unstable with respect to the
1 3 1 Ga adlayer. However, for n 3 we find that the
AOA structure becomes stable in Ga-rich conditions. In
the 3 3 3 structure, the extra Ga atom resides only 0.9 Å
above the adlayer plane, compared to a 1.35 Å separation
in the
p
3 3
p
3 and 1.25 Å in the 2 3 2. In the absence
of lateral relaxation, the Ga adatom must be positioned
1.8 Å above the adlayer to preserve a reasonable Ga-Ga
distance. The larger inward relaxation of the adatom in
the 3 3 3 structure is enabled by a 0.5 Å lateral relaxation
of the nearest-neighbor Ga adlayer atoms, which allows
the adatom to move much closer to the adlayer plane,
thereby stabilizing the structure. We may therefore refer
to the proposed structure as an in-plane adatom model,
as illustrated in Fig. 4(b). Images of the calculated local
density of states for this model are found to be in
qualitative agreement with the experimental results.
We examined two types of 3 3 3 models in which two
Ga atoms were added to the 1 3 1 adlayer: a trimer-
in-vacancy model where an adlayer atom is replaced by
a Ga trimer, and a structure having 2 Ga adatoms per
3 3 3 cell, with each placed in a threefold coordinated
site. The total energies of these models were calculated
with the nlcc approximation and were found to be less
stable than the proposed 3 3 3 AOA structure by about
0.9 eVys3 3 3d and 1.1 eVys3 3 3d in the Ga-rich limit.
From a comparison of energies of structures calculated
with the nlcc and with the Ga-3d electrons included
in the valence band, we think the maximum error in
these relative energies is less than 0.5 eVys3 3 3d. [For
example, in calculations for the 2 3 2 AOA model we
found that the nlcc gave an energy relative to the 1 3 1
Ga-adlayer model which was within 0.04 eVys2 3 2d
of the full calculations.] It is clear that these nlcc
calculations support the experimental determination that
the 3 3 3 contains only one additional Ga atom per cell.
In conclusion, we have observed a new family of
reconstructions on the GaNs000
1
d
surface. The 1 3 1
structure is determined to consist of a monolayer of
Ga atoms bonded in atop sites above N atoms of a
N-terminated bilayer. The 3 3 3 reconstruction consists
of Ga adatoms bonded on top of this adlayer. Adatom-on-
adlayer models for the other observed reconstructions are
also possible, although such structures have not yet been
explored in detail.
We gratefully acknowledge M. J. DeGraef and Chimin
Hu for their transmission electron diffraction studies of
our GaN films [7], V. Ramachandran for film character-
ization, and M. F. Brady for technical assistance. This
work was supported by the Office of Naval Research un-
der contracts at CMU: N00014-95-1-1142 and N00014-
96-1-0214, and at Xerox: N00014-95-C-0169.
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