)
surfaces. 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 and electronic
applications.
Gallium
nitride and other III-nitrides have attracted considerable interest recently
because of their applications for blue light-emitting diodes and lasers and for
high frequency/high power transistors [1] [2] [3] [4] [5] [6] [7]. These materials have
several unique properties compared to the more conventional III-V
semiconductors (GaAs, InP, etc.): they exist in both cubic (zincblende) 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
been explored in several papers for the (001) growth surface of cubic GaN
[8] [9] [10]. For the technologically more relevant (0001) growth surface of
hexagonal GaN, reports over the past 5 years have led to considerable understanding of its structure, for both bare and adsorbate covered surfaces.
This article presents a review of these studies of the surface science of
wurtzite GaN (0001) and (000)
surfaces. 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 and electronic
applications.
Common growth methods for GaN films include metal-organic vapor phase epitaxy (MOVPE) and molecular beam epitaxy (MBE). The latter can be performed using a plasma source for nitrogen (plasma-assisted MBE, or PAMBE) or using ammonia, which thermally decomposes on the growth surface (reactive MBE, or RMBE). The MBE technique by virtue of its ultra-high vacuum apparatus is more amenable to surface science studies, and most surface science work to date has been performed on samples grown by PAMBE. Such work constitutes the bulk of the material reviewed in this article. Reports of the surface science of GaN films grown by RMBE have also appeared [11] [12] [13], and one group has reported surface science results for MOVPE-grown material [14]. Those works are discussed below in Section 3.5.
It is important to note that the (0001) and (000)
directions of GaN are inequivalent, as illustrated in Figure 1 (by convention,
the positive (0001) direction is given by a vector pointing from a Ga atom to a
nearest-neighbor N-atom along (0001)). Thin films having either polarity have
been grown. Films with (0001) surface normal are called Ga-polar, and those
with (000)
surface normal are called N-polar. The surfaces of such films are sometimes
called Ga-face or N-face, respectively. The identification of film polarity,
and the factors influencing the nucleation of a particular polarity, are
discussed in the early review by Hellman et al. [15]. Two additional issues
which have been addressed since that article are: (a) for MBE growth on
sapphire, the formation of Ga- or N-polarity is largely influenced by the
choice of AlN or GaN buffer layers used for the initial film nucleation
[11] [16] [17] and (b) the observation of a clear 2x2 reconstruction during
PAMBE growth of Ga-polar material (which is argued by Hellman to provide a
means of identifying the Ga-polarity) has been recently argued to arise from
the unintentional presence of arsenic on the growth surface [18] [19], as further
discussed below. This arsenic occurs in a number of growth systems since they
were previously used for MBE growth of GaAs, and the influence of residual
arsenic has also been established for the case of cubic GaN [8] [9] [10]. However,
notwithstanding the role of arsenic, it should be noted that even comparing
results from arsenic-free growth systems leads in some cases to disagreement in
the precise reconstructions reported; it is clear that for certain conditions
(e.g. intermediate stoichiometries) the GaN surface symmetry can be modified by
rather low levels of contamination.
Regarding nomenclature, we repeat here the recommendation made by Hellman et al., that the terms "Ga-terminated" or "N-terminated" should be avoided when referring to film or surface polarity. The actual termination of a film depends, of course, on the surface reconstruction and surface stoichiometry. These terms, Ga- or N-terminated, will however be occasionally used below when referring to the actual presence of a particular terminating layer of atoms on a surface.
In this article we review results for surface reconstructions of GaN (000)
and (0001) surfaces, focusing first on reconstructions of the bare surfaces and
then discussing the addition of various adlayers including In, Mg, Si, and H to
the surfaces. The kinetics of the surface atoms during growth is also discussed.
A
number of early works have reported surface symmetries other than 1x1 for
GaN surfaces, but the nature of these reconstructions was completely unknown
[15] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]. The first paper to determine geometrical
arrangements of reconstructions was the work of Smith et al. for the GaN(000)
surface [30]. These films were grown by PAMBE on sapphire. Their polarity was
not known prior to the study; an outcome of the work was the determination of
N-polarity, and subsequent studies by other workers upheld this conclusion
[11]. The surface structure varies with surface stoichiometry. Figure 2 shows
scanning tunneling microscopy (STM) images of the four most common
reconstructions: 1x1, 3x3, 6x6, and c(6x12), in order
of increasing Ga coverage.
The 1x1 reconstruction appears as a hexagonal array of corrugation
maxima, with a lateral spacing equal to the c-plane lattice constant of GaN,
3.19 Å. The 3x3 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
three-fold symmetry. STM images confirm that this asymmetry reverses upon
descending a single bilayer-high step on the surface. The 6x6 is made up
of ring-shaped structures. Each ring has three-fold symmetry with lobes from
three neighboring rings coming close together. This results in two different
kinds of "'holes" around the rings, one appearing deeper than the other.
The c(6x12) reconstruction is qualitatively different in appearance from
the previous three. Row-like structures are observed running parallel to
<100>
directions of the crystal. Circular corrugation maxima appear in pairs along
the rows; there are two possible angular orientations of these pairs of maxima
with respect to the row directions in addition to the three possible row
directions. Voltage dependence of the STM images for each reconstruction has
been studied; no strong dependence is observed, except for the c(6x12)
structure where the appearance of the row-like features differs between empty
and filled states [31].
For determining structural models of the observed reconstructions, an important constraint is the number of Ga (and N) atoms involved in each structure. The observed surface reconstructions form when the surface is Ga-rich [11] [30]. Formation of the 3x3 reconstruction was found to require 0.145 ± 0.025 ML (ML = monolayer = 1.14 x 1015 atoms/cm2) more Ga than the 1x1 structure, corresponding to 1.3 ± 0.2 atoms per 3x3 unit cell. The 6x6 and c(6x12) require additional amounts of Ga, estimated to be 0.43 and 0.58 ML respectively relative to the 1x1 surface [31]. It is important to note that this "excess" Ga (over that required for the 1x1) is only weakly bound onto the surface. Above a temperature of about 200°C, the 3x3, 6x6, and c(6x12) all transform reversibly to a 1x1 arrangement believed to consist simply of the 1x1 Ga-terminated surface (described below) together with the excess Ga in a mobile, disordered (probably lattice gas) arrangement on the surface.
First
principles total energy calculations of the relative stability of possible
models of surface reconstructions can provide definitive determinations of the
surface structure provided certain conditions are met. One requirement is that
the system under consideration must be reasonably close to equilibrium. It is
not obvious a priori that this requirement is satisfied in general by
surface structures prepared by an MBE growth process. Nevertheless theorists
have moved forward using a thermodynamic approach and there is now a widespread
consensus that it is possible to obtain a reasonably complete mapping of the
observed reconstructions by calculating the surface formation energies as a
function of one or more of the atomic chemical potentials of the constituents.
Prototypical examples of systems where this approach has achieved some success
include the GaAs(001) and ZnSe(001) surfaces. The approach has also been
successful in chemisorption systems such as Si(001)H. One of the objectives of
work on GaN surfaces is to determine if the same theoretical approach will be
successful for GaN and the other highly ionic wide-band-gap materials. At
present the theoretical mapping for GaN is not complete: some of the observed
reconstructions - such as the 6x6 and c(6x12) on the (000)
surface and the 5x5 and 6x4 on the (0001) surface discussed below
- are too large and complex for theoretical analysis at this time. A
second requirement is that a sufficiently large number of structural models
should be considered. Input from experiment is crucial, both in suggesting
possible structures and limiting the number of models that must be considered.
For GaN one calculates the relative formation energies of surfaces as a
function of the Ga and N chemical potentials (µGa and
µN). The formation energy of a system comprised of Ga and N is
defined as 
= E - nGaµGa -
nNµN. In this expression E is the total energy per
supercell that is calculated for a structure containing the specified number of
gallium and nitrogen atoms (nGa,nN). We assume
equilibrium with bulk GaN: This implies the relation µGa +
µN = µGaN(bulk), where µGaN(bulk) is
the calculated energy per Ga-N pair for wurtzite GaN. This relation between the
chemical potentials is used to eliminate either the gallium or nitrogen
chemical potential as an independent variable and to write the formation energy
as a function of a single chemical potential. The formation energy may then be
written as = Ega - (nGa -
nN)(µGa - µGa(bulk)), where
Ega is the formation energy corresponding to the Ga-rich limit,
where by definition µGa = µGa(bulk). The relative
energy difference between any two reconstructions may then be expressed as
= Ega - (nGa -
nN)(µGa - µGa(bulk)). The
Ga chemical potential is bounded from above by µGa(bulk) and from
below by µGa(bulk) - |H| where H is the heat
of formation of GaN. We refer to the two endpoints of the allowed Ga chemical
potential, µGa = µGa(bulk) and µGa =
µGa(bulk) - |H|, as the Ga-rich and N-rich limits.
The thermodynamically allowed structures are those that have the lowest energy
for some value of the Ga chemical potential within the allowed range [32].
Total energy calculations for the (000)
surface shown in Figure 3(b) [30], indicate that the only feasible candidate for
the experimentally observed 1x1 structure is the Ga adlayer model. This
structure is shown in Figure 4(a) [30]. In this structure each Ga atom is
positioned in an atop site with vertical N-Ga bonds of length 1.99 Å.
The atop registry of the Ga atoms is preferred by a wide margin over
registrations in which the Ga is located over T4 or H3 sites. Electronic
structure calculations predict that the Ga adlayer structure gives rise to
highly dispersive bands of surface states inside the bulk band gap [33]. A
recent experimental study by Ryan et al. [34] appears to corroborate the
existence of such highly dispersive states. The correspondence between the
theory and the photoemission experiment is not complete, however, and further
work is required to account for all the features seen in the experiment.
In N-rich conditions the most stable structure that has been obtained
theoretically is the 2x2 Ga adatom model, with the adatom in an H3 site.
The adatom forms three bonds to the N atoms in the layer below, and the length
of these bonds is 1.98 Å. So far, a 2x2 structure has not been
observed on the GaN(000)
surface. The ideal 1x1 surface having one threefold coordinated N atom in
each unit cell is not stable for any allowed value of the Ga chemical potential.
The Ga atoms in the 1x1 adlayer structure are each bonded to a single N
atom and are separated from 6 other Ga atoms in the adlayer by a distance
corresponding to a second-nearest-neighbor distance of bulk GaN, i.e. they are
separated by about 3.2 Å. The relative stability of this type of
structure is, at first sight, very surprising. To establish the plausibility of
this structure a set of calculations was performed in order to determine how
much of the binding energy of a Ga atom arises from intra-adlayer Ga-Ga
interactions and how much arises from the Ga-N bonds [33]. Starting from a
GaN(000)1x1
N-terminated surface and a collection of isolated Ga atoms, the energy of the
system decreases by 4.0 eV per Ga atom when the adlayer is formed. Of this 4.0
eV/atom, a 2.2 eV reduction can be attributed to the formation of the Ga-N
bonds and 1.8 eV can be attributed to the formation of the Ga-Ga bonds within
the adlayer. The first point to be made is that the 4.0 eV/atom energy
reduction is larger than the cohesive energy of bulk Ga (2.8 eV/atom). In other
words the 1x1 Ga adlayer is much more stable than a surface with Ga
droplets residing on a N-terminated 1x1 surface. The second point is that
a substantial fraction - about 45% - of the binding energy of the
Ga atoms can be attributed to intra-adlayer Ga-Ga bonding. For perspective,
consider the analogous (hypothetical) reaction for Ga on an As-terminated
GaAs()1x1
surface. The Ga atoms in such an adlayer would be separated from each other by
about 4.0 Å. Now, the calculated energy reduction of the system that
results from bringing isolated Ga atoms onto the As-terminated surface is found
to be 2.4 eV/atom. Of this 2.4 eV, a 1.6 eV reduction arises from the Ga-As
bond and 0.8 eV arises from the intra-adlayer Ga-Ga bonds. In this case, since
the cohesive energy of Ga is 2.8 eV/atom, a 1x1 Ga adlayer would actually
be unstable with respect to formation of Ga droplets on a 1x1
As-terminated surface. It is important to note that the energy reduction
arising from intra-adlayer Ga-Ga bonding is only 0.8 eV/atom - just about
33% of the total reduction. It was found that the strength of the intra-adlayer
Ga-Ga bonding increases by about 1.0 eV/atom as the Ga-Ga separation in the
adlayer is reduced from 4.0 Å (for GaAs) to 3.2 Å (for GaN). The
increased strength of the intra-adlayer Ga-Ga bonding is an important part of
the reason why Ga adlayer structures can occur on GaN(000)
surfaces, but not on the GaAs()
surface.
The other observed reconstruction of the GaN(000)
surface which has been examined is the 3x3 structure [30]. The preferred
model is obtained by adding a single Ga atom per 3x3 unit cell to the
1x1 Ga adlayer model. This additional Ga adatom is located in a hollow
site 0.75 Å above its three neighboring Ga atoms as shown in Figure 4(b).
To accommodate the additional atom the three neighboring Ga atoms relax
laterally away from the adatom by more than 0.5 Å so that the length of
the three Ga-Ga bonds is 2.50 Å. This structure is indeed found to be
energetically favorable compared to the 1x1 adlayer model in Ga-rich
conditions (those results are not shown in Figure 3 since they were performed by
including the Ga 3d electrons as part of the core using the nonlinear core
correction [30]). On the basis of these calculations it is concluded that the
(000)
surface consists of an atop-registered Ga adlayer, and that this adlayer is
decorated by additional Ga adatoms.
The atop-registered 1x1 adlayer model is also energetically favorable in the
case of In-terminated GaN(000)
surfaces, as discussed in more detail below. The In-In separation in bulk In is
approximately 3.3 Å and so In is a much larger atom than Ga. (In bulk Ga
the corresponding Ga-Ga separation is 2.7 Å.) [a] In fact, the optimal In-In separation is slightly larger
than the in-plane lattice constant of a 1x1 adlayer on the (000)
surface (~3.2 Å). In contrast to the case of Ga adlayer structures, it
appears that In atoms are too large to enable the insertion of additional atoms
into the In adlayer to form stable adatom-on-adlayer structures. One may
conclude that it is not likely that additional In adatoms can decorate a 1 ML
In adlayer termination of the GaN(000)
surface. This conclusion is supported by total energy calculations showing that
a 2x2 structure containing 1/4 ML of In adatoms on the In adlayer is very
high in energy [35].
Reconstructions
of the GaN(0001) surface have been reported by Smith et al. [36]. Those
Ga-polar films were grown by PAMBE, using homoepitaxy on MOVPE-grown Ga-polar
GaN, or using Si-polar SiC(0001) substrates. Compared to the (000)
surface, results for the (0001) surface are less well understood. In order of
increasing Ga coverage, Smith et al. find 2x2, 5x5, 6x4, and
"1x1" (pseudo-1x1) structures.
The origin of the 2x2 surface reconstruction, in particular, is quite controversial. Smith et al. observe this structure only under N-rich conditions (it is not seen during growth, but it does appear when the Ga-flux is interrupted). They thus suggest that it arises from a 2x2 arrangement of N adatoms. In contrast, a number of groups have reported an intense 2x2 diffraction pattern during growth, as seen by reflection high energy electron diffraction (RHEED) [15] [25] [26] [37]. This pattern has been attributed to a 2x2 arrangement of Ga adatoms [15] [37]. Following an exhaustive but unsuccessful search for this 2x2 structure seen during growth, utilizing different growth conditions and multiple N-sources, Smith et al. finally proposed that it might arise from some unintentional adsorbate in the growth systems, e.g. arsenic [38]. Subsequent installation of an arsenic source into their MBE system led to an immediate detection of the intense 2x2 pattern (seen during growth), thus confirming its origin as being due to arsenic, as further discussed below in Section 3.3. Indeed, in several cases, the growth systems which reveal intense 2x2 patterns during PAMBE growth are known to have been previously used for GaAs growth [39] [40]. It is important to note that the above comments regarding the identity of the commonly observed 2x2 pattern apply only to PAMBE growth; for RMBE, a 2x2 pattern with different characteristics than that seen during PAMBE has been reported [13].
The 2x2 reconstruction observed by Smith et al. is prepared by nitriding the surface at a temperature of about 600°C. STM images reveal a disordered surface with small domains of 2x2, consistent with the fact that the 1/2-order lines seen in RHEED are not very sharp [36]. From total energy calculations for the Ga face, two different 2x2 structures are found to be energetically favorable within certain ranges of the Ga chemical potential as described below: a N-adatom (H3) 2x2 and a Ga-adatom (T4) 2x2 [30]. The fact the 2x2 seen by Smith et al. is formed by nitridation led them to suggest that it arises from N adatoms.
The 5x5 reconstruction is obtained by annealing the Ga-face at
750°C, depositing 1/2 ML of Ga, then re-annealing the surface to about
700°C [36]. The surface obtained by annealing at 750°C alone is
found to be disordered, but the Ga deposition and re-annealing process
stabilizes the surface via the 5x5 reconstruction. Compared to
reconstructions found on the N-face, the Ga-face 5x5 is strongly
bias-dependent, suggestive of a semiconducting surface. Shown in Figure 5 is a
pair of STM images of the 5x5 reconstruction acquired at positive sample
bias (empty states) in (a), and negative sample bias (filled states) in (b),
from nearby surface locations. At positive sample bias, the unit cells of the
5x5 can be readily identified by the dark trenches traversing the image
in all three of the <11
0>
directions. One 5x5 unit cell is marked in the image. Typically, four
topographic maxima are observed within each unit cell. However, the height and
shape of these maxima vary from one unit cell to the next. This lack of
translational equivalence is even more evident at negative sample bias, where
the topographic maxima appear to be grouped together on the surface into pairs,
or in some cases, triplets. The more common pair features have a specific
rotational orientation, namely along one of the <110>
directions, with the particular orientation varying randomly over the surface.
Detailed analysis of the voltage-dependent images of the 5x5 leads to the model shown in Figure 6. The topographic maxima seen in the images are interpreted in terms of N and Ga adatoms, residing on T4 and H3 sites respectively, together with some residual dangling bonds in the unit cell. A complete theoretical description of this surface is lacking at present, although some results are available for the relative stability of Ga and N adatoms on the surface as discussed in Section 2.2.2 below.
The 6x4 is formed by depositing 1/2 ML of Ga onto the 5x5 and then
briefly heating the surface up to 700°C. Ga deposition alone will not
produce the 6x4, suggesting that the formation of the 6x4 must
involve extensive rearrangement of surface atoms. Surfaces showing clear
6x4 RHEED patterns obtained in this manner, however, are also found to
contain large domains of 5x5, as shown in Figure 7. Seen there are STM
image of both the 5x5 and 6x4 regions, at both positive sample bias
and negative sample bias. As with the 5x5, the row-like 6x4
structure shows a strong bias-dependence, again suggesting a semiconducting
surface. At positive sample bias, each row is clearly defined by a line of
bright features spaced 4xa (a = 3.19 Å) apart along the [110]
direction, except where a structural defect breaks the periodicity. At negative
sample bias, these maxima do not appear, but the rows are still clearly defined
by a line of dark features
As seen in Figure 7 the 6x4 appears topographically lower, on the average, than the 5x5. This is counter-intuitive since the 6x4 is formed by adding Ga to the 5x5. One possible explanation is that the height difference is electronic in nature. However, this seems insufficient to explain the difference since the 5x5 is higher than the 6x4 at both positive sample bias (by 0.3 Å) and negative sample bias (by 0.4 Å). A second possibility is based on the observation that 6x4 surfaces not only contain 5x5 but also "1x1" [36]. This latter structure as described below is known to contain much more Ga compared to the other reconstructions, as measured by Auger electron spectroscopy (AES). The fact that all three reconstructions are found together suggests that the 5x5 and 6x4 may not be very different from each other in terms of energy, and possibly also Ga coverage. The "1x1", on the other hand, appears to be energetically much more favorable, effectively acting as a Ga "sink". In any case, it is hard to imagine that the 6x4 could contain less Ga than the 5x5. The additional Ga in the 6x4 could form a structural arrangement allowing a denser packing of Ga compared to the 5x5. The observed height difference might then be explained by a combination of both structural and electronic effects.
As reported by Smith et al. [33] the most stable structure at high Ga coverage
is one which displays a diffraction pattern dominated by 1x1 spots, so
that this structure is known as pseudo-1x1 or "1x1". The structure
can be formed in several ways, one of which is by depositing about 1 ML of Ga
onto the 6x4, followed by a rapid anneal to 700°C. Another way to
form the "1x1" is to terminate the growth of GaN under slightly Ga-rich
growth conditions. As the sample cools, the entire surface can become
"1x1" although 5x5 and 6x4 may also be observed, depending on
the precise amount of Ga present on the surface. The diffraction patterns of
this surface show mainly 1x1 streaks (in RHEED) or spots (in low-energy
electron diffraction, LEED), but includes sidebands or satellite spots in these
patterns as described below. Hence this structure is referred to as
"1x1", using the quotation marks to indicate that the symmetry is not
truly 1x1. During growth, this Ga-rich surface shows only 1x
streaks, as illustrated in Figure 8(a). However, as the surface is cooled down to
<350°C, distinct sidebands appear on the high wavevector sides of the
first-order streaks along the [110]
azimuth, as shown in Figure 8(b). Depending on the Ga coverage, the spacing of
the sidebands from the first-order streaks at room temperature is either 0.16
± 0.01 (
1/6) or 0.08 ± 0.01 (1/12) of the 1x
spacing k1=0.361 Å-1, as illustrated
by the two LEED patterns shown in Figs. 8(c,d). These structures are referred
to as "1+ 1/6"
and "1+ 1/12"
respectively; the precise difference between these structures is not well
understood at present. The 1+ 1/6
structure, pictured in Figure 8(c), can exist down to room temperature for a
narrow range of Ga coverage (just above that needed to form the 6x4), but
for all higher coverages, the 1+ 1/6
converts to 1+ 1/12
as the temperature is reduced to about 200°C.
The temperature dependence of the 1x1 surface is illustrated in Figs. 8(e-h), focusing on the vicinity of the integral order (0,1) spot. Between room temperature and about 100°C, as seen in Figure 8(e), a modulated ring of intensity with radius 0.08 k1 is observed around the (0,1) spot with modulation at 60° intervals. This ring has greater intensity on the high wavevector side of the spot. As the temperature is increased to about 150°C, the ring modulation decreases slightly [Figure 8(f)]. As the surface temperature increases further to around 200°C, the ring modulation decreases further [Figure 8(g)]. It is also seen that the radius of the ring appears to have decreased slightly to about 0.07 k1. As the temperature is raised past 200°C, the pattern converts to 1+ 1/6 (although not observed in this particular LEED experiment, the conversion from 1+ 1/12 to 1+ 1/6 in this temperature range has been observed consistently in RHEED experiments). Above 350°C, one sees only the integral order LEED spot [Figure 8(h)]. This sequence of phase transitions is reversible. Thus we find that the ring modulation decreases with increasing temperature. At the same time, the ring radius decreases slightly from 0.08 k1 to 0.07 k1 with increasing temperature until about 200°C, at which point it increases by a discrete amount to 0.16 k1.
The "1x1" diffraction patterns described above are typical of a
incommensurate surface structure. The modulated ring structure and its
temperature dependence indicate that this incommensurate structure possesses
considerable dynamic, fluid-like character, even at room temperature. Thus, it
was inferred that the "1x1" surface at room temperature is best
characterized by a discommensuration-fluid phase [33], similar to that seen for
Au(111) and Pt(111) at elevated temperatures [41]. Since the melting point of
bulk Ga (29.8°C) is very near room temperature, such a structural phase
for this Ga-rich surface is most reasonable. STM image for this surface
generally do not display any atomic corrugation. Rather, the "1x1"
regions appear quite featureless. Sometimes corrugation is seen, and in those
cases it has precise 1x1 spacing (rather than some much longer
corrugation, as would be expected from the diffraction results) [33]. This
apparent discrepancy between the STM and diffraction results was resolved by
postulating a model in which the surface contains two monolayers of excess Ga
in an incommensurate arrangement, with this Ga existing in the mobile,
fluid-like state at room temperature. Thus, the STM images reflect the time
averaged position of the Ga atoms, which reflects the underlying 1x1
structure of the GaN bilayer below the excess Ga. In one exceptional case of
STM imaging on the (000)
surface, a small reconstructed domain was observed in STM which has structure
close to that expected for the "1x1". It was speculated that this
structure occurred at the top of an inversion domain and that the
incommensurate arrangement of the "1x1" was frozen-in there due to the
limited size of the domain [42].
STM images acquired at room temperature for a surface containing a mixture of "1x1", 5x5, and 6x4 domains reveal a height difference of "1x1" islands relative to surrounding 6x4 and 5x5 regions of about 2.1 Å. Electronic effects can of course influence this height, but typically by only a few tenths of an Å. As discussed above, the 5x5 and 6x4 regions are believed to contain adatoms with height (from theory [36]) of about 1.7 Å above the Ga atoms in the outermost GaN bilayer. Thus, the thickness of the "1x1" Ga layer is estimated to be about 3.8 Å, corresponding to about 1.8 ML. This estimate suggests that the "1x1" reconstruction contains around 2 ML of excess Ga. Similarly, AES measurements indicate that the "1x1" surface contains 2-3 additional ML of Ga above the outermost GaN bilayer [33]. Recent results of RHEED studies for Ga on GaN(0001) and AlN(0001) also yield a value for the stable coverage of Ga on those surfaces under Ga-rich conditions of about 2 ML [43].
The above diffraction results for the "1x1" structure have recently also been clearly observed using low energy electron microscopy (LEEM) [44] [45]. Transitions between the 1+ 1/6 and 1+ 1/12 structures were found to occur reversibly, as a function of temperature and Ga coverage. The state of the surface was monitored in real-time during growth, and it was found, in agreement with prior work, that the presence of the Ga bilayer associated with the "1x1" structure stabilizes the (0001) surface and gives rise to the flat morphology. Under Ga-poor conditions the bilayer disappeared and the morphology became rough and microfaceted (for more discussion of this phenomena see Section 4). So long as the microfaceting was not too severe, it could be eliminated by restoring the Ga double layer during growth.
Based on the data of Smith et al. a model was proposed in which the "1x1"
surface consists of a double layer of Ga atoms, with 7 unit cell of the Ga
atoms residing on 6 unit cells of the GaN [33]. The resulting spacing between
the Ga atoms in the double layer is then close to what is ideally obtained in
bulk Ga, and in energy minimization calculations for free-standing Ga bilayers.
This laterally contracted bilayer model is illustrated in Figure 9. Although a
complete theoretical description of such a model is currently not possible
(because a 6x6 unit cell would be required), a simplified version of the
model with 
3x3 symmetry has been shown to be energetically
favorable under Ga-rich conditions [46], as further discussed in the following
Section.
Let us now turn to theoretical results for structures on the (0001) surface. A large number of possible structures were considered theoretically by Smith et al. [30] and many could be ruled out on the grounds that they are thermodynamically unstable. A simple 1x1 Ga terminated N-Ga bilayer model (i.e. the "ideal" surface) can certainly be excluded. In this structure the Ga atoms at the surface are threefold coordinated - each Ga is bonded to three N atoms and there is one Ga dangling bond per atom. The total energy calculations shown in Figure 3(a) indicate that there is no region of the chemical potential space for which this structure is stable. Adding one monolayer of Ga to this 1x1 Ga-terminated bilayer leads to the 1x1 Ga adlayer structures. Several possible adlayer registries (H3, T4, atop) were considered but in no case was a thermodynamically stable structure found. It is interesting to note that the surface energies of these Ga adlayer structures are rather insensitive to the registry. This has implications for the existence of stable incommensurate adlayer structures discussed below. After an extensive search it was ultimately surmised that there exists no stable structure having a true 1x1 symmetry for the clean GaN(0001) surface [30]. It was also determined that the 2x2 Ga vacancy model is not stable on the (0001) surface. This structure is slightly higher in energy than the N-H3 adatom model. The instability of the Ga vacancy model for GaN(0001) is interesting in view of the fact that a 2x2 Ga vacancy structure is known to exist on the GaAs(111) surface [47] [48].
On the basis of the results shown in Figure 3(a) only the 2x2 N adatom and the 2x2 Ga adatom survive as potential candidates as thermodynamically stable structures on the GaN(0001) surface. The question then is which, if either, of these two models corresponds to the 2x2 structure that is observed. Given that the 2x2 structure seen in experiment is the least Ga-rich of all the observed reconstructions, and that it is often observed following an interruption in the Ga flux, it seems more likely that the observed 2x2 structure arises from N rather than Ga adatoms.
Of the two possible adsorption sites for the N adatom, the H3 site is preferred over the T4 site in the calculations by 0.7 eV/(2x2) cell [36]. A qualitatively similar result has been predicted for N adatom structures on the AlN(0001) surface, where the preference for the H3 site is 3.3 eV/(2x2) cell [49]. As yet there exist no experimental determinations of the site preference of N adatoms on either GaN or AlN surfaces. In the case of the 2x2 Ga adatom model a slight preference for the T4 site is predicted: the energy difference is about 0.12 eV/(2x2) cell [36]. The different site preference exhibited by the N and Ga adatoms on the (0001) surface is related to their very different ionicities.
Concerning the Ga-adatom 2x2, it appears that it has a higher energy than the 5x5 and "1x1" structures (described below), so that the Ga-adatom 2x2 is not actually energetically allowed (even though it is employed in many theoretical computations since it is a relatively simple structure).
Let us now consider the pseudo-1x1 structure that is observed under very
Ga-rich conditions. Although the STM corrugation pattern exhibits 1x1
symmetry the electron diffraction patterns obtained at temperatures less than
350°C reveal, in addition to the 1x1 spots, additional diffraction
intensity in satellite spots [33]. These diffraction patterns indicate that the
lattice vectors of the unit cell are in fact larger than those corresponding to
a 1x1 cell, and furthermore it is found from Auger spectroscopy that the
structure contains 2-3 ML of Ga in excess of that expected for a bulk
terminated GaN surface. To explain these observations a laterally contracted
Ga bilayer model has been proposed [46], shown in Figure 10. In this model
the atoms in layer 1 are located in atop sites and are separated by a = 3.19
Å. However, the atoms in the top layer (layer 0) are contracted. This
lateral contraction of the top layer is proposed because calculations have
shown that a lateral contraction of such an adlayer - so that the Ga-Ga
separation is reduced from 3.19 to 2.75 Å - is energetically
favorable. This reduction in the spacing results in an increased density of
atoms in the adlayer and therefore provides a natural explanation of the Auger
data, which is suggestive of an increased Ga content (greater than 2 ML) on the
surface. Total energy calculations for such an adlayer were performed using a
3 x3 unit cell. Different registries of layer 0 were
considered, as shown in Figure 10, but the energies were found to be independent,
within 0.01 eV/atom, of the registry. As seen in Figure 11 the laterally
contracted bilayer structure becomes energetically favorable with respect to
the Ga adatom model in Ga-rich conditions. This increase in stability has been
traced to the energy benefit of reducing the in-plane Ga-Ga spacing [33].
InGaN
is the dominant alloy material used for III-nitride light emitters. The larger
size of indium compared to gallium leads to a variety of phenomena, including
surface segregation, alloy phase separation, inhomogeneous incorporation, etc.
Surface studies of InGaN have been performed by Chen et al. for both (000)
and (0001) surfaces [35] [50] [51] [52]. For the (000)
surface it was found that In substitutes for Ga in the surface layer. STM
results are shown in Figure 12, for a sample prepared by growth at 670°C
with In/(In+Ga) flux ratio of 20%. An x-ray diffraction (XRD) scan of this
sample showed no InGaN peak, meaning that there is negligible indium
incorporation in the bulk. However, AES indicated a significant amount of
indium on the surface, with In/Ga Auger emission ratio of about 0.5. In the
middle of the STM image, there is a step, and the image shows two separate
terraces. Each terrace displays two types of regions, one bright and the other
dark. In this type of STM constant-current image, roughly speaking, the bright
areas are higher in morphology and dark areas are lower. As can be seen from
the line cut, the height difference between bright and dark area is 0.30
± 0.05 Å.
Theoretical computations permit the identification of the bright and dark areas
in the STM image. Those results are pictured in Figure 13. The total energy
calculation is performed for various GaN(000)1x1:GayIn1-y
adlayer structures. The calculations are performed in a 2x2 unit cell
with various numbers of In and Ga atoms in the top site. The equilibrium
adlayer In-N bond length is found to be about 2.23 Å while the
equilibrium Ga-N bond in the adlayer is 1.99 Å. These values are
essentially independent of y. From explicit examination of charge
density contours for states located near the Fermi-level, it is found that the
different height of the adatoms above the surface (~0.2 Å) is
manifested in a corrugation in the charge density of a similar magnitude at a
height of several Å above the adatoms. The bright regions in the STM
image are thus identified as arising from indium atoms in the surface adlayer,
and the dark regions as arising from gallium atoms in the adlayer.
STM results for the InGaN(0001) surface are shown in Figure 14. The films shown there were known from AES measurements to have surface indium coverage of about 1 ML, and bulk indium content of several % or less. Figure 14(a), shows several regions of apparently different structure. In the lower right hand corner is a region of uniform, 1x1 corrugation. Elsewhere on the surface are seen areas of brighter (higher) corrugation, with 1x and 2x spacing, and in these regions of brighter corrugation the presence of small black vacancy islands is observed. Total energy calculations performed for a large number of InGaN(0001) surfaces indicate that a 1x1 surface with 1 ML of In in atop sites (layer 1 in Figure 14) is energetically favorable under In and Ga-rich conditions [53]. This structure was associated with the 1x1 region seen in the lower right hand corner of Figure 14. For more Ga-deficient conditions the calculations show that it becomes energetically favorable to incorporate some In atoms into layer 2 as well. The height of the observed bright maxima, typically 0.2 Å above the nominal height of the 1x1 region, is consistent with the calculated 0.3 Å increase in height of a layer 1 atom produced by substitution of In for Ga in layer 2. The bright corrugation maxima observed elsewhere in the image were thus attributed to the presence of layer 2 In-atoms.
The surfaces pictured in Figs. 14(b) and (c) contain slightly higher indium than that of Figure 14(a), and in this case the surface phase containing vacancy islands covers the entire surface. The vacancy islands appear dark (lower surface height) for both positive and negative sample bias voltage, indicating that atoms are indeed missing from those areas. The vacancy islands do not grow with time, but rather, they have an equilibrium diameter of 10-20 Å. The depth of the smallest vacancy islands seen in Figure 14 is typically 0.8 Å, but this value is probably limited by the shape of the STM probe tip. For the larger vacancy islands, a depth of about 2.5 Å was found, indicating that at least one layer of atoms is missing from the surface. As seen in Figure 14(c), bright rings of atoms are sometimes (depending on imaging condition) see surrounding the vacancy islands. These bright features were attributed to In atoms at the edge of the islands, as revealed in the theoretical analysis below.
In order to identify the underlying mechanism giving rise to the observed structural instabilities, first-principles total energy calculations for a variety of InGaN(0001) surface structures were performed [51]. Because InGaN films must be grown under very N-rich (Ga-deficient) conditions to obtain In concentrations greater than a few percent, attention was focussed on surface structures that could be stable under Ga-deficient conditions [53]. Specifically, surfaces were considered in which layer 1 is completely occupied by In atoms and layer 2 is occupied by both In and Ga. Structures of this type are indicated schematically in Figs. 14 and 15. Because the In-N bond is about 0.23 Å longer than the Ga-N bond, partial occupation of the second layer by In leads to a substantial surface strain. It was found that for sufficiently large In concentrations in layer 2 it is energetically favorable to create N vacancies in layer 3. For example, for the structure shown in Figure 15(a) containing 7/4 ML of In (1 ML in layer 1 and 3/4 ML in layer 2), it was found that the creation of a N-vacancy in layer 3 of this structure, as shown in Figure 14(b), is exothermic. The energy of the reaction depends on the N chemical potential, but is at least 0.85 eV per vacancy. The exothermicity of vacancy formation in a system having a full monolayer of In atoms in layer 2 is even greater, being at least 1.07 eV per vacancy. It is important to note that in both of these exothermic reactions each of the three layer 2 sites adjacent to the vacancy is occupied by an In atom. The relative weakness of the In-N bonds compared to Ga-N is an important component in this structural instability.
Given the above results it is quite plausible that the vacancy islands seen in the STM images form in order to relieve surface strain and permit the segregation of In atoms to sites where they exhibit reduced N coordination, i.e. around the edges of the vacancy islands. This idea was tested on a structure consisting of an array of trenches. As shown in Figure 15(c), the trenches in this model system are created by removal of rows of layer 3 N-atoms and layer 1 In-atoms. Total energy calculations employing a 6x1 unit cell to model such an array of trenches indicate that trench formation is exothermic and leads to strain relief [51]. It was concluded that this type of structural instability, in which surface strain is relieved and In segregates to the edges of the vacancy islands, is the fundamental mechanism giving rise to the vacancy islands.
During MBE growth of GaN, the surface undergoes a transition from smooth to
rough morphology when the growth condition is switched from Ga-rich to N-rich,
as discussed below in Section 4. It was reported by Widmann et al. for the
(0001) surface that indium atoms serve as a surfactant, keeping the growth in
the smooth regime when the gallium flux is slightly reduced beneath the
transition flux [54]. This surfactant effect was studied by Chen et al. in a
study where they compared the influence of In on the kinetics for both the
(0001) and (000)
faces [52]. A dramatic difference in the smooth/rough behavior between the two
faces was found, as shown in Figure 16. For these experiments, the nitrogen flux
was kept constant. Then, a certain indium flux was applied, and gallium flux
was adjusted to find the smooth/rough transition point. For comparison, dashed
lines in Figure 16 show where the total metal flux (indium + gallium) is
constant. Figure 16(a) shows that for the (000)
face, even when a large indium flux is applied, the gallium flux can only be
reduced slightly before the growth becomes rough. In contrast, for the (0001)
face, it is found that when the indium flux is applied the gallium flux can be
greatly reduced (by an amount considerably greater than that of the added
indium flux) before the growth becomes rough. Thus, indium serves as a
surfactant for the (0001) surface but not for the (000)
surface. The interpretation of these observations is discussed below in Section
4.
Magnesium is an important p-type dopant in GaN. To understand Mg incorporation kinetics during growth, a determination of the Mg-induced surface reconstructions is required. In MBE growth of p-doped GaN, the high vapor pressure of Mg at GaN growth temperatures is an issue and dopant incorporation may be rather inefficient [55] [56]. Studies have shown that the Mg concentration decreases from the surface to the interior of the film [57], suggesting dopant incorporation from a surface Mg layer. Some workers have noted Mg-induced changes in the growth rate of GaN on different crystallographic planes [58], pointing to a surfactant effect of Mg on GaN. The presence of Mg atoms during the growth of GaN has also been associated with the appearance of stacking faults [59].
The surface science of Mg adlayers on the GaN(0001) surface has been studied by Ramachandran et al. using RHEED and STM [60] [61]. During PAMBE growth, films are briefly exposed to a Mg flux. A surfactant effect of Mg is seen on the Ga-polar films in the Ga-poor regime, where reducing the Ga-flux in the absence of Mg causes the RHEED pattern to change from streaky to spotty indicative of a growth mode transition from 2-dimensional to 3-dimensional [38]. Exposing this surface to about 0.2 ML of Mg under Ga-poor conditions leads to a reversal of the RHEED pattern to streaky. Also, when the growth is made severely N-rich, by reducing the Ga flux to about one half of that at the transition point, exposure to Mg often produces a streaky 2x2 pattern, as shown in Figure 17. The origin of this surfactant behavior of Mg has not been considered in detail, although a model has been suggested in which 1/4 or 3/4 ML of Mg substitutes for Ga in a GaN bilayer [56] [61], yielding a surface which satisfies electron counting and thus may produce reduced barriers for surface diffusion.
When the film is exposed to 1.2±0.4 ML or more of Mg during growth, it is found that the polarity switches to N-polar. After terminating the growth and cooling the sample to below about 300°C, a 1x1 RHEED pattern is obtained. Exposing this surface to Ga produces 3x3, 6x6, and c(6x12) surfaces with increasing Ga coverage, as shown in Figure 17. This sequence of RHEED patterns definitively indicates the N-polarity of the film. Transmission electron microscopy (TEM) results reveal an inversion domain boundary extending along the c-plane, as shown in Figure 18 [60]. The inverted film was found to contain numerous defects, perhaps arising from small inversion domains. More recent results from Romano et al. reveal an inverted film with fewer defects, and in that case the inversion boundary occurs on facetted planes [62].
To understand the origin of the polarity inversion, first principles
pseudopotential calculations were performed of the total energy of various
possible inverted structures. An IDB may form if, for a Mg concentration above
a certain threshold, it is energetically favorable to form a Mg-terminated
(000)
surface atop an IDB instead of a Mg-terminated (0001) surface. One such
structure which was found is shown in Figure 19(a) [60]. In this case the IDB
consists of a plane of Ga-Ga bonds and the surface is terminated by a monolayer
of Mg in H3 sites. The N atoms in the outermost layer are six-fold coordinated
with a local structure that is more like that of bulk
Mg3N2 than bulk GaN. It is found that this inverted
structure is more stable (by 0.05 eV/1x1 cell) than the non-inverted,
stoichiometrically identical, structure shown in Figure 19(b). It was conjectured
that the inverted structure forms the template for subsequent growth of GaN,
with the IDB frozen in place as a thicker N-face film grows on top. It may also
be possible that a few layers of bulk Mg3N2 form above
the IDB. The role of Mg in the formation of inversion domain boundaries on the
facetted planes is discussed in Ref. [62].
As discussed above, the role of arsenic on the surface of GaN is controversial. A number of workers have reported an intense 2x2 diffraction observed during and after PAMBE growth on Ga-polar surfaces, and they interpret that in terms of a 2x2 arrangement of Ga adatoms. However, Ramachandran et al. [19] have presented convincing evidence that this structure arises, in fact, from arsenic atoms which are unintentionally present in the MBE growth systems. The presence of the arsenic may actually be beneficial for growth (it has a surfactant effect, described below), although the possibility remains of point defects arising from arsenic incorporation.
To understand the effect of arsenic, it is necessary to first describe the RHEED patterns observed on bare GaN(0001). During PAMBE growth under Ga-rich conditions, the RHEED pattern is generally 1x1 (occasionally 5x5 can be seen) and streaky, indicating smooth growth. If one changes the Ga/N flux ratio so that N-rich conditions are obtained, the pattern quickly changes to spotty, indicating rough growth, as shown in Figure 20(a)-(c). This smooth/rough transition is a hallmark of PAMBE growth, and its origin is discussed below in Section 4.
The effect of arsenic on the RHEED patterns during growth is dramatic, as shown in Figure 20(d)-(f) [19]. Arsenic was introduced by resistive heating of a GaAs wafer located in the growth chamber about 5 cm from the substrate holder. For arsenic beam equivalent pressure (BEP) below 1x10-9 Torr, no change is detected in the RHEED sequence mentioned above. However, for higher arsenic BEP, as the Ga flux is reduced, a bright streaky 2x2 RHEED pattern is observed as shown in Figure 20(e). This transition to a 2x2 pattern is reversible, and it provides an unambiguous signature of the surface arsenic. Upon cooling, the 2x2 surface persists down to room temperature. Subsequent mild annealing of such a surface can cause the 2x2 pattern to switch to 4x4 [19]. This same 2x2/4x4 behavior was reported by previous workers (who did not attribute the patterns to arsenic [37] [39]), and provides evidence that the 2x2 and 4x4 patterns they observe are indeed due to the presence of arsenic on the surface.
The streaky 2x2 pattern, occurring for a Ga/N flux ratio near unit, demonstrates a surfactant nature of the arsenic adatoms. The window for this streaky 2x2 pattern in terms of fluxes is relatively broad and easily achieved during PAMBE growth. In contrast, if one wants to grow precisely at the Ga/N=1 point in the absence of arsenic (where the 1x1 RHEED pattern shows some brightening), the growth window is vanishingly small. Concerning the structure of the arsenic-induced 2x2, it seems likely that it arises simply from a 2x2 arrangement of arsenic adatoms which is a very low energy surface as described below. This surface satisfies electron counting (i.e. anion dangling bonds are doubly occupied and cation dangling bonds are empty [33]), and thus, qualitatively, it is expected to have relatively low diffusion barriers which may account for its surfactant behavior.
Possible models for the As-induced 2x2 structure include the adatom model as well as the As-trimer structure [19]. In both structures As atoms are bonded to Ga atoms in the layers below. A comparison of the stability of the possible structures as a function of the As chemical potential can be made and indicates that both adatom and trimer models can be stable with respect to the clean surfaces, depending on the chemical potentials of As and Ga. The As-adatom structure is preferred over the As-trimer structure for low values of the As chemical potential. Specifically, when µAs < µAs(bulk) - 0.49 eV the As-adatom model is favored. For higher values of the chemical potential the As-trimer structure would be preferred. Because the surface energies of the Ga-rich surfaces are lower than those for N-rich conditions, the formation of As-terminated surfaces is more likely to occur under N-rich conditions. An analysis of the relative stability of As-terminated surfaces compared to clean surfaces [19] indicates that As-terminated surfaces are likely to be more stable than clean GaN surfaces under the As deposition conditions employed in the experiments discussed above.
Silicon is commonly used as a n-type dopant in GaN. As in the case of Mg discussed above, aspects of its surface science can determine limits on the incorporation efficiency and structural quality of the resulting films. In addition, it has been shown that silicon has a strong effect on the surface morphology of GaN films: small amounts of silicon on GaN modify the growth mode from step-flow to 3-dimensional giving rise to the formation of small islands in MOVPE and gas source molecular beam epitaxy (GSMBE) [63] [64].
Lee et al. studied the effect of silicon adlayers on the surface structures of GaN(0001) surfaces [65]. Depositing Si on a Ga-rich (0001) surface, displaying a "1x1" reconstruction in RHEED, resulted in no change in the surface structure. The Si appears not to have modified the surface structure, as further discussed below. If, alternatively, Si is deposited on a (0001) surface displaying a 5x5 reconstruction, a Si-induced 2x2 reconstruction results. Figure 21(a) shows a STM image of neighboring areas of the 2x2 and 5x5 reconstructions. Silicon exposure was performed at a temperature near 300°C. With sufficient silicon exposure, a 2x2 pattern appears gradually. The temperature window for formation of the 2x2 reconstruction is quite narrow. With increasing substrate temperature the 2x2 disappears after it has formed, implying that it is metastable, and for lower temperatures no ordered surface structure is found. AES indicates a saturated 2x2 intensity for a Si coverage of roughly 0.5 ML.
Surfaces containing the Si-induced 2x2 structure also invariably
display small regions of "1x1" structure. As the amount of 2x2
structure increases (due to additional Si deposition), the total area
"1x1" regions also increases. When additional Si, above 0.5 ML, is
deposited on the surface, the 1/2-order diffraction lines seen in RHEED
become dim. The resulting surface appears in STM to be disordered, with small
domains of well-ordered 2x2 reconstructions surrounded by disordered
regions, and containing as well numerous islands with "1x1"
reconstruction.
Upon continuing the silicon exposure up to 1 ML at 300°C, the
2x2 reconstruction becomes weak and a new 4x4 pattern appears. This
RHEED pattern is diffuse, indicating some surface disorder. In addition to
4x4, RHEED also shows a weak "1x1" pattern at room temperature.
After annealing at around 350°C for 2 minutes, RHEED shows a clear
4x4 reconstruction. A large scale STM image for this sample is shown in
Figure 22(a), and a detailed view of the 4x4 is shown in Figure 22(b). As
seen there, the featureless "1x1" region is dominant and the 4x4
region is seen only near step edges. With increasing anneal temperature, the
4x4 RHEED pattern disappears completely, and at room temperature only the
"1x1" pattern is seen. This indicates that the whole surface is covered
by 2 ML Ga and the silicon atoms have moved to subsurface sites. Thus,
based on these experimental observations it was concluded that the silicon
adatoms tend to reside in subsurface sites on the Ga-polar surface.
In
order to identify the atomic structure of the Si induced reconstructions
density-functional theory calculations for a large number of possible
geometries had been employed [66]. Specifically, starting from the known
structures for bare GaN(0001) Si atoms were systematically added on top of the
surface or replaced Ga/N atoms in the first, second and third layer. Si
coverages 0<
Si<2 ML have been considered. To determine
the stability of the different configurations the surface energy had been
calculated as function of nitrogen (µN) and silicon
(µSi) chemical potential. Using these results a surface phase
diagram had been derived which shows what surface is stable for a given set of
chemical potentials (see Figure 23). The corresponding surface structures are
shown in Figure 24. At low Si concentrations the incorporation of Si atoms into
the surface is energetically unfavorable and only bare GaN surfaces are stable.
Indeed going from Ga to N rich conditions the phase diagram reproduces the
above described bare GaN surface structures (Ga-bilayer, Ga-adatom, N-adatom).
When going towards more Si-rich conditions (close to the formation of
Si-precipitates, i.e., µSiµSi(bulk)) a number
of Si-induced reconstructions are found. At Ga-rich conditions the Ga-bilayer
structure with a Si in the third layer (Figure 24(c)) is energetically preferred.
Going towards more N-rich conditions a structure with 1ML of Si is
energetically most favorable (Figure 24(a)). At extreme N and Si rich conditions
a structure with two Si and N layers is energetically favorable (Figure 24(g)).
An important result of the phase diagram is that all Si induced surface
reconstructions are thermodynamically unstable against the formation of
Si3N4.
Based on these calculations, the structures and structural changes observed in STM have been explained as follows. If Si adsorbs on the surface it kicks out surface Ga atoms and induces a 2x2 reconstruction (Figure 24(f); experiment: Figure 21). It is important to note that this Si induced 2x2 structure is metastable and therefore does not appear in the phase diagram. The metastability of the 2x2 structure is also found experimentally: The structure disappears if the sample is annealed above 350°C. To create the 2x2 structure two Ga atoms per 2x2 cell have to be kicked out. These excess Ga atoms cluster in islands and increase locally the Ga-chemical potential. Based on the phase diagram one finds that under these conditions a Ga-bilayer with a pseudo-1x1 structure stabilized by Si in the third layer is most stable. With increasing Si coverage more and more excess Ga atoms are created and the area covered by the Ga-bilayer will increase until eventually it covers the entire surface (as in Figure 22).
From the phase diagram trends concerning the incorporation of Si on GaN surfaces have also been deduced. For more N-rich conditions surface reconstructions with high Si-concentrations in the surface layer are found. Therefore, under those conditions, the Si concentration at the surface may be significantly higher than in GaN bulk and surface segregation might be an important issue. For more Ga-rich conditions, however, a fundamentally different behavior can be deduced from the phase diagram: Under these conditions Si prefers subsurface configurations rather than surface sites, i.e., surface segregation does not occur and Si can be efficiently incorporated in GaN bulk.
The above discussion gives also insight why in some experiments (employing MOVPE or GSMBE [63] [64]) Si acts as antisurfactant and roughens the surface while in others (PAMBE) it does not have this effect. The main difference between the two cases is that in MOVPE and GSMBE growth hydrogen is highly abundant while in PAMBE it is virtually absent. As will be shown in the next Section, hydrogen stabilizes N on the surface making the surface more N-rich. The structures found under these conditions (Figs. 24(a) and (g)) have in the top surface layers exclusively Si and N atoms and the activation barrier to form Si3N4 is thus expected to be rather low. In fact, calculations for an isolated Si-N double layer indicate that the surface layer of these structures is rather unstable and under large tensile strain: Going from an in-plane lattice constant of 3.19 Å for GaN to the smaller value of 2.86 Å leads to a reduction in energy of 0.92 eV per N atom. The formation of Si3N4 has important consequences. On one side, it explains the antisurfactant behavior of Si on GaN(0001). Si3N4 islands/precipitates are well known to chemically passivate the GaN surface and to block growth [67]. Since growth occurs then only on areas not covered by Si3N4 three-dimensional growth results.
Under Ga-rich conditions (which are characteristic for PAMBE growth), the Si induced surfaces are essentially free of Si in the top surface layer. Since for these structures Si is already incorporated in a bulk-like GaN environment the formation of Si3N4 is expected to be largely suppressed by kinetic barriers. Further, since the topology of these surfaces is very similar to the bare surfaces Si has no effect on the adatom kinetics or the growth mode. Ga-rich conditions are therefore expected to be the optimum regime to incorporate Si in GaN.
Hydrogen is present in high concentrations in commonly used growth techniques for nitride semiconductors, including MOVPE, hydride vapor-phase epitaxy (HVPE) and GSMBE (using an NH3 source). Hydrogen has been observed to have important effects on the growth of GaN. For example, Yu et al. [68] observed that the introduction of H during MBE growth of GaN using an RF-plasma source can increase the growth rate by as much as a factor of two. Hydrogen has been also found to improve the quality of GaN in PAMBE [69].
Experimental investigations of how hydrogen modifies the GaN surfaces and
surface kinetics are rare. Sung et al. [20] investigated the composition and
structure of GaN(000)
surfaces grown by MOVPE using time-of-flight scattering and recoiling
spectrometry, LEED, and thermal decomposition mass spectrometry. Based on these
studies they concluded that hydrogen is on the surface, that it removes surface
states, and facilitates autocompensation (i.e. partially occupied dangling
bonds are passivated by hydrogen). Hydrogen desorption was studied by several
groups [70] [71]. Bellitto et al. [71] demonstrated by high resolution
electron energy loss spectroscopy, electron energy loss spectroscopy, and LEED
that hydrogen desorption from Ga sites occurs between 250 and 450°C.
Vibrational modes of hydrogen on GaN have been observed by several groups.
Bellitto et al. [71] and Grabowski et al. [72] observed Ga-H modes at 1880
cm-1 and 1900 cm-1, respectively. N-H modes where found
at 3255 cm-1 [70].
All of the above described studies were performed far away from realistic growth conditions. Using thermal desorption mass spectrometry Held et al. [73] determined surface reactivity and growth kinetics during RMBE growth. A model for the observations was developed involving multiple adsorption states for Ga on the surface. Based on the structural studies of Smith et al. [30] discussed above the origin of these adsorption states can be identified. Additional models for surface kinetics during RMBE growth have also been reported [12] [74] [75]. Those models assume, in general, the existence of surface layers of particular types in order to match the observed kinetic data, thereby gaining valuable insight concerning the composition of the surface layers. Nevertheless, it should be noted that the detailed structures and composition of such surface layers for RMBE are not yet well understood on the basis of independent surface structural studies.
Using grazing incidence x-ray scattering Munkholm et al. [14] performed in situ
studies of surface reconstructions on GaN(0001) surfaces in an MOVPE
environment. In that study it was found that the surface equilibrium phase
diagram as a function of temperature and ammonia partial pressure shows a
transition between two phases: at high temperatures, a 1x1 reconstruction
was observed, while at lower temperatures and sufficiently low NH3
pressures, a different reconstruction with
23x23-R30° periodicity was seen. From the
temperature dependence of p(NH3) at the transition, an
activation energy of 3.0±0.2eV was extracted.
Early theoretical studies of H on GaN(0001) and/or (000)
surfaces gave important insight but were restricted on a few selected
structures and did not include temperature and pressure dependence [76] [77] [78].
A main conclusion from these studies was that H strongly binds to GaN surfaces.
Further studies by Northrup et al. [79] for GaN(100)
and by Van de Walle et al. [80] however showed that at typical MOVPE or HVPE
conditions (T=1050°C, p~1atm) hydrogen is only weakly
bound to the surface and affects the surface energy only slightly.
Van de Walle et al. [80] investigated over 30 different surface reconstructions
of hydrogenated GaN(0001) including structures with 1x1, 2x2 and
3
x3
periodicity. An important conclusion of this study was that only structures
obeying the electron counting rule are energetically favorable, i.e. hydrogen
efficiently removes surface states and compensates partially occupied surface
states. All hydrogen terminated surfaces are therefore semiconducting, in
contrast to bare GaN(0001) where metallic structures (such as the Ga bilayer
[33]) are found. Based on the calculated surface energies a surface phase
diagram (Figure 25) has been constructed that shows which surface is
energetically most stable for a given set of Ga and H chemical potentials. The
corresponding reconstructions are shown in Figure 26. For H poor conditions (low
µH) the phase diagram reproduces the reconstructions as
calculated [30] [46] for bare GaN(0001): Going from N-rich to Ga-rich conditions
a N adatom, a Ga adatom and a Ga-bilayer structure are most stable. In the
presence of hydrogen the structure most favorable at zero temperature
(µH = 0 eV) is the NH3+3NH2 reconstruction.
In this structure one NH3 and three NH2 molecules are
attached on the Ga-terminated surface in on-top positions (i.e. with the N
atoms of the molecules above the Ga surface atoms). It can thus be concluded
that at low temperatures NH3/NH2 molecules are
thermodynamically stable - dissociation of these molecules is forbidden.
Going towards less hydrogen rich conditions not all the N atoms can be kept at
the surface and Ga-H bonds are formed. Examples are the NH3+3Ga-H
structure (where compared to the NH3+3NH2 surface the 3
NH2 molecules have been replaced by H atoms), the 3Ga-H structure
(where all NH3/NH2 have been removed), or the
Nad-H+Ga-H structure (where only a single NH group remains). An
important conclusion that can be drawn from these results is that dissociation
of the NH3 molecule is only possible at sufficiently low hydrogen
chemical potential and that the tendency to dissociate is strongly enhanced
when going towards Ga-rich conditions.
Van de Walle et al. [80] also give an explicit dependence of the hydrogen chemical potential on temperature and pressure which allows to relate experimental growth conditions to surface structures in the phase diagram. For realistic growth conditions (between 700 and 1100°C) and not too N-rich conditions surfaces with only NH3/NH2 molecules are unstable, i.e., a dissociation of ammonia molecules is thermodynamically favorable. The explicit knowledge of the hydrogen chemical potential made it also possible to include in the phase diagram the above mentioned and thus far only experimentally observed transition between two surface reconstructions (see the dotted line in Figure 25) [14]. As can be seen the experimental data are (within the estimated error bar of 0.1 eV) consistent with a transition between the NH3+3Ga-H and the 3Ga-H structure, i.e., with adding/removing a NH3 molecule.
A
major goal of the surface science studies presented above is to serve as a
basis for developing an understanding of surface kinetics. With the detailed
knowledge of surface structures gained over the past number of years, realistic
models of kinetic processes are now becoming possible. Several such studies of
kinetics during RMBE were mentioned in the previous Section on hydrogen
adsorbates. For the case of PAMBE of GaN, as discussed above in Section 3.1, a
hallmark of that growth process is a smooth to rough transition which occurs
with decreasing Ga flux [38] [81] [82] [83] [84]. This behavior is illustrated in Figure 27. Similar behavior occurs for both (000)
and (0001) surfaces. The transition from rough to smooth morphology occurs when
the Ga flux exceeds some critical flux, which itself scales with the incident N
flux. (The absolute Ga to N flux ratio is generally not quoted due to
difficulties in measuring the active N flux, but often the flux ratio is simply
defined to be unity at the transition point [38]). Given this smooth/rough
growth behavior, PAMBE growth is nearly always performed under Ga-rich
conditions. For very Ga-rich conditions Ga droplets are observed to form on the
surface, whereas for less Ga-rich conditions pits form on the surface in the
vicinity of threading dislocations [82] [83] [84]. Achieving an operating point
between these regimes is generally believed to provide an optimal growth
condition.
The origin of this smooth to rough behavior of the GaN surface has been
discussed by Zywietz et al. [85]. They computed surface diffusion barriers for
Ga- and N-adatoms on Ga-terminated (0001) and (000)
surfaces, finding much larger barriers for the N-adatoms on both surfaces. It
was argued that this limited diffusivity of the N-adatoms will lead, under
growth conditions, to a significant surface coverage of N (although in general
one does not expect a significant coverage of N atoms on the surface since the
stable reconstructions are almost all terminated by Ga atoms, the N adatoms may
kinetically accumulate during growth under N-rich conditions). It was
furthermore found that on N-terminated surfaces, the diffusion barrier for Ga
adatoms increases to about 1.8 or 1.0 eV for (0001) or (000)
surface respectively. These barriers are believed to be large enough to produce
a rough growth morphology.
An alternative model for the smooth to rough behavior has been suggested by
Chen et al. [52] based on kinetic effects in the presence of indium. As
described above in Section 3.1, the addition of indium to the surface produces
much different behavior of the smooth to rough transition for (000)
and (0001) surfaces. In the former case the transition point (i.e. flux ratio
at which the transition occurs) is nearly unchanged as additional indium is
added, whereas in the latter case the addition of only a small amount of indium
leads immediately to smooth growth even under N-rich conditions. This behavior
has been correlated with the amount of metal (In or Ga) on the surface. Under
N-rich conditions, the N-polar surface is terminated by only 1 ML of metal,
with this metal layer being bonded to underlying N-atoms. N-adatoms are
expected to diffuse on top of this metal layer, with relatively large diffusion
barriers. In contrast, on the Ga-polar surface there are two layers of metal
even under N-rich conditions. N-adatoms can then diffuse in between
these metal layers. The top metal layer is bonded with metallic bonds to
underlying metal atoms and is thus relatively easy to move. The double layer of
metal can thus rearrange to accommodate the N atoms, thereby producing
substantially reduced diffusion barriers for the N.
This model of enhanced N diffusivity in the presence of multiple metal layers
also is applicable to the case of bare GaN growth, under Ga-rich conditions.
Indeed, Ga has been argued to provide a surfactant effect for the growth of GaN
[43]. For both the (000)
and (0001) surface, there are excess metal atoms on the surface, and these
atoms may act to provide greater coordination to diffusing N adatoms, thereby
enhancing their diffusivity. It should be noted that the two models described
above - reduced Ga diffusivity in the presence of an accumulation of N
(N-rich conditions) or enhanced N diffusivity in the presence of excess Ga
(Ga-rich conditions) - both act in the same direction to produce the
observed smooth/rough behavior of the surface morphology. Indeed, since excess
Ga atoms present under Ga-rich conditions will necessarily act to suppress any
accumulation of N-atoms, it is not completely clear whether both models are
required to produce the observed behavior. Further study is required to allow
discrimination of the various kinetic mechanisms.
Growth at reduced temperature is a commonly used technique in the study of growth kinetics. This method has been used by Zheng et al. to elucidate some kinetic aspects of GaN growth [86]. Using PAMBE, they deposit GaN on GaN(0001) surfaces at temperatures of about 400°C. Small, isolated islands are formed on the surface (at higher growth temperature, the growth proceeds by step flow so that islands are not formed). It is found that two types of islands form: "normal" islands which display a regular bilayer (2.6 Å) step height, and "ghost" islands which in STM image display a distinct boundary around the island but have a island height much less than 1 bilayer. AFM studies revealed that the ghost islands do in fact have height of nearly 1 bilayer, so that their different appearance in STM images could be ascribed to electronic effects (i.e. implying different structure for those islands) [86]. It was noted that for ideal growth, N atoms should substitute for the Ga atoms in the second layer of the Ga double layer terminating the surface [86]. To achieve the different structure of the ghost islands, it was thus proposed that the N-atoms substituted instead for Ga atoms in the first layer of the Ga double layer. The resulting structure would then have this N-layer bonded on top of two layers of Ga atoms (i.e. the lower layer of the double layer plus the Ga-layer of the uppermost GaN bilayer). These two Ga layers have a Ga-Ga bonding arrangement similar to that shown in Figure 19 above; this arrangement provides a relatively low energy structure. The ghost islands are thus seen to constitute regions of inverted polarity on the surface [86].
In
summary, we have reviewed here most of the studies reported to date concerning
the surface structures of GaN(0001) and (000)
surfaces. Structures of the bare surfaces, as a function of surface
stoichiometry, are now fairly well understood. The surface structures of InGaN
are also largely understood, and good progress has also been made in
determining the structure and energetics for adsorbed atoms of Mg, As, Si and
H. A defining feature of many of these surface structures, as they occur
during PAMBE, is the occurrence of one or more layers of metal atoms on the
surface. This is contrary to what occurs on most other semiconductor surfaces
(where non-metallic surfaces generally have lower energy, i.e. due to the
opening of a band gap), but it occurs in the case of GaN due in part to the
large difference in size between Ga and N so that monolayers of Ga (or In) can
more or less fit onto the GaN surface. These metallic layers then have great
influence on the surface kinetics. An open question at this time is whether or
not similar metallic layers also exist during growth by other methods such as
MOVPE, RMBE or HVPE. Future work should lead to a greater understanding of the
stable surface structures during growth by those methods, thus enabling a
comparison of the relative efficacy of the different methods for processes such
as alloy formation and dopant incorporation.
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