APPLIED PHYSICS LETTERS
VOLUME 82, NUMBER 11
17 MARCH 2003
Step-edge kinetics driving the formation of atomically flat „110… GaAs
surfaces
Ji-Won Oh,a) Masahiro Yoshita,b) and Hidefumi Akiyamab)
Institute for Solid State Physics (ISSP), University of Tokyo, and CREST, JST, 5-1-5 Kashiwanoha,
Kashiwa, Chiba 277-8581, Japan
Loren N. Pfeiffer and Ken W. West
Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 07974
共Received 11 October 2002; accepted 17 January 2003兲
Atomically flat 共110兲 GaAs surfaces fabricated by the cleaved-edge overgrowth method and
high-temperature growth-interrupt annealing are characterized at the atomic scale. We observe
atomically flat 共110兲 surfaces extending over areas more than 100 ␮m in size. Moreover, deposition
of slightly less or more than integral monolayers 共MLs兲 causes the appearance of characteristic
step-edge shapes such as 1-ML-deep pits, or 2-to-3-ML-high isolated islands. Statistical analysis on
the size and shape distribution of the 1-ML-deep pits supports a simple model based on the stability
of Ga and As atoms on step edges with different bonding configurations, and reveals driving force
to form an atomically flat 共110兲 surface. © 2003 American Institute of Physics.
关DOI: 10.1063/1.1560575兴
Molecular beam epitaxial 共MBE兲 growth of GaAs on
共110兲 surfaces is a key process to fabricate T-shaped quantum
wires by cleaved-edge overgrowth 共CEO兲.1,2 However, the
short residence time of As atoms on the growing GaAs 共110兲
surface limits the MBE growth conditions to low substrate
temperatures of 490 °C and high As4 overpressure. But these
conditions result in rough surfaces on the 共110兲 overgrowth
film,3 which degrades the quality of T-shaped quantum
wires.2
In previous papers,4,5 we developed a high-temperature
growth-interrupt annealing technique and measured annealed
surfaces of 共110兲 GaAs layer via atomic force microscope
共AFM兲, where atomically flat surfaces are observed together
with islands or pits having characteristic shapes. Furthermore, photoluminescence imaging measurements have
shown that the surface perfection and flatness are preserved
even after MBE growth of barrier layers to make a quantum
well.5 However, the detailed evolution mechanism, whereby
the annealed 共110兲 film evolves toward a flat surface has
remained unclear since in situ observation of surface morphology is difficult during MBE growth. In this letter, we
characterize annealed 共110兲 GaAs layers with intentionally
introduced surface morphological change, and propose an
atomic model for flat surface formation.
To fabricate a sample, we grew a 5– 6-nm-thick 共25–30
MLs兲 GaAs layer on an in situ cleaved 共110兲 surface of a
共001兲 GaAs substrate with the CEO method by MBE under a
substrate temperature of 490 °C and a rate of 0.43 ␮m/h.
Right after the growth, we shuttered Ga flux, raised substrate
temperature to 600 °C, and annealed the sample for 10 min
under an As4 flux in the MBE chamber. During the growth
the substrate was not rotated but aligned along the Ga flux
gradient, which introduced spatial distribution of GaAs layer
a兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
b兲
Also: visiting scientists at Bell Laboratories, Lucent Technologies.
thickness around the nominal thickness by 1%/mm with respect to the local positions on the sample surface. Because
the 共110兲 growth is on the cleaved edge, the entire 共110兲
sample surface is 80 ␮m wide in the 关001兴 direction and 3– 4
mm long in the 关 11̄0 兴 direction with the layer-thickness gradient. We fabricated several samples for the present study.
The surface morphology of the sample surfaces was measured by AFM in air. We measured 261 local positions over
the samples, each of which had a scanned area of 5 ␮ m
⫻5 ␮ m each.
Figure 1 shows AFM images observed at different positions on a 共110兲 GaAs surface for a nominally 5-nm-thick
sample by the method described above. An atomically flat
surface without any step edge was observed at positions with
integral layer thickness 共integer ML: ⫹0.00 ML). The thickness deviation from integer ML causes a fractional-
FIG. 1. AFM images of 5 ␮ m⫻5 ␮ m 共110兲 surface areas of GaAs layers
fabricated by the CEO method and growth-interrupt annealing. The labels
show thickness deviation in ML from a integer-ML position. As a reference,
a nonannealed surface with 2 ␮ m⫻2 ␮ m observation area labeled as asgrown is also shown.
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© 2003 American Institute of Physics
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Appl. Phys. Lett., Vol. 82, No. 11, 17 March 2003
monolayer surface coverage to form characteristic step-edge
shapes. At ⫹0.01 ML coverage, we observed isolated 2 or 3
ML rising islands shaped like boats above the otherwise
atomically flat 共110兲 surface. These islands are always elongated in the direction 关001兴 and are formed by the excess
atoms to make flat surface. For slightly negative surface coverage by ⫺0.16 ML and ⫺0.07 ML, on the contrary, 1-MLdeep isolated pits shaped like tropical fish pointing towards
关 11̄0 兴 are observed. At a more negative coverage of
⫺0.21 ML, we found coexistence of 1-ML-deep pits with
irregular shapes and a small boat-shaped island with 2 ML
height relative to the pits. As will be discussed later, this
shows that the evolution of a 1-ML-deep pit to create a fish
shape is pinned by the small island. Note that these islands,
observed at borders of pits have 2 ML steps relative to pits.
As a reference, we show a surface without annealing labeled
as as-grown (2 ␮ m⫻2 ␮ m), which entirely consists of irregular steps and pits.
Note the wide area showing atomic flatness over several
␮m as well as the extended flat background areas between
the islands and pits. One of our samples with a 6 nm GaAs
layer nominal thickness shows an atomically flat area without islands or pits over the entire 80 ␮m sample width in the
共001兲 direction by 0.38 mm in 关001兴 and 关 11̄0 兴 directions.
This result implies that the Ga atoms are moving on the
surface up to 100 ␮m in either direction during the 10 min
600 °C anneal. The monitored tip signal on the atomically
flat region indeed showed fluctuation less than 0.05 nm, or a
quarter ML, which is most probably ascribed to system
noise. Since the curvature radius of the tip is 5 nm, such an
AFM image excludes existence of islands with any lateral
sizes and pits not less than 2nm in width. It is impressive that
this height fluctuation of less than 0.05 nm over 380 ␮m
corresponds on a more human scale to a flatness perfection
of less than 0.5 mm height fluctuation over a 3.8 km region.
It is known that an original as-grown surface of a 5– 6nm-thick 共110兲 GaAs layer without annealing has large
roughness larger than 1 nm, or 5 MLs.4 Therefore, the observed atomically flat surfaces suggest that a strong driving
force to form an atomically flat surface exists in the stepedge kinetics. On the 共110兲 surface at a substrate temperature
of 600 °C under As4 vapor overpressure for annealing, desorption and incorporation of As atoms are in equilibrium,
while the Ga atoms on the surface have negligible desorption. Thus, the surface migration of Ga atoms determines the
surface morphology. The fact that islands and pits evolve
toward self-similar characteristic shapes on a ␮m scale indicates that the migration length of the Ga atoms is larger than
that scale, and the details of these shapes reflect relative stability of Ga atoms at variously oriented step edges on the
共110兲 surface.
To investigate the step-edge kinetics more quantitatively,
we measured sizes of the fish-shaped 1-ML-deep pits, length
b along the long axis in the 关 11̄0 兴 direction and length a
along the short axis in the 关001兴 direction. In Fig. 2共a兲, we
plot length a versus length b for each fish. A polynomial
fitting curve to fourth order shows that a increases superlinearly with b. The data points of a and b are mostly distributed between 0 and 2 ␮m, and larger fish beyond these
sizes are rare. Figure 2共b兲 shows the a/b ratio plotted as a
Oh et al.
FIG. 2. 共a兲 Distribution of short axis a vs. long axis b in 1-ML-deep pits. A
fitting curve is drawn to guide the eyes. The width and height of a fish pit
denoted as a and b are measured in the 关001兴 and 关 11̄0 兴 directions, respectively, as shown in the inset. 共b兲 The a/b ratio vs the area ab/2 of fish pits
are plotted. A rising fitting line with increasing fish areas shows that large
fish have round shape.
function of ab/2, which approximately represents an area of
fish by the formula for triangle areas. The data are scattered
around a fitting line with a positive slope of 0.03/␮ m2 and an
intercept of 0.3. This result indicates that the ratio a/b gradually increases with increasing size of fish. Namely, large fish
tend to have round shapes and look fat, while small fish have
thinner shapes along longer b axis.
To model and discuss formation of characteristic flat surfaces, we show, in Fig. 3共a兲, the atomic arrangement of the
1-ML-deep fish-shaped pit on the 共110兲 GaAs surface corresponding to the AFM images of Fig. 1. In this letter, we label
each step edge on the 共110兲 plane with an index of a plane
that is parallel to the step edge and perpendicular to the 共110兲
plane; the A – B edge is denoted as a 共001兲 step edge, and the
C – D edge as a (001̄) step edge. Note here that the longest
step edge with length b is the 共001兲 edge A – B consisting of
Ga atoms capping three bonds from As atoms. The curved
edges come from the edges B – C and A – D formed by Ga
atoms capping two As bonds, and the short (001̄) edge C – D
consists of As atoms capping three Ga bonds.
The atomic arrangement in Fig. 3共a兲 suggests that the
edges A – B and C – D consisting of three bond sites are more
stable than the edges B – C and A – D having two-bond Ga
sites. In addition, the edge A – B is more stable than the edge
C – D because occasional desorption of an As atom at the
C – D step edge leaves two near-neighbor Ga atoms bonded
by only two bonds. Therefore, we reach a simple evolution
model of 1-ML-deep fish-shaped pits where the Ga atoms
leave from the least stable edges B – C and A – D having
two-bond Ga site are incorporated most probably into the
step edge A – B having three-bond Ga sites.
This model predicts the time evolution of the fish-shaped
pits: fish should become elongated in the 关 11̄0 兴 direction
along A – B and get thinned in the 关001兴 direction normal to
A – B as a function of time, because this tends to minize the
number of less-stable two-bond step edges. Note that shape
evolution of larger pits is slower than that in smaller pits,
because atom migration in larger pits requires more time.
Thus, the dependence of shape on pits area should reflect
time evolution. In fact, the result of Fig. 2 shows that smaller
fish have thinner shape, and is consistent with the above
prediction. It is important to note that an atomically flat 共110兲
surface consists entirely of three-bond sites, while step edges
forming pits or islands have two-bond sites. Therefore, the
driving force to form an atomically flat surface could be
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Oh et al.
Appl. Phys. Lett., Vol. 82, No. 11, 17 March 2003
FIG. 3. 共Color兲 共a兲 Top and side views of the atomic arrangement model of
a 1-ML-deep pit observed on the annealed 共110兲 surface. The symbol size of
those atoms in the topmost atomic layer is enlarged. 共b兲 Atomic step kinetics
of the surface evolution during annealing. Proposed schematic drawings of
the evolution for the island and pit structures from an assumed square initial
shape are obtained by considering detachment and incorporation of Ga atoms from the (1̄10) or (11̄0) edges to the 共001兲 and (001̄) edges at the
surface during annealing.
explained by the same model, namely Ga atom migration
occurs from two-bond sites to three-bond sites having higher
stability.
The surface images in Fig. 1 also show that islands are
always elongated along the 关001兴 direction, while pits elongated along the 关 11̄0 兴 direction. This can be also be interpreted on the basis of different stability for Ga atoms on
different edges. As shown in Fig. 3共b兲, faster detachment of
Ga atoms from the less stable (1̄10) or (11̄0) edges causes
the residual island to become elongated along the 关001兴 direction. In case of pits, on the other hand, the same detachment from (1̄10) or (11̄0) edges and incorporation to more
stable sites at 共001兲 and (001̄) edges causes an asymmetricshape pit elongated along the 关 11̄0 兴 direction.
At ⫹0.01 ML in Fig. 1, all islands have 2–3-ML-height,
and 1-ML-high island is rarely found, indicating that 2 or
higher-ML step edges are more stable than 1-ML step edges.
In terms of our atomic model, this is because a Ga atom at
1-ML-high edge can immediately migrate away from the island after detachment from its initial site, while in the case of
the 2-ML-height step edge a Ga atom at higher ML edge
must move to an empty site in the lower ML, and only then
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can a Ga atom at lower ML edge leave the step edge. The
kinetics of such a two-step process leads to the conclusion
that 2 or higher-ML islands are more stable than 1-ML-high
islands. Note in the AFM image at the ⫺0.21 ML position in
Fig. 1 that the 2 ML step edge of a small boat-like island is
blocking the shape evolution of 1 ML step edge of a pit. It
also supports the above conclusion that 2 or higher ML step
edges are more stable than 1 ML step edges. Our simple
model together with the notion that islands lose Ga atoms to
adjacent structures, but pits do not, explains the characteristic shapes, relative sizes, and step heights of the islands and
pits in the AFM images.
Our experiment and model both suggest that annealing at
even higher temperatures than 600 °C works and most likely
shortens the annealing time to achieve flat 共110兲 surfaces.
Improvement of this annealing technique is important, because it is applied to improve optical quality of T-shaped
quantum wires and wire lasers formed by the CEO method,6
and to achieve a single wire laser lasing from the quantum
wire ground state with low threshold pumping power.7
In summary, we have characterized atomically flat 共110兲
GaAs surfaces as well as pits and islands with characteristic
shapes, which were fabricated by the CEO method with
growth-interrupt annealing. We explain all the results with a
proposed atom migration model to form the flat 共110兲 surfaces, islands and pits based on notion that atomic-step edge
of Ga capping three bonds is more stable than the edge capping two bonds.
This research is partly supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan, and
by the Japan Society for the Promotion of Science.
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