How annealing conditions influence the fluctuation of step edgesof step bunching on vicinal GaAs(100) formed by annealingin AsH3 and H2 ambient
K. Hataa)
Institute of Materials Science, TARA, University of Tsukuba, Tsukuba 305, Japan and Institute of Industrial
Science, The University of Tokyo, Tokyo 106, Japan

H. Shigekawa
Institute of Materials Science, TARA, University of Tsukuba, Tsukuba 305, JapanT. Ueda and M. Akiyama
Oki Semiconductor Technology Laboratory Company Ltd., Tokyo 193, JapanT. OkanoInstitute of Industrial Science, The University of Tokyo, Tokyo 106, Japan~Received 8 October 1996; accepted 24 March 1997!
We report how annealing conditions influence the degree of fluctuation of step edges of stepbunching formed by annealing a vicinal GaAs~001! surface in AsH3 and H2 and ambient. At 700 °C,
when the partial pressure is high, B steps are straighter than A steps as reported before, however, as
the AsH3 partial pressure is decreased, A steps becomes straighter, finally, than the B steps at apartial pressure of 131022 Torr. This reversal of the type of straight step edges can be explainedby considering the (234) – c(434) phase transition. We will also apply the electron counting
model established by Pashley in order to explain the experimental results, and by discussing its
usefulness and limitations, finally conclude that we cannot determine the stability of steps only by
this model. © 1997 American Vacuum Society. @S0734-2101~97!60203-1#

I. INTRODUCTION
No step is free from fluctuations. A step’s fluctuations
play a critical role during crystal growth, its characteristics
ultimately determine the equilibrium shape of crystals, andits regulation is indispensable in using steps as a template tofabricate quantum wires. In this sense, it is very important toclarify how step edges fluctuate with experimental conditions
and understand what factor determine the degree. The characteristics of steps of GaAs are not clearly clarified. This ispartly because the degree of fluctuation, characteristics, andmorphology of steps are influenced by the reconstruction of
the surface, which depends on the surface As stoichiometry.
This means that the characteristics of steps of GaAs varywith the preparation procedure of surfaces in a complicatedfashion.
One eminent phenomenon concerning steps is step bunching. Step bunching is a phenomenon in which the surface
breaks up into regions with high step densities and regionswith little or no steps. On vicinal GaAs~001!, step bunching
was first observed on layers grown by metal–organic
chemical-vapor deposition ~MOCVD!.1–4 In a previous
article,5 we have shown that MOCVD epitaxial growth is notindispensable in inducing step bunching; a similar stepbunching to those observed on epitaxial grown layers can beformed by annealing vicinal GaAs~001! in AsH3 /H2 ambient. Previous studies3,5 show that this annealing-induced stepa!

Electronic mail: hata@mat.ims.tsukuba.ac.jp; colored and unpublished images are presented on the World Wide Web at http://
www.ims.tsukuba.ac.jp/lab/shigekawa/index.html

1269

J. Vac. Sci. Technol. A 15(3), May/Jun 1997

bunching does not grow indefinitely with annealing time but,after it evolves into a particular size, its development stops,
and the surface morphology remains unchanged. The surface
has reached a stationary state with its ambient.5,6
In this article, we report that AsH3 partial pressure( PAsH3) and the miscut directions of substrates influence
the degree of fluctuation of the step edges of the step bunching in its stationary state. The reason we stick to the stationary state is that we believe it serves as the most simple
sample to elucidate the characteristics of this step bunching.
We will show that under high AsH3 partial pressure, B steps
are straighter than A steps as reported before, while as the
AsH3 partial pressure is decreased, A steps becomestraighter, and, finally, straighter than the B steps. This is areport to show that it is possible to produce a surface withstraight A steps in the ambient of MOCVD. Our result showsthat one can produce a surface with straight steps both on A
and B vicinal surfaces by choosing annealing conditions.
However, when one considers the density of branches ~additional step bunchings that do not run in the miscut direction!
on the surface, the situation is totally different for high andlow AsH3 partial pressure regions. In the low AsH3 partialpressure region, many branches are observed on both A and
B substrates. On the other hand, in the high AsH3 partialpressure region, many branches are observed on the A substrate, though there were almost no branches observed on the
B substrates. Indeed, annealing at high temperature and high
AsH3 partial pressure seems to provide a surface with thelowest density of branches and the straightest step edge.

0734-2101/97/15(3)/1269/6/$10.00©1997 American Vacuum Society

1269

1270

Hata et al.: Step bunching on vicinal GaAs(100)1270

II. EXPERIMENT
We used vicinal substrates miscut toward @110#A, and@11̄0#B by 2.0°. To impart the necessary conductivity tocarry out scanning tunneling microscope ~STM! observations, Si-doped substrates with a carrier concentration of 431017 cm23 were used. The annealing process is quite similar to that of MOCVD growth, in fact, it is carried out in thesame reactor used for MOCVD growth. The only difference
between the annealing process and MOCVD growth is thatthe surface is not exposed to III species in the former, therefore, no crystal growth takes place. Before annealing, firstthe sample was cleaned by H2SO4 dipping, followed bychemical etching in a H2SO4, H2O2, H2O; 4:1:1, solution.
Approximately 2 mm of the surface layers were removed bythis etching process to obtain a surface free from contamination. After chemical etching, the substrate was introduced
into the MOCVD reactor system, and was placed on a GaAscoated carbon susceptor and annealed by rf heating. The temperature was increased at a rate of approximately 50 °C/min
to the annealing temperature and kept constant. In this study,
we fixed the annealing temperature at 700 °C. After the
sample was annealed, the temperature was decreased at therate of 100 °C/min to room temperature. During cooling
down of the sample, it was exposed to AsH3 and hydrogen to
avoid surface roughening due to As desorption. After the
sample was quenched to room temperature, it was placed ina nitrogen-purged transfer box and the STM measurement
was done as quickly as possible.
Previous studies showed that increasing and decreasing
the substrate to 700 °C is sufficient for the step bunching todevelop into the stationary stage, and the duration of annealing up to 40 min does not influence the stationary stage.5 To
confirm that we are certainly observing the stationary surface
and not an intermediate stage, we prepared two substrates,
annealed for 5 s and 20 min at 700 °C, compared the morphologies of these surfaces for every experimental condition,and verified that the surface has reached the stationary stage
by checking that there was no major difference between
them.

III. RESULTS
Figure 1 shows a set of STM images showing the stationary surface morphology of GaAs~001!2°-@110#A and -@11̄0#B
annealed at 700 °C with PAsH3 ranging from 131022 to 1
Torr. These STM images clearly show that PAsH3 and thesubstrate miscut direction do influence the stationary surface
morphology, and various step bunchings differing in size andshape can be observed. Strips observed on these images running against the miscut direction represent facets composedfrom several monosteps up to 15.5 No, or little steps, exist
between these strips, and they are ~001! terraces.5 It should
be noted that a regular monostep array was not observed, andalways step bunching formed for our experimental
conditions.7 The main features of these STM images wereinterpreted and analyzed from three points; degree of stepedge fluctuation, existence of branches, and size of step
J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997

FIG. 1. STM images showing the surface morphology of stationary stepbunching on GaAs~001!2°-@110#A and -@11̄0#B substrates annealed at
700 °C with different PAsH3: ~a!, ~c!, and ~e! are STM images of an A
substrate, and ~b!, ~d!, and ~f! of a B substrate. The PAsH3 is 1 Torr for ~a!
and ~b!, 131021 Torr for ~c! and ~d!, and 131022 Torr for ~e! and ~f!.
Scale is 5003875 nm.

bunching. Here, in this article, we will focus our attention on
the degree of the step-edge fluctuation, other aspects will be
discussed elsewhere.7,8
As Fig. 1 clearly shows, additional strips ~branches! connecting two facets can be observed. These strips are notmonosteps but also represent facets composed by several
monosteps. Branches do not run in arbitrary directions but,as the STM images show, they have a peculiar azimuth of^210&, ^21̄0&, ^310&, and ^31̄0&. Branches having the sameazimuth were also observed on the step bunched vicinal sur-

1271

Hata et al.: Step bunching on vicinal GaAs(100)face with a miscut direction of @100#. The strong tendency ofthe branches with these peculiar azimuths to appear suggeststhat these facets have a relatively low free energy.8 If thesebranches represent bunched forced kinks, which are due tomisorientation against the net misoriented direction, then the
population of the branches with azimuth reflecting the misorientation direction ~^210& and ^310&, or ^21̄0& and ^31̄0&!
should dominate the opposite. Such domination of population was not observed, which means that these branches are
not generated by external conditions but are an intrinsic factor of this step bunching.
As can be seen easily from Fig. 1, step edges of facets are
not exactly straight but they are fluctuating. Also, its degree
depends strongly on experimental conditions. The moststraight step edge can be obtained on the B-vicinal surface
annealed with high PAsH3. These are practically the experimental conditions used to fabricate fractional layer
superlattices.9 At 700 °C, in the high PAsH3 region ~HP!
~PAsH3'1 Torr, HP!, B step edges are straighter than thoseof the A steps, while in the medium region ~MP!
~PAsH3'0.1 Torr, MP! there is no conspicuous difference,and in the low PAsH3 region ~PAsH3'131022 Torr, LP! A
step edges become straighter. This is a report of a surface
with straight A steps in the ambient of MOCVD. In contrast,
at 600 °C ~not shown!, there is no such major differencecompared with 700 °C, though, also, B step edges are generally straighter than A step edges.
IV. DISCUSSION
The degree of fluctuation of the step edges of the facets ofstep bunching depends on the miscut direction of the substrates and the partial pressure of PAsH3. Here, I will interpret the observed reversal of the substrate having thestraighter step edge with PAsH3 by considering the (234) – c(434) phase transition.
A phase diagram of the reconstruction of the GaAs surface as a function of substrate temperature and PAsH3 hasbeen investigated by reflectance difference spectroscopy.10 It
shows that at 700 °C, the surface reconstruction is a mixed
structure of c(434)/d(434) and (234) in the highPAsH3 region, while as the PAsH3 goes lower, the c(434) reconstruction cannot maintain its extra As-rich condition and the top As dimers desorb, resulting in the (234)reconstruction. STM observations carried out on these tworeconstructions have shown that they have different types ofstraight step edges; the (234) reconstruction has a straight
A step edge and a rough B step edge,11 while the opposite
holds true for the c(434) reconstruction.2 The step-edge
fluctuation observed above is consistent with these wellaccepted experimental results; in the high PAsH3 region, thesurface takes the c(434) reconstruction, which has astraight B step edge, and in the low PAsH3 region the reconstruction switches to (234), which has a straight A stepedge.
This means that the A step structure is more stable thanthe B step structure in the (234) phases, while the opposite
hold true in the c(434) phases. The most simple guide to
JVST A - Vacuum, Surfaces, and Films

1271

FIG. 2. Three top As dimers of the missing dimer model. Shaded and open
circles represent As and Ga atoms. The larger circles are atoms in the top
layer, the smaller circles in the second layer. The second layer atoms form abond with the lower bulk ~not shown!. Atoms with excess electrons areindexed with a1 mark, while those that lack electrons are indexed witha2 mark.

consider whether a structure is stable or not is the electron
counting model proposed by Pashley.12 He applied the electron counting model to the supposed step structures of (234) phase and explained why the (234) reconstruction has
a stable A step edge and an unstable B step edge by showingthat the structure of the A step edge satisfies the electron
counting model while that of the B step edge does not.12
In this section, we will consult whether or not the electron
counting model can be applied to the c(434) reconstruction
and successfully explain the reason why the fluctuation ofsteps on the c(434) reconstruction has a completely different characteristic from that of (234). Our conclusion is that
we cannot determine whether or not the steps are stable fromthe electron counting model only. If we follow the method
proposed by Pashley,12 we can see that the B steps are morestable than the A steps in the c(434) phases. However, we
will show that by slightly modifying the original step-edge
structure proposed by Pashley, it is possible to provide a B
step-edge structure in the (234) phase and an A step-edge
structure in the c(434) phase, which satisfies the electron
counting model.
The electron counting model asserts that a stable surface
must satisfy a condition where the available electrons in thesurface layer exactly fill all the states of As dangling bonds,
and leave those of Ga empty. The excess/deficient number ofelectrons for each atom is counted according the following
rules: As supplies 5/4 electrons to each As–Ga bond, andone for an As–As bond. The dangling bonds of As are filled,therefore, requiring 2 electrons. Ga supplies 3/4 electrons toeach As–Ga bond. The dangling bonds are empty, requiring
no electrons. Each As and Ga has 5 and 3 electrons available.
The excess/deficient number of electrons for each atom is
calculated by subtracting the available number of electronfrom the number of required electrons. The result is indexedin Fig. 2 as 1; for excess electrons, and 2; for deficient1272

Hata et al.: Step bunching on vicinal GaAs(100)1272electrons. If the total balance of the excess and deficient
cancels out in a unit island cell, that structure is said tosatisfy the electron counting model.
Figure 2 shows schematics of the missing dimer modeland the extra As dimer model, which are generally accepted
as the typical surface structure of the (234) and c(434)phases, respectively. In Fig. 2, only the three top As dimerrows and atoms in the second layer are shown. Atoms in thesecond layer form a covalent bond with the lower bulk ~notdisplayed!. Shaded and open circles represent As and Ga
atoms, respectively, and large circles, atoms near to the surface. Atoms with excess and deficient electrons are indicatedby the 1 and 2 mark. For the case of the missing dimer
model, the four side atoms have 0.75 excess electrons each,while the six middle atoms lack 0.5 electrons. Thus, the total
excess number of electrons for this structure is 0.75
34 – 0.53650; this structure satisfies the electron counting
model. Similarly, in the case of the extra As dimer model,
the four side As atoms at the second layer lack 0.5 electron
each, and the four middle As atoms at the second layer have
0.5 excess electrons, thus, the extra As dimer model alsosatisfies the electron counting model.
Next, we will follow the method embodied by Pashley12
to estimate the stability of steps. A perfect reconstructed surface is used as a template. Steps are modeled as an island

FIG. 4. ~a!, ~b! Structure model for the A and B steps of the c(434)reconstruction constructed following the procedure proposed by Pashley.
Shaded and open circles represent As and Ga atoms, respectively, and large
circles represent atoms near to the surface. The A and B steps do not satisfy
the electron counting model. ~c! Modified B step model structure that satisfies the electron counting model.

FIG. 3. ~a!, ~b! Structure model for the A and B steps of the (234) reconstruction proposed by Pashley. Shaded and open circles represent As and Ga
atoms, respectively, and large circles, atoms near to the surface. The A step
satisfies the electron counting model while the B step does not. ~c! The
modified B step model structure that satisfies the electron counting model.
J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997

structure extending infinitely along one direction and only
one unit cell wide in the perpendicular direction. Under theisland, we replace all of the extra As dimers for the c(434) phase and fill the missing dimer rows for both thec(434) and (234) phases with Ga atoms so that atoms
buried by the island are in bulklike configurations. As shownin Figs. 3 and 4, the model island is made up from complete(234) or c(434) unit cells. Since the island overlaps twounit cells of the template surface, a unit cell of the island@enclosed by the dash–dotted line in Fig. 4~c!# is one unit
wide in the infinitely extended direction and two units widein the perpendicular direction.
Figures 3~a! and 3~b! show the A and B step-edge structures of the (234) phase originally proposed by Pashley. In
Figs. 3 and 4, we have not indexed atoms that have the same
excess/deficient electrons as the missing and extra As dimer
models shown in Fig. 2, because as mentioned above, thesestructures satisfy the electron counting model. Considering
this aspect, it is easy to see that the A step of the (234)reconstruction @Fig. 3~a!# satisfies the electron counting
model. Indeed, this structure has no difference from the1273

Hata et al.: Step bunching on vicinal GaAs(100)1273

TABLE I. The numbers of excess/deficient electrons in the step-edge structures formed by a procedure proposed
by Pashley, and structures slightly modified from it. The rows correspond to the locations indexed in Figs. 3
and 4.
(234)
A step(234)
B stepC(434)
A stepC(434)
B stepModified(234) B step

ModifiedC(434) A stepNone

Row A 0
Row B 23

Row A 13
Row B 0
Row C 12

Row A 21
Row B 22
Row C 22
Row D 11

Row A 21
Row B 23
RemoveAs dimer 14

Row A 13
Row B 21
Row C 12
RemoveAs dimer 24

Total 24

Total 0Total 0Total 0Total 23

Total 15

missing dimer model in regard of the electron counting
model. On the other hand, the situation completely differs for
the B step structure shown in Fig. 3~b!. While the excess anddeficient electrons in row A counterbalance, there remains a
deficit of three electrons in row B. The number of excess/deficient electrons of all of the structures shown in this article are arranged in Table I.
By the same process, we can construct the A and B stepedge structures of the c(434) reconstruction as shown in
Figs. 4~a! and 4~c!. As Table I shows, A and B steps have
five excess and four deficit electrons, respectively. Therefore,both structures do not satisfy the electron counting model.
There is no conclusive reason for the step-edge structures
to take the form proposed by Pashley. In this section, we willconsider whether or not we can reasonably modify the step
structures proposed by Pashley to satisfy the electron counting model. The most simple modification is to replace orremove the As dimers and the dimer vacancy on the islands.
Table II lists the change of the excess/deficient electron numbers by these modifications. The modifications consideredwere filling the dimer vacancy by a ~I! Ga or ~II! As dimer,
removing the top As dimer, and ~III! leaving the dangling
bonds unbonded ~formation of a dimer vacancy!, or ~IV!
rebonding the dangling bonds ~formation of a rebonded vacancy!, and ~V! replacing the top As dimer with a Ga dimer.
We found out operations ~IV! and ~V! do not change the total
number of excess/deficient electrons for both (234) andc(434) reconstructions, and regardless of the location, theoperation is carried out. However, for other operations, thesituation is completely different for the (234) and c(434) reconstructions. Operations ~I! and ~II! increase, andoperation ~III! decreases the total excess electrons by 4 forthe c(434) reconstruction, while for the (234) reconstruction, the situation is completely inverted. Therefore, any
combination of these operations changes the total number ofexcess or deficient electrons only by a multiple of 4. Regarding this fact, we can see that among the three step-edge structures that did not satisfy the electron counting model a priori, the c(434) B step-edge structure can easily satisfy theelectron counting model by filling one of the two dimer vacancy rows by a As dimer, while the (234)-B and c(434)-A step-edge structures can never, by any combinationsof the operations listed in Table II.
Therefore, considering the above discussion, one may
conclude that the (234)-A and c(434)-B steps are morestable than the (234)-B and c(434)-A steps, because theformer two satisfy the electron counting model while thelatter ones do not. However, in this section, we will showthat it is possible to construct (234)-B and c(434)-A step
structures, for which the number of excess/deficient electrons
is a multiple of 4 by slightly modifying the structure of thestep edge. Then, by modifying the As dimer or dimer vacancy on the island, we can construct a structure that satisfies
the electron counting model. The modified structures are displayed in Figs. 3~c! and 4~b!. As shown in Table I, byslightly modifying the step-edge structure, we have adjusted
the number of excess/deficient electrons to 14 for the c(434)-A step and 24 for the (234)-B step. Therefore, re-

TABLE II. Table showing how the numbers of excess/deficient electrons in the (234) and c(434) reconstructions change by modifying the top As dimer or the dimer vacancy. DP is an abbreviation of depends on places.
Reconstruction

Operation

Change in electron number

C(434)

Dimer vacancy→Ga dimer
Dimer vacancy→As dimer
As dimer→dimer vacancy
As dimer→vacancy rebonded
As dimer→Ga dimer

22→12
22→12
DP
DP
DP

14
14
24
0
0

(234)

Dimer vacancy→Ga dimer
Dimer vacancy→As dimer
As dimer→dimer vacancy
As dimer→vacancy rebonded
As Dimer→Ga dimer

13→21
13→21
DP
DP
DP

24
24
14
0
0

JVST A - Vacuum, Surfaces, and Films

1274

Hata et al.: Step bunching on vicinal GaAs(100)moving one of the top As dimers on the island will cause thewhole structure to satisfy the electron counting model. Also,
we will state that the proposed step-edge structure is as likely
to exist as the (234)-B step structure proposed by Pashley@Fig. 3~b!#, which focuses the grounds of his statement thatthe (234)-B step is unstable compared to the (234)-A
step.
Summarizing, we have shown that we can construct for
all of the steps considered in this article, a structure modelthat satisfies the electron counting model. This means that
we cannot judge the stability of steps only from the electron
counting model. In order to definitely state that a step isunstable, we have to show that all of the possible step-edge
structures fail to satisfy the electron counting model, which
would be a troublesome task because numerous possible
structures exist. In order to make efficient use of the electron
counting model, we need, at least, a STM image of the stepwith an atomic resolution to reduce the possible model structures to a manageable number. Finally, we would state thatthe electron counting model is not a perfect guideline tojudge the stability of a structure, the real structure is determined by a competition of the energy gain obtained bycharge transfer and the energy loss due to the strain. It is
possible that the energy loss due to the strain is too large forthe charge transfer to take place. In that case, the electron
counting model would fail to judge the stability of the structure.
V. CONCLUSION
In conclusion, we have studied how the annealing conditions influence the degree of fluctuation of step edges of step

J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997

1274

bunching formed by annealing a vicinal GaAs~001! surface
in AsH3 and H2 and ambient. We show that it is possible toproduce a surface that has straighter A steps than B steps byannealing in low AsH3 partial pressure at high temperatures.
When the substrate was annealed with high AsH3 partialpressure, the B steps were straighter than the A steps asreported before. This reversal of the type of straight steps canbe understood by considering the (234) – c(434) phasetransition. We will also apply the electron counting model
proposed by Pashley to consider whether or not it can explain why the A step edges are more stable than the B steps
in the (234) phase, while the opposite holds true in thec(434) phase. Our results are that we cannot determine thestability of steps only by this model. Also, we have discussed
the limitations and application of this model.
T. Fukui and H. Saito, Jpn. J. Appl. Phys. 129, L483 ~1990!.
M. Kasu and T. Fukui, Jpn. J. Appl. Phys. 131, L864 ~1992!.
3
M. Kasu and N. Kobayashi, Appl. Phys. Lett. 62, 1262 ~1993!.
4
J. Ishizaki, S. Goto, M. Kishida, T. Fukui, and H. Hasegawa, Jpn. J. Appl.
Phys. 133, 721 ~1994!.
5
K. Hata, A. Kawazu, T. Okano, T. Ueda, and M. Akiyama, Appl. Phys.
Lett. 63, 1625 ~1993!.
6
K. Hata, T. Ikoma, H. Hirakawa, T. Okano, A. Kawazu, T. Ueda, and M.
Akiyama, J. Appl. Phys. 76, 5601 ~1994!.
7
K. Hata, H. Shigekawa, T. Ueda, M. Akiyama, and T. Okano, Phys. Rev.
B 55, 7039 ~1997!.
8
K. Hata, H. Shigekawa, T. Ueda, M. Akiyama, and T. Okano ~unpublished!.
9
T. Fukui and H. Saito, Appl. Phys. Lett. 50, 824 ~1987!.
10
I. Kamiya, D. E. Aspnes, H. Tanaka, L. T. Florez, J. P. Harbison, and R.
Bhat, Phys. Rev. Lett. 68, 627 ~1992!.
11
M. D. Pashley, K. W. Haberern, and J. M. Gaines, Appl. Phys. Lett. 58,
406 ~1991!.
12
M. D. Pashley, Phys. Rev. B 40, 10 481 ~1989!.
12