Ab Initio-Based Approach to Structural Change in InAs (001)-(2&times;3) Wetting Layer Surfaces during MBE Growth

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The structural change in InAs(001)-(2×3) wetting layer surfaces grown on GaAs is investigated using ab initio-based approach incorporating temperature T and beam equivalent pressure p. Our calculated results reveal that the (2×3) surface fully covered by As dimers is unstable while the (n×3) surfaces (n =4, 6, and 8) with (n −1) dimers including In-As and one missing dimer is more stable at the conventional molecular beam epitaxial (MBE) growth conditions such as T = 703 K under pIn = 1:0×10-7 Torr and pAs4 = 7:5×10-7 Torr. On the (n×3) surfaces, In atoms are incorporated through In-As dimer formation with As desorption. The resultant (4×3) surface consists of three In-As dimers and one missing dimer. The (6×3) surface has three In-As dimers, two As dimers, and one missing dimer. Only one In-As dimer emerges with six As dimers and one missing dimer on the (8×3) surface. The missing dimer region becomes favorable site for further In adsorption. Moreover, the (8×3) can easily change to the (4×3) with In adsorption and subsequent As dimer desorption on the initial (8×3). The existence ratio R for the (4×3) and (6×3) units is respectively estimated to be R = 0:70 and 0.30 satisfying 0.375 ML desorption of As on the (2×3) to form the (2×4)α2. This is consistent with experimental results. Consequently, the (n×3) surfaces including In-As dimers appear during MBE growth instead of the (2×3) surface with As-dimers. [DOI: 10.1380/ejssnt.2015.190]

본문

_Ab_ _Initio_ -Based Approach to Structural Change in InAs (001)-(2 _×_ 3) Wetting Layer

Surfaces during MBE Growth _∗_

Tomonori Ito, _†_ Toru Akiyama, and Kohji Nakamura
_Department_ _of_ _Physics_ _Engineering,_ _Graduate_ _School_ _of_ _Engineering,_

_Mie_ _University,_ _Kurima-Machiya_ _1577,_ _Tsu_ _514-8507,_ _Japan_
(Received 22 December 2014; Accepted 16 March 2015; Published 25 April 2015)

The structural change in InAs(001)-(2 _×_ 3) wetting layer surfaces grown on GaAs is investigated using _ab_ _initio_ based approach incorporating temperature _T_ and beam equivalent pressure _p_ . Our calculated results reveal that the
(2 _×_ 3) surface fully covered by As dimers is unstable while the ( _n×_ 3) surfaces ( _n_ =4, 6, and 8) with ( _n −_ 1) dimers
including In-As and one missing dimer is more stable at the conventional molecular beam epitaxial (MBE) growth
conditions such as _T_ = 703 K under _p_ In = 1 _._ 0 _×_ 10 _−_ 7 Torr and _p_ As4 = 7 _._ 5 _×_ 10 _−_ 7 Torr. On the ( _n×_ 3) surfaces, In
atoms are incorporated through In-As dimer formation with As desorption. The resultant (4 _×_ 3) surface consists
of three In-As dimers and one missing dimer. The (6 _×_ 3) surface has three In-As dimers, two As dimers, and one
missing dimer. Only one In-As dimer emerges with six As dimers and one missing dimer on the (8 _×_ 3) surface. The
missing dimer region becomes favorable site for further In adsorption. Moreover, the (8 _×_ 3) can easily change to
the (4 _×_ 3) with In adsorption and subsequent As dimer desorption on the initial (8 _×_ 3). The existence ratio _R_ for
the (4 _×_ 3) and (6 _×_ 3) units is respectively estimated to be _R_ = 0 _._ 70 and 0.30 satisfying 0.375 ML desorption of As
on the (2 _×_ 3) to form the (2 _×_ 4) _α_ 2. This is consistent with experimental results. Consequently, the ( _n×_ 3) surfaces
including In-As dimers appear during MBE growth instead of the (2 _×_ 3) surface with As-dimers.

[DOI: 10.1380/ejssnt.2015.190]

Keywords: _Ab_ _initio_ quantum chemical methods and calculations; Surface thermodynamics; Indium arsenide

I. INTRODUCTION

Hetero-epitaxial InAs/GaAs grown by molecular beam
epitaxy (MBE) is successfully employed to fabricate quantum dots (QDs). During the MBE growth, the formation
of the wetting layer (WL) as a function of substrate temperature, reconstruction, and the amount of InAs deposition has been investigated in detail by Belk _et al._ [1] using
a combination of reflection high energy electron diffraction (RHEED) and scanning tunneling microscopy (STM)
measurements. The RHEED results indicate that the surface in InAs/GaAs changes its structure from substrate
GaAs(001)- _c_ (4 _×_ 4) to InAs(001)-(2 _×_ 4) via (1 _×_ 3)/(2 _×_ 3)
wetting layer (WL) with increase of InAs coverage over
the temperature range of 350–500 _◦_ C [1]. Grabowski _et_
_al._ [2] observed a complete transition into (2 _×_ 3) at InAs
coverage of 0 _._ 76 _±_ 0 _._ 07 monolayer (ML) with many missing dimers at 450 _◦_ C in STM. Eisele _et_ _al._ [3] found that
the (4 _×_ 3) surface unit cells are arranged either in-line
or brick-lined at about 2 _/_ 3 of monolayer (ML) of InAs
deposited on the GaAs(001)- _c_ (4 _×_ 4) surface . Moreover,
Konishi and Tsukamoto [4] found that the domains of
(1 _×_ 3)/(2 _×_ 3) and (2 _×_ 4) are distributed in an ordered pattern closely related to the density of QD precursors just
after nucleation on the basis of _in_ _situ_ STM observations.
Although many studies have been also done for surface
structures on the InAs/GaAs(001) from theoretical viewpoints, there have been only a few theoretical studies for
the (2 _×_ 3) surfaces. Kratzer _et_ _al._ [5] showed that the
(2 _×_ 3) reconstruction can be regarded as the main build

_∗_ This paper was presented at the 7th International Symposium

on Surface Science, Shimane Prefectural Convention Center (Kunibiki Messe), Matsue, Japan, November 2-6, 2014.

_†_ Corresponding author: tom@phen.mie-u.ac.jp

ing unit of the InAs WL.

Our previous _ab_ _initio_ -based study incorporating the
growth conditions has revealed that the (2 _×_ 3) surface
fully covered by As-dimers is unstable and In adsorption
on the (2 _×_ 3) does not occur at the conventional growth
conditions [6]. Instead of the (2 _×_ 3), the ( _n×_ 3) ( _n_ =4,
6, and 8) surfaces with ( _n −_ 1) As dimers and one missing dimer are stable to favorably incorporate In at the
missing dimer site. The In adsorption resulting from As
desorption can qualitatively interpret the growth process
on the InAs(001) WL surface, where 0.708 ML adsorption
of In with simultaneous 0.375 ML desorption of As on the
(2 _×_ 3) is necessary to realize the final (2 _×_ 4) _α_ 2 [6]. However, it is necessary to study further In adsorption and As
desorption on the ( _n×_ 3) surface to quantitatively clarify
the growth processes on the InAs(001) WL. In this study,
we investigate the change in the (2 _×_ 3) surfaces, including
( _n×_ 3) with _n_ =4, 6, and 8, during MBE growth using _ab_
_initio_ -based approach incorporating temperature _T_ and
beam equivalent pressure _p_ . Our calculated results reveal
that further In adsorption and As desorption no longer occur on the ( _n×_ 3) surfaces to prevent the InAs growth on
the ( _n×_ 3) surfaces. On the basis of this fact, novel surface
structure along with In-As dimer formation is proposed
to make the InAs growth proceed on the (2 _×_ 3) surfaces.

II. COMPUTATIONAL METHODS

Figure 1 shows top view of initial InAs(001)-( _n×_ 3) surfaces such as (a) InAs(001)-(2 _×_ 3), (b) -(4 _×_ 3), and (c)
-(6 _×_ 3), and (d) -(8 _×_ 3) WL surface structures considered
in this study. The adsorption-desorption behavior of In
atom and As molecule on these surfaces can be determined by comparing the free energy of ideal gas per one
particle (chemical potential) _µ_ gas with the adsorption en

ISSN 1348 0391 _⃝_ c 2015 The Surface Science Society of Japan (http://www sssj org/ejssnt) 190

FIG. 1. Top view of initial InAs(001)-( _n×_ 3) surfaces such as
(a) InAs(001)-(2 _×_ 3), (b) -(4 _×_ 3), (c) -(6 _×_ 3), and (d) -(8 _×_ 3)
WL surface structures considered in this study.

ergy _E_ ad [7]. The chemical potential _µ_ gas of ideal gas is
given by the following equations:

]

_µ_ In = _−k_ B _T_

_µ_ As4 = _−k_ B _T_

[ _k_ B _T_

_p_ In

[ _k_ B _T_

_p_ As4

_gζ_ trans

_,_ (1)

]

FIG. 2. Calculated adsorption-desorption boundaries of (a)
In and (b) As-dimer on the InAs(001)-( _n×_ 3) WL surface as
functions of temperature and BEP of In and As4, respectively.
Schematics of the ( _n×_ 3) surfaces at the growth conditions are
also shown in this figure.

electronic-structure calculation and the geometry optimization [10]. The valence wave functions are expanded
by the plane-wave basis set with a cutoff energy of 16 Ry.
We take the InAs(001) models with a slab geometry of
eight atomic layers with artificial H atoms [11] and a vacuum region equivalent to nine atomic layer thickness.

III. RESULTS AND DISCUSSIONS

Calculated adsorption-desorption boundaries of In on
the InAs(001)-( _n×_ 3) WL surfaces are shown in Fig. 2(a)
as functions of _T_ and _p_ In. This indicates that In adsorption does not occur on the (2 _×_ 3) but is allowed on
the (4 _×_ 3), the (6 _×_ 3), and the (8 _×_ 3) at growth conditions. This is because the adsorption energy for In atom
is very large such as _−_ 1 _._ 68 eV on the (2 _×_ 3) in contrast
with _−_ 3 _._ 87 eV on the (4 _×_ 3), _−_ 3 _._ 66 eV on the (6 _×_ 3), and

_−_ 3 _._ 33 eV on the (8 _×_ 3). This is because the stable adsorption site of In on the (2 _×_ 3) is around the center position between upper As-dimer and lower As-dimer quite
different from the missing As-dimer site on the ( _n×_ 3)
as shown in Fig. 2(a). Figure 2(b) shows the calculated

_gζ_ trans _ζ_ rot _ζ_ vib

_._ (2)

Here, _k_ B is the Boltzmann’s constant, _T_ the gas temperature, _g_ the degree of degeneracy of electron energy
level, _p_ the beam equivalent pressure (BEP) of In atom
or As molecule (As4), and _ζ_ trans, _ζ_ rot and _ζ_ vib are the
partition functions for translational, rotational, and vibrational motions, respectively.

The adsorption energy _E_ ad is obtained by

_E_ ad = _E_ total _−_ _E_ substrate _−_ _E_ atom _,_ (3)

where _E_ total is the total energy of the surface with
adatoms, _E_ substrate the total energy of the surface without
adatoms, and _E_ atom is the total energy of isolated atoms.
Using the chemical potential and adsorption energy, the
adsorption and desorption behaviors on the surfaces under growth conditions are obtained as functions of _T_ and
_p_, _i.e._, the structure corresponding to adsorbed surface is
favorable when _E_ ad is less than _µ_ gas, whereas desorbed
surface is stabilized when _µ_ gas is less than _E_ ad. Based
on these results, we obtain adsorption-desorption boundaries for In and As to investigate structural change of
InAs(001)-( _n×_ 3) surfaces. In this study, the total-energy
calculations are performed within the generalized gradient
approximation (GGA) [8] and norm-conserving pseudopotentials with partial core corrections [9]. The conjugategradient minimization technique is used for both the

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FIG. 3. Calculated adsorption-desorption boundaries for As
dimer and In-As dimer on the InAs(001)-(4 _×_ 3) WL surface
with respect to replacement processes of As dimer and In-As
dimer as functions of temperature and As4 BEP at In BEP
_p_ In = 1 _._ 0 _×_ 10 _−_ 7 Torr. Schematics of the stable (4 _×_ 3) surfaces
at the growth conditions are also shown in this figure.

adsorption-desorption boundaries for As dimer on the stable In-adsorbed InAs(001)-( _n×_ 3) WL surfaces as functions of _T_ and _p_ As4 . This implies that In adsorption does
not induce As desorption, indispensable for InAs growth
to change the surface structure from the (2 _×_ 3) to the
(2 _×_ 4) _α_ 2, on the (4 _×_ 3) and (6 _×_ 3). Although As dimer
desorption can be found on the (8 _×_ 3) shown in Fig. 2(b)
schematically, it should be noted that newly appeared
missing dimer is quickly occupied by In adatom to form
the surface structure equivalent to the In-adsorbed (4 _×_ 3)
also schematically shown in Fig. 2(b) that prohibits As
desorption. Moreover, it is found that further In adsorption also no longer occurs to prevent InAs growth on these
( _n×_ 3) WL surfaces.

According to the results shown in Fig. 2, another
growth processes should be considered to allow In adsorption with simultaneous As desorption. Figure 3 shows the
calculated adsorption-desorption boundaries for As dimer
and In-As dimer on the (4 _×_ 3) WL surface with respect
to In-As dimer formation processes replacing As dimer as
functions of _T_ and _p_ As4 at _p_ In = 1 _._ 0 _×_ 10 _−_ 7 Torr. It is
found that In-As dimers stably reside on the (4 _×_ 3) instead of As dimers at the conventional growth conditions.
Desorption of As dimer after forming In-As dimer in the
missing dimer region shown in Fig. 3(a) is due to the
fact that desorption energy of As dimer (1.44 eV) dramatically decreases from 2.84 eV on the initial (4 _×_ 3) and
2.38 eV on the In-adsorbed (4 _×_ 3). This is because adsorp

FIG. 4. Structural change sequence of the InAs(001)-(4 _×_ 3)
WL surface and calculated adsorption-desorption boundary of
In-As dimer on the (4 _×_ 3) at the final process D as functions
of temperature and As4 BEP at In BEP _p_ In = 1 _._ 0 _×_ 10 _−_ 7 Torr.
Schematics of the stable (4 _×_ 3) surfaces before/after In-As
dimer desorption are also shown in this figure.

tion of In-As dimer with bond length 1.5 ˚ A larger than
As dimer largely deforms As dimer to destabilize it on
the (4 _×_ 3). Furthermore, In-As dimer adsorption replacing As dimer increases the number of In-As interatomic
bond energetically more favorable than As-As interatomic
bond to stabilize the (4 _×_ 3). Figure 4 summarizes the exchange sequence between As and In-As dimers reflecting
the decrease of desorption energy of As dimer shown in
Figs. 3(b)–3(f). Finally, the (4 _×_ 3) WL surface consisting of three In-As dimers and one missing dimer appears
reflecting adsorption-desorption boundary of In-As dimer
on the (4 _×_ 3) fully covered by In-As dimers as functions of
_T_ and _p_ As4 also shown in Fig. 4. This final (4 _×_ 3) WL surface results from 0.25 ML adsorption of In and 0.417 ML
desorption of As on the (2 _×_ 3). It should be noted that
0.417 ML desorption of As almost agrees with 0.375 ML
desorption of As to realize (2 _×_ 4) _α_ 2 from the (2 _×_ 3).

Figures 5 and 6 depict the processes of In-As dimer
formation on the InAs(001)-(6 _×_ 3) and -(8 _×_ 3) WL surfaces and adsorption-desorption boundary of In-As dimer
at final state as functions of _T_ and _p_ As4, respectively. In
contrast to the dimer constituents o the (4 _×_ 3), the (6 _×_ 3)
consists of three In-As dimers, two As dimers, and one
missing dimer on the surface, while only one In-As dimer
emerges on the (8 _×_ 3) with six As dimers and one missing dimer. These results reflect the difference in adsorp

192 http://www sssj org/ejssnt (J Stage: http://www jstage jst go jp/browse/ejssnt/)

FIG. 5. Structural change sequence of the InAs(001)-(6 _×_ 3)
WL surface and calculated adsorption-desorption boundary
of In-As dimer on the final (6 _×_ 3) at the final process D as
functions of temperature and As4 BEP at In BEP _p_ In =
1 _._ 0 _×_ 10 _−_ 7 Torr. Schematics of the stable (6 _×_ 3) surfaces before/after In-As dimer desorption are also shown in this figure.

tion energy of In-As dimer on the ( _n×_ 3) surfaces as listed
in Table I. This implies that adsorption energy of In-As
dimer is the smallest (for example, _−_ 3 _._ 96 eV at the process A) on the (4 _×_ 3) and the largest ( _−_ 3 _._ 59 eV at the
process A) on the (8 _×_ 3) during the formation processes
of surface dimers on the ( _n×_ 3) surfaces. Based on the
electron counting model (ECM) [12, 13], the number of
electrons in the surface dangling bonds ∆ _Z_ before the
process denoted by letters in Figs. 4–6 is estimated to be
∆ _Z_ = _−_ 2 on the (4 _×_ 3), ∆ _Z_ = _−_ 1 on the (6 _×_ 3), and
∆ _Z_ = 0 satisfying the ECM on the (8 _×_ 3). Adsorbing
In-As dimer on these surfaces changes their ∆ _Z_ to +2
on the (4 _×_ 3), +3 on the (6 _×_ 3), and +4 on the (8 _×_ 3).
This suggests that adsorption of In-As dimer destabilizes
the (8 _×_ 3) and the (6 _×_ 3) but does not affect the stability
of the (4 _×_ 3). Therefore, the (8 _×_ 3) does not favor In-As
dimer adsorption with the largest adsorption energy to
form the smallest number of In-As dimer on its surface.
Resultant (6 _×_ 3) and (8 _×_ 3) WL appears with 0.444 ML
adsorption of In with simultaneous 0.278 ML desorption
of As and 0.417 ML adsorption of In with 0.125 ML desorption of As on the (2 _×_ 3), respectively.

Previously reported STM observations indicate that the
(2 _×_ 3) consists of the (4 _×_ 3) and the (6 _×_ 3) units at InAs
coverage of 0 _._ 76 _±_ 0 _._ 07 ML without (8 _×_ 3) unit [2]. This
can be interpreted by considering the results shown in

FIG. 6. Structural change sequence of the InAs(001)-(8 _×_ 3)
WL surface and calculated adsorption-desorption boundary of
In-As dimer on the (8 _×_ 3) at the final process B as functions
of temperature and As4 BEP at In BEP _p_ In = 1 _._ 0 _×_ 10 _−_ 7 Torr.
Schematics of the stable (8 _×_ 3) surfaces before/after In-As
dimer desorption are also shown in this figure.

TABLE I. Calculated adsorption energies (in eV) of In-As
dimer on the InAs(001)-( _n×_ 3) WL surfaces during In-As dimer
formation processes. The letters A-D correspond to the processes shown in Figs. 4–6.

Surface A B C D

(4 _×_ 3) _−_ 3 _._ 96 _−_ 3 _._ 81 _−_ 3 _._ 63 _−_ 3 _._ 17

(6 _×_ 3) _−_ 3 _._ 67 _−_ 3 _._ 46 _−_ 3 _._ 50 _−_ 2 _._ 95

(8 _×_ 3) _−_ 3 _._ 59 _−_ 3 _._ 30  -

Fig. 2(b). Considering In-As dimer formation resulting
from In adsorption preceding As adsorption, In adsorption
on the (8 _×_ 3) induces As-dimer desorption to enhance further In adsorption to form In adsorbed (4 _×_ 3), where subsequent As adsorption to form In-As dimer on the (4 _×_ 3).
Therefore, considering this In-As dimer formation process, the (8 _×_ 3) is equivalent to the (4 _×_ 3). On the basis
of this idea, we estimate the existence ratio of the (4 _×_ 3)
and the (6 _×_ 3) units satisfying 0.375 ML desorption of As
to realize (2 _×_ 4) _α_ 2 from the (2 _×_ 3) that simply derives
following equations.

5
(4)
12 _f_ (4 _×_ 3) + 18 5 _f_ (6 _×_ 3) = 3 8 _,_

_f_ (4 _×_ 3) + _f_ (6 _×_ 3) = 1 _,_ (5)

where _f_ (4 _×_ 3) and _f_ (6 _×_ 3) are the existence ratio of the
(4 _×_ 3) and the (6 _×_ 3) units, respectively. The calculated

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_f_ (4 _×_ 3) = 0 _._ 70 and _f_ (6 _×_ 3) = 0 _._ 30 can be favorably compared with _f_ (4 _×_ 3) = 0 _._ 83 and _f_ (6 _×_ 3) = 0 _._ 17 estimated by
directly counting the number of the units from Fig. 2 in
Ref. 2. Moreover, it should be noted that further 0.5 ML
of In adsorption necessary to realize (2 _×_ 4) _α_ 2 on the (4 _×_ 3)
is similar to GaAs(001), where 0.5 ML of Ga changes
_c_ (4 _×_ 4) with Ga-As dimers to (2 _×_ 4) [14, 15].

Ohtake _et_ _al._ found the GaAs(001)- _c_ (4 _×_ 4) consisting
of Ga-As dimers that has been confirmed by _ab_ _initio_
calculations, RHEED, and STM observations [16]. They
pointed out that their large-scale STM images from the
_c_ (4 _×_ 4) surface show a conventional brickwork pattern of
bright rectangular blocks. Observing carefully the magnified image, however, the position of rectangular block
is slightly shifted to mean the existence of an asymmetric
unit cell with Ga-As dimers on the _c_ (4 _×_ 4). This asymmetric unit cell results from the large displacements of Ga
atoms in Ga-As dimers down by large amount. The similar asymmetric unit cell is also found on the InAs(001)( _n×_ 3) WL surfaces, where In atoms in In-As dimers move
downward to keep their bond lengths in the range of 2.652.71 ˚ A close to 2.61 ˚ A in bulk InAs. Thus, further careful STM observations are desirable for the InAs(001) WL
surfaces in the process of the structural change from the
(2 _×_ 3) to the (2 _×_ 4). Although these InAs(001)-( _n×_ 3) WL
surfaces should be checked from various viewpoints including recalculation of the surface phase diagram taking
into account In-As dimers, In-As dimer formation gives
one possible interpretation for the structural change on
the InAs(001) WL during MBE growth.

IV. CONCLUSIONS

We have systematically investigated structural change
in InAs(001)-(2 _×_ 3) WL surfaces as functions of _T_, _p_ In,
and _p_ As4 using _ab_ _initio_ -based approach. The ( _n×_ 3) surfaces ( _n_ =4, 6, and 8) with ( _n−_ 1) dimers and one missing

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dimer are stable around the conventional growth conditions such as _T_ = 703 K under _p_ In = 1 _._ 0 _×_ 10 _−_ 7 Torr
and _p_ As4 = 7 _._ 5 _×_ 10 _−_ 7 Torr. On these ( _n×_ 3) surfaces, In
atom can adsorb in the missing dimer region, while further In adsorption and As desorption, indispensable for
the structural change from the ( _n×_ 3) to the (2 _×_ 4), no
longer occur. Further growth on the ( _n×_ 3) surfaces proceeds with In incorporation and As desorption through InAs dimer formation in the missing dimer. The resultant
(4 _×_ 3) surface consists of three In-As dimers and one missing dimer where further In can adsorb, while the (6 _×_ 3)
surface has three In-As dimers, two As dimers, and one
missing dimer. Although only one In-As dimer emerges
with six As dimers and one missing dimer on the (8 _×_ 3)
surface, the (8 _×_ 3) unit has not been observed in the previous studies using STM. This contradiction can be interpreted by employing our calculated results that the
(8 _×_ 3) can easily change to the (4 _×_ 3) with In adsorption
and subsequent As dimer desorption on the initial (8 _×_ 3).
The existence ratio _R_ for the (4 _×_ 3) and (6 _×_ 3) units is
respectively estimated to be _R_ = 0 _._ 70 and 0.30 to satisfy 0.375 ML desorption of As on the (2 _×_ 3) to form the
(2 _×_ 4) _α_ 2. This is consistent with experimental results. In
conclusion, the ( _n×_ 3) surfaces including In-As dimers are
crucial for MBE growth on the InAs(001) WL instead of
the (2 _×_ 3) surface with As-dimers.

ACKNOWLEDGMENTS

This work was supported in part by a Grant-in-Aid for
Scientific Research (No. 24560025) from the Japan Society for the Promotion of Science. Computations were
performed at RCCS (National Institutes of Natural Sciences).

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<i>Ab Initio</i>-Based Approach to Structural Change in InAs (001)-(2×3) Wetting Layer Surfaces during MBE Growth<i><sup> </sup></i>