Conference-ISSS-7-Ab Initio-Based Approach to Structural Change in InAs ( 001 )-( 2 × 3 ) Wetting Layer Surfaces during MBE Growth

The structural change in InAs(001)-(2×3) wetting layer surfaces grown on GaAs is investigated using ab initiobased 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]


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±0.07monolayer (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-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)α2 [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.ergy E ad [7].The chemical potential µ gas of ideal gas is given by the following equations:

II. COMPUTATIONAL METHODS
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 (As 4 ), 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 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 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).According to the results shown in Fig. 2, another growth processes should be considered to allow In adsorption with simultaneous As desorption. Figure 3  tion of In-As dimer with bond length 1.5 Å 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  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±0.07ML without (8×3) unit [2].This can be interpreted by considering the results shown in  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)α2 from the (2×3) that simply derives following equations.
2. Moreover, it should be noted that further 0.5 ML of In adsorption necessary to realize (2×4)α2 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 2.65-2.71Å close to 2.61 Å 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 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 In-As 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)α2.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.

FIG. 2 .
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.
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 pIn = 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)α2, 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.
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 pIn = 1.0×10 −7 Torr.Schematics of the stable (4×3) surfaces before/after In-As dimer desorption are also shown in this figure.
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 pIn = 1.0×10 −7 Torr.Schematics of the stable (6×3) surfaces before/after In-As dimer desorption are also shown in this figure.

FIG. 6 .
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 pIn = 1.0×10 −7 Torr.Schematics of the stable (8×3) surfaces before/after In-As dimer desorption are also shown in this figure.

Fig. 2 (
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)α2 from the (2×3) that simply derives following equations.