# Formation Energies of Antiphase Boundaries in GaAs and GaP: An ab Initio Study

^{1}

^{2}

^{*}

## Abstract

**:**

_{{113}}≈ γ

_{{112}}< γ

_{{111}}, which suggests {113} and {112} as possible planes for faceting and annihilation of antiphase boundaries in GaAs and GaP.

## 1. Introduction

_{wb}calculated for antisite defects. Assuming E

_{wb}= 0.3 eV for the case of GaAs [15], simple bond counting arguments yield γ = 27 and 22 meV/Å

^{2}for the {110} and {111} APB’s, respectively. In this case, the difference between the specific formation energies of various APB’s is solely governed by the difference in the wrong bond density. The calculations reveal that the formation energy of the {111} APB’s is lower than the {110} APB’s. This result contradicts the first-principle calculations [16] that suggest the opposite trend, hereby indicating that the simple bond counting model is not appropriate for calculating the energetics of the APB’s.

## 2. Computational Details

_{max}parameter) was equal to 7 for all structures, which corresponds to the cut-off energy of approximately 12 Ry. The local density approximation [20] was employed for the exchange-correlation functional. The energy needed to separate core and valence electrons was set to −6 Ry, wich results in treating of semi-core electrons as valence electrons.

^{2}, and 0.01 eV, respectively.

## 3. Results and Discussion

^{2}. The calculated asymptotic formation energies are in good agreement with the corresponding values of 34 and 44 meV/Å

^{2}obtained in Ref. [16] using an extrapolation technique for distant {110} and {111} APB’s, respectively.

_{wb}was calculated to be 0.31 eV (Table 1), which is close to the energy of 0.3 eV per bond estimated for an antisite pair (Ga)

_{As}+ (As)

_{Ga}[15].

_{g}is the energy gap of a semiconductor, ε

_{r}is the static dielectric constant, ε

_{0}is the permittivity of free space, and σ is the APB areal charge density associated with wrong bonds under assumption of the full compensation. The substitution of E

_{g}= 1.5 eV and ε

_{r}= 13 for GaAs, combined with the substitution of E

_{g}= 2.3 eV and ε

_{r}= 11 for GaP yields L

_{c}≈6 – 7 Å for {111} APB’s. In calculations, we observe the metallic transition for {111} APB’s at the separation of 6 – 10 Å. In order to explore the saturation of the formation energy with DFT, a relatively large (about 100 atoms) supercell is necessary to meet the condition L ≫L

_{c}, which is referred to as distant APB’s. The results of the calculations gathered in Table 1 suggest that the wrong bond energy for distant {111} APB’s is almost by a factor of two larger than the corresponding value for the {110} APB, which yields a magnitude of about 0.3 eV for the compensation energy per bond.

_{wb}≈ 0.26 eV and is independent of the APB type for both GaAs and GaP. This is because full compensation can be achieved at a small separation and a similar lattice of wrong bonds is formed, which results in a similar Madelung contribution to the total energy. Under these circumstances, the lowest energy has the {111} APB due to the lowest wrong bond density (Figure 3).

^{2}, which is at the limit of accuracy of the calculations. We did not perform this calculations for GaAs/Ge, as a similar result was expected owing to an even smaller value of the lattice mismatch between Ge and GaAs.

^{2}in GaAs and GaP, respectively.

## 4. Conclusions

## Acknowledgments

## References

- Tobin, S; Vernon, S; Bajgar, C; Haven, V; Geoffroy, L; Lillington, D. High-efficiency gaas/ge monolithic tandem solar-cells. IEEE Electr. Device. L
**1988**, 9, 256–258. [Google Scholar] - Kunert, B; Volz, K; Stolz, W. Dilute nitride Ga(NAsP)/GaP-heterostructures: Toward a material development for novel optoelectronic functionality on Si-substrate. Phys. Status Solidi B
**2007**, 244, 2730–2739. [Google Scholar] - Kunert, B; Zinnkann, S; Volz, K; Stolz, W. Monolithic integration of Ga(NAsP)/(BGa)P multi-quantum well structures on (001) silicon substrate by MOVPE. J. Cryst. Growth
**2008**, 310, 4776–4779. [Google Scholar] - Hudait, MK; Krupanidhi, SB. Self-annihilation of antiphase boundaries in GaAs epilayers on Ge substrates grown by metal-organic vapor-phase epitaxy. J. Appl. Phys
**2001**, 89, 5972–5979. [Google Scholar] - Kunert, B; Klehr, A; Reinhard, S; Volz, K; Stolz, W. Near room temperature electrical injection lasing for dilute nitride Ga(NAsP)/GaP quantum-well structures grown by metal organic vapour phase epitaxy. Electron. Lett
**2006**, 42, 601–603. [Google Scholar] - Nemeth, I; Kunert, B; Stolz, W; Volz, K. Antiphase Boundaries in GaAs/Ge and GaP/Si. 15th Conference on Microscopy of Semiconducting Materials, Cambridge, England, April 02–05, 2007, In Microscopy of Semiconducting Materials 2007; Cullis, A, Midgley, P, Eds.; Springer-Verlag: Berlin, Germany, 2008; Volume 120, pp. 107–110. [Google Scholar]
- Kawabe, M; Ueda, T. Self-Annihilation of antiphase boundary in GaAs on Si(100) grown by molecular beam epitaxy. Jpn. J. Appl. Phys
**1987**, 26, L944–L946. [Google Scholar] - Cho, NH; Cooman, BCD; Carter, CB; Fletcher, R; Wagner, DK. Antiphase boundaries in GaAs. Appl. Phys. Lett
**1985**, 47, 879–881. [Google Scholar] - Cho, NH; Carter, CB. Formation, faceting, and interaction behaviors of antiphase boundaries in GaAs thin films. J. Mater. Sci
**2001**, 36, 4209–4222. [Google Scholar] - Cohen, D; Carter, CB. Structure of the (110) antiphase boundary in gallium phosphide. J. Microsc
**2002**, 208, 84–99. [Google Scholar] - Narayanan, V; Mahajan, S; Bachmann, KJ; Woods, V; Dietz, N. Antiphase boundaries in GaP layers grown on (001) Si by chemical beam epitaxy. Acta Mater
**2002**, 50, 1275–1287. [Google Scholar] - Nemeth, I; Kunert, B; Stolz, W; Volz, K. Heteroepitaxy of GaP on Si: Correlation of morphology, anti-phase-domain structure and MOVPE growth conditions. J. Cryst. Growth
**2008**, 310, 1595–1601. [Google Scholar] - Matsushita, T; Yamamoto, T; Kondo, T. Epitaxial growth of spatially inverted GaP for quasi phase matched nonlinear optical devices. Jpn. J. Appl. Phys
**2007**, 46, L408–L410. [Google Scholar] - Petroff, PM. Nucleation and growth of GaAs on Ge and the structure of antiphase boundaries. J. Vac. Sci. Technol. B
**1986**, 4, 874–877. [Google Scholar] - Baraff, GA; Schlüter, M. Binding and formation energies of native defect pairs in GaAs. Phys. Rev. B
**1986**, 33, 7346–7348. [Google Scholar] - Vanderbilt, D; Lee, C. Energetics of antiphase boundaries in GaAs. Phys. Rev. B
**1992**, 45, 11192–11201. [Google Scholar] - Dandrea, RG; Froyen, S; Zunger, A. Stability and band offsets of heterovalent superlattices: Si/GaP, Ge/GaAs, and Si/GaAs. Phys. Rev. B
**1990**, 42, 3213–3216. [Google Scholar] - Lambrecht, WRL; Amador, C; Segall, B. ”Wrong” bond interactions at inversion domain boundaries in GaAs. Phys. Rev. Lett
**1992**, 68, 1363–1366. [Google Scholar] - Blaha, P; Schwarz, K; Madsen, GKH; Kvasnicka, D; Luitz, J. Wien2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties; Karlheinz Schwarz, Techn. Universität: Wien, Austria, 2001. [Google Scholar]
- Kohn, W; Sham, LJ. Self-consistent equations including exchange and correlation effects. Phys. Rev
**1965**, 140, A1133–A1138. [Google Scholar] - Monkhorst, HJ; Pack, JD. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188–5192. [Google Scholar] - Kokalj, A. Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale. Comp Mater Sci. 2003, 28, pp. 155–168.

**Figure 1.**(color online) Formation of the APB’s at the interface between group IV and group III-V semiconductors. ABP’s emerge at monosteps on the group IV (001) surface. Several possibilities are considered: (a) APB growth along the {110} plane extended to the free surface, (b) APB growth along the {111} plane and subsequent annihilation, (c) APB growth along the {110} plane (segments AB and DE), subsequent kinking in {112} plane (BC) or {113} plane (CD) and annihilation. The wrong bonds at the interface between inversion domains are marked red.

**Figure 2.**(color online) Atomic structure of the smallest unit cells representing various APB’s: (a) {110}, (b) {111}, (c) {113}, and (d) {112}. Arrows indicate the APB planes. (Visualized with XCrySDen [22].)

**Figure 3.**Specific formation energy of the {110}, {111}, {112}, and {113} APB’s in GaAs (a) and GaP (b). ”Relaxed” and ”unrelaxed” refer to calculations that include or exclude relaxation of atomic coordinates within the supercell.

**Figure 4.**Lattice of charges in the plane of the {112} APB (a) and the {110} APB (b) that forms as a result of the charge transfer q between wrong bonds. The open and filled circles correspond to the positively charged V-V bonds and negatively charged III-III bonds, respectively. The primitive cell is shown by dashed lines with dimensions given in terms of the equilibrium lattice constant a

_{0}. The Madelung (Coulomb) potential due to this distribution of charges is indicated in the units of 4πε

_{r}ε

_{0}a

_{0}/q.

APB plane | W.B. density ( $\times \hspace{0.17em}{a}_{0}^{2}$) | Excess stoichiometry | γ(meV/Å^{2}) | E_{wb} (eV) | ||
---|---|---|---|---|---|---|

GaAs | GaP | GaAs | GaP | |||

{110} | $2\sqrt{2}\hspace{0.17em}\approx \hspace{0.17em}2.8$ | 0 | 28 | 341 | 0.31 | 0.35 |

{111} | $4/\sqrt{3}\hspace{0.17em}\approx \hspace{0.17em}2.3$ | 1 | 43 | 53 | 0.59 | 0.67 |

{113} | $12/\sqrt{11}\hspace{0.17em}\approx \hspace{0.17em}3.6$ | 1/3 | 39 | 46 | 0.34 | 0.37 |

{112} | $8/\sqrt{6}\hspace{0.17em}\approx \hspace{0.17em}3.3$ | 0 | 39 | 48 | 0.37 | 0.43 |

^{1}${\gamma}_{\left\{110\right\}}^{\text{GaP}/\text{Si}}\hspace{0.17em}=\hspace{0.17em}33.6\hspace{0.17em}{\text{meV}}^{/}$

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Rubel, O.; Baranovskii, S.D.
Formation Energies of Antiphase Boundaries in GaAs and GaP: An *ab Initio* Study. *Int. J. Mol. Sci.* **2009**, *10*, 5104-5114.
https://doi.org/10.3390/ijms10125104

**AMA Style**

Rubel O, Baranovskii SD.
Formation Energies of Antiphase Boundaries in GaAs and GaP: An *ab Initio* Study. *International Journal of Molecular Sciences*. 2009; 10(12):5104-5114.
https://doi.org/10.3390/ijms10125104

**Chicago/Turabian Style**

Rubel, Oleg, and Sergei D. Baranovskii.
2009. "Formation Energies of Antiphase Boundaries in GaAs and GaP: An *ab Initio* Study" *International Journal of Molecular Sciences* 10, no. 12: 5104-5114.
https://doi.org/10.3390/ijms10125104