First-Principles Analysis on Stability of Interstitial O Atomin Si and Ge Crystals
Tatsunori Yamato, Hiroaki Kariyazaki and Koji Sueoka

Dept. of Communication Eng., Okayama Prefectural University, Japan1Introduction

In recent years, Large Scale Integration (LSI) devices
have been developed with downsizing. In this technology trend,high quality and large diameter Si wafers are used as substrates
with controlling the impurities. It is well known that O atoms
are incorporated in Si crystals during Czochralski crystal growth[1]. O atoms have an advantage for increasing the strength of Siwafers [2].
Furthermore, Ge film/Si substrate is under consideration for thechannel material as the carrier mobility in Ge is higher than thatin Si [3]. Therefore, Ge film/Si substrate structure is considered
for the next generation LSI materials. In this structure, O atoms
diffuse into Ge thin film from the Si substrate during thethenmal treatments. The purpose of this study is to clarify theproperties of O atoms in Si and Ge crystals. Furthermore, theinfluence of lattice strain in Ge/Si structure on the stability of Oatoms was considered.
2Calculation Details

In this study, first-principles calculation was performed
within the generalized gradient approximation (GGA) using theCASTEP code [4]. The wave functions were expanded with theplane waves, and the ultra-soft pseudo-potential method wasused to reduce the number of plane waves. The cut off energy
was 310eV. The expression proposed by Perdew et al, was used
for the exchange-correlation energy in the GGA [5]. Periodic
boundary conditions were used with cubic super cells of 64
atoms, k-points ampling was performed at 1 × 1 × 1 special
points in a Monkhorst-Pack grid [6].
In the 64-atom calculation cell, one O atom was arranged atfour sites as shown in Fig. 1. Geometry optimization wasperformed, and total energies Etot were calculated for eachcalculation cell. Furthermore, the formation energy Ef of O atom
was calculated by the following equations, and the stability of O
atom at each site was estimated.
1
Si : Ef = Etot(Si64O1) – {Etot(Si64)+ Etot(O2)}2(1)

1Ge : Ef = Etot(Ge64O1) – {Etot(Ge64) + Etot(O2)} (2)2Isotropic tensile-strain of 1%~4% was imposed to Si cell,and isotropic compressive-strain of 1%~4% was imposed to Gecell. Similar analysis to the unstrained cell was performed.
3Results and discussion

The calculated formation energy of O atom in Si crystal isshown in Fig. 2. It was found that Ef of O atom at B-, S- and Hsite was almost equal, and became lower than that at T-site.
Moreover, O atom arranged at S- and H-site moves to near Bsite during geometry optimization, as shown in Fig. 3. Therefore,
the most stable position of O atom in Si crystal is considered tobe near B-site.

The calculated formation energy of O atom in Ge crystal isshown in Fig. 4. The formation energy of O atom arranged at Band S-site was almost equal, and became lower than that at Tand H-site. Moreover, O atom arranged at S-site moved to nearB-site during geometry optimization, as shown in Fig. 5.
Therefore, the most stable position of O atom in Ge crystal isconsidered to be near B-site.
The strain dependence of formation energy of O atom isshown in Figs. 6 and 7. For Si crystal. B-site was the most stable
independent of tensile-strain.
On the other hand, for Ge crystals, the formation energy ofO atom at B-site with 4 % compressive-strain became higher
than that at T-site.
4Conclusion

In this study, first-principles analysis on stability ofinterstitial O atom in Si and Ge crystals was performed
with considering the stain. The main results can besummarized as follows.
(1)

In non-strained Si and Ge crystals, the most stable
position of O atom is near B-site.

(2)

In the tensile-strained Si crystal, the most stable positionof O atom is near B-site independent of the strain.

(3)

In the compressive-strained Ge crystal, the formationenergy of O atom at B-site with 4% compressive strain
became higher than T site.

References[1] R. A. Craven, Semiconductor Silicon 1981,(1981),pp.254271[2] F. Shimura, Handoutai Silicon Kessyou Kougaku (inJapanese), (1993), p307, Maruzen[3] C. Claeys and E. Simoen, Germanium-based Technologies:
From Materials to Devices, Elsevier, Amsterdam, 2007.
[4] The CASTEP code is available from Accelrys Software Inc.
[5] J. Perdew. K. Burke and M. Ernzerhof, Phys.Rev.Lett.
77.3865(1996)[6] H. Monkhorstand J.Pack. Phys.Rev.B13.5188(1976)

Fig.1 B-,S-,T- and H-site in diamond structure.

Fig.2 Calculated Ef of O atom in non-strained Si.

Fig.3 Movement of O atom in Si during geometry
optimization.

Fig.5Movement of O atom in Ge during geometry
optimization.
Fig.4 Calculated Ef of O atom in non-strained Ge.

Fig.6 Calculated Ef of O atom in tensile-stained Si.

Fig.7 Calculated Ef of O atom in compressive stained Ge.