First-Principles Analysis on Stability of Interstitial H Atomin Si and Ge crystals
Syunsuke Kobayashi, Tatsunori Yamato, Hiroaki Kariyazaki and Koji Sueoka

Dept. of Communication Eng., Okayama Prefectural University, Japan
Introduction

2Calculation Details
In the calculation cell of 64 atoms, one H atom has beenarranged to B-, S-, T- or H-site as shown in Fig. 1. Geometry
optimization was carried out by first principles calculation.
The formation energy (Ef) of H atom in Si was obtained byeq. (1) with the three-dimensional periodic boundary condition.
For Ge, Ef was obtained by eq. (2).
Ef = E (Si64 H1) – {E (Si64) + E (H2)/2}(1)

Ef = E (Ge64H1) – {E (Ge64) + E (H2)/2}(2)

Furthermore, the calculation cell of Si crystal was deformed
with isotropic strain from +1 to +4%. One H atom has beenarranged to B-, S-, T- or H-site. Geometry optimization wascarried out by first-principles calculation, and the formationenergy was obtained. For Ge crystal, the compressive strain in 1 to -4% was imposed to the calculation cell, and the similarcalculations were performed.

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].

Results and discussion
The formation energy of H atom in Si crystal is shown inFig. 2. It was found that H atom in Si has an almost equal Ef
among S-, T- and H-site, and lower than that at B-site. Similar
result was obtained for Ge crystal as shown in Fig. 3.

Formation energy (eV)Large Scale Integrations (LSIs) have been developed withdownsizing in recent years. In this technical trend, the impurities
such as O, H and metals should be controlled as they interact
with intrinsic point defects in Si. Furthermore, Ge thin film on
Si substrate attracts attentions as the carrier mobility is higher
compared to Si [1-3]. Therefore, it becomes necessary tounderstand the behaviour of the impurities and their interactions
3with point defects in Ge and Ge/Si structure. In this study, thestability of interstitial H atom in Si, Ge, and SiGe was analysedby first principles calculation. It was found that H atom is moststable at T-site in Si, Ge and SiGe. Furthermore, H atom isstable at T-site in tensile strained Si when the strain is up to+1%. However, when the strain is +2 ~ +4%, H atom is moststable at B-site in Si. In compressive strained Ge, H atom ismost stable at T-site when the strain is up to -4%.

2.5
21.5
10.50B-site

S-siteT-siteH-siteFig. 2 Calculated Ef of H atom in Si crystal.

Formation energy (eV)

12.5
21.510.5
0B-siteS-siteT-siteH-siteFig. 3 Calculated Ef of H atom in Ge crystal.
Fig. 1 B-, S-, T- and H-site in diamond structure.
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

The movement of H atom during geometry optimizationfrom H- and S- to T-site in Si crystal is shown in Fig. 4. Thismovement indicates that there is no energy barrier among S-, Tand H-site. This is the reason why the formation energies of H
atom at H atom at H-, S- and T-site are almost equal in Si. For
Ge crystal similar movement was confirmed.
These results indicate that H atom in Si and Ge crystals ismost stable near T-site.

4Conclusion
First-principles analysis was performed to the stability ofinterstitial H atom in Si and Ge crystal. Following results wereobtained.
(1) H atom is most stable near T-site in both Si and Ge crystals.
(2) B-site is metastable in both Si and Ge crystals.
(3) When the isotropic tensile strain is 1% in Si crystal, H atom
is most stable near T-site. On the other hand, when strain is
2 to 4%, B-site is most stable.
(4) For Ge crystal, H atom is most stable near T-site with theFig.4 Movement of H atom during geometry optimisation.
Next, the formation energy of H atom in the isotropictensile strained Si crystal is shown in Fig. 5. It was found thatthe formation energy of S-, T- and H-site is lower than B-site up
to 1% as well as no strained Si. In this case, each H atom moved
near T-site.
Furthermore, when tensile strain is larger than 2%, B-site ismore stable than the other sites.

Formation energy (eV)7654321001B-site

23Strain in Si (%)
S-site4T-site

5H-siteFig.5 Calculated Ef of H atom in tensile strained Si.

Formation energy (eV)The formation energy of H atom in the isotropic
compressive strained Ge crystal is shown in Fig. 6. It was foundthat the formation energy of S-, T- and H-site is lower than Bsite up to -4% as well as no strained Ge. In this case, each H
atom moved near T-site.

8765432
10-5-4
B-site-3-2-1
Strain in Ge (%)
S-siteT-site0H-siteFig.6 Calculated Ef of H atom in compressive strained Ge

compressive strain up to -4%.
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