Molecule Dynamics Calculation on Formation of Void Defects
in Si and Ge Crystals
Shusaku Ota and Koji Sueoka

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

In recent years, Large Scale Integration (LSI) devices havebeen developed with downsizing. In this technology trend, highquality and large diameter Si wafers are used as substrates withcontrolling the point defects. It is well known that void defects
are formed by the vacancy aggregation in Si during crystal
growth. Since the void defects at the Si wafer surface degrade
the LSI performance, it is important to understand theformation mechanism of vacancies.
Furthermore, Ge crystal is under consideration for the LSI
substrate as the carrier mobility in Ge is higher than that in Si[1].
In recent studies, void defects with larger sizes are found in Ge
crystals compared to Si crystals[2]. However, the mechanism of
the void formation in Ge crystals is not fully understood. In thisstudy, the formation of void defects in Si and Ge crystals wasanalyzed by moleculer-dynamics (MD) simulations.
2 Calculation detailFigure 1 shows the calculation cell of 1000 atoms for Siand Ge crystals. The side length of the cell is 27.154 Å (Si) and28.285 Å (Ge). One vacancy is introduced at the center of thecell by removing one atom. Furthermore, the nearest atoms
were eliminated one by one, and voids with different sizes up
to including 17 vacancies are modeled. The three dimensional
periodic boundary condition was imposed. Materials Explorerof Fujitsu Ltd. for Molecular-dynamics simulation was used inthis study[3]. The Tersoff potential was used with an ensembleof NTV. Formation energy of void was calculated from theobtained internal energy of the cell.

Formation energy Ef (N) of void including the Nvacancies(V) was obtained with equation (1).
Eｆ(N)=EN‐(1000-N)E0/1000(1)Here, E0 is the internal energy of the perfect cell.

3. Calculation results and discussion
3.1 Calculation results of formation energy Ef (N)Figure 2 shows the calculated Ef (N) of void in Si and Gecrystals.

40

Formation energy (eV)1 Introduction

Si35
30

Ge25
2015
105013579111315

17N

Fig.2 Calculated Ef(N) of Si and Ge crystals.
It was found that the formation energy of one vacancy is
3.70 eV (Si) and 3.58 eV (Ge), respectively. Furthermore, theenergy of the void formation in Ge crystal is found to be lower
than that in Si crystal.
Next, the binding energy of void and one vacancy was
obtained with equation (2).
Eb(N+1) = (EN+E1) - (EN+1+E0)(2)The calculated results from Eb(2) to Eb(17) are shown inFig. 3.

Fig.1 MD calculation cell including 1000 atoms.

Binding energy (eV)

2.5

SiIt was found that the vacancy should not be isolated but to beincorporated into void.

2.0

1.5

Ge
1.00.5-246810121416N

4. Conclusion
In this study, we have analyzed the formation of void
defect in Si and Ge crystals by molecule-dynamics calculation.
The obtained results are summarized as follows.
(1) Formation energy of one vacancy is 3.70 eV (Si) and3.58 eV (Ge), respectively. Furthermore, the energy of the void
formation in Ge crystal is found to be lower than that in Sicrystal.
(2) The average binding energy of void and one vacancy
from N=1 to N=17 is 1.74 eV (Si) and 1.68 eV (Ge),respectively.
(3) The vacancy should not be isolated but to beincorporated into void.

Fig.3 Calculated Eb(N) of Si and Ge crystals.
Reference
It was found that the average binding energy of void and one
vacancy from N=1 to N=17 is 1.74 eV (Si) and 1.68 eV (Ge),respectively.

3.2 Interaction of void and vacancy
Here, we calculated the internal energy of the cell with
one V approaching to the void including 4 vacancies. In thisstudy, Ei(1) is the internal energy of one V at the nearest to thevoid, and Ei(2) is the internal energy of one vacancy which is at
the second nearest to the void. In this way, the calculation wasperformed with L=1 to L=9, and the results are shown Fig. 4.

Internal energy (eV)-4533.0-4533.5-4534.0-4534.5-4535.0Si-4535.5-4536.0-4536.5-4537.0

1

2

3

4

5

6

7

8

989L

Internal energy (eV)-3755.5-3756.0-3756.5

Ge-3757.0-3757.5-3758.0-3758.5-3759.01234

567LFig.4 interaction four V and void

[1] C. Claeys and E. Simoen, Germanium-based
Technologies: From Materials to Devices, Elsevier, Amsterdam,
2007[2]. J. Vanhellemont, P. Spiewak, K. Sueoka and I.
Romandic, Phys. Status Solidi C 6, 1906–1911, 2009[3]Materials Explorer“http://www.cache.fujitsu.com/materialsexplorer/index.sht
ml”