First Principles Analysis on Mechanical Propertiesof SiO2 and GeO2
Takahiro Hosokawa and Koji Sueoka

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

2Calculation Details

The calculation method is the first principles calculation, in
which the ground state of the system is found by solving theKohn-Sham equation that is a rule equation of the electronicsystem for a given atomic configuration. The program package
used in this study is CASTEP [2]. In this calculation, the KohnSham equation is solved self-consisyently in order to obtain theground state of the system for given atomic configurations [3].
Wave function is expanded by plane-waves, and ultrasoft
pseudopotential [4] is used to reduce a number of planewaves.The cut-off energy for the plane-wave expansion was 340
eV. The expression proposed by Perdew et al. [5] was used forthe generalized gradient approximation (GGA) for theexchange-correlation term. The density mixing method [6] andBFGS geometry optimization method [7] are used to optimize
the electronic structure and configurations, respectively.
The atomic configurations of Cristobalite type, Quartz type,and Stishovite type for SiO2 and GeO2 are shown in Fig. 1(a) to1(c). In this figure, a yellow ball is Si (Ge) atom and a red ball isO atom.

3Results and discussion

The calculated total energies of SiO2 of Cristobalite type,Quartz type, and Stishovite type per unit structure (one SiO2molecule) are shown in Fig. 2.
Cristobalite Quartz

Stishovite-984
To tal e n e rg y ( e V/SiO 2 u n it)

1Large scale integration (LSI) has been developed to behigher performance with downsizing. For the insulator thin film,
a lot of studies were performed to SiO2 which is currently acomponent of a transistor. On the other hand, Ge thin film isconsidered to be used on the Si substrate as the carrier mobility
is higher than that in Si crystal [1]. However, there are few
studies on GeO2. In this study, the mechanical properties ofGeO2 were analyzed by first principles calculation, and theresults were compared with SiO2.
It is quite difficult to analyze the amorphous structure ofactual SiO2 and GeO2 by first principles calculation. Therefore,
in this study, we considered the Cristobalite type, the Quartztype, and the Stishovite type for SiO2 and GeO2.

- 9 8 4 .2
- 9 8 4 .4
- 9 8 4 .6
- 9 8 4 .8-985- 9 8 5 .2

Fig. 2 Total energy of SiO2 modelThis result indicates that Cristobalite type is the most stablefor SiO2. The obtained densities are 2.18 g/cm3 (Cristobalitetype), 2.65 g/cm3 (Quartz type) and 4.18 g/cm3 (Stishovite type).
The calculated total energies of GeO2 of Cristobalite type,Quartz type, and Stishovite type per unit structure (one GeO2molecule) are shown in Fig. 3.

-980.6

Cristobalite Quartz

Stishovite(a)(b)

Fig. 1 Calculation model of(a) Cristobalite type，(b) Quartz type，(c) Stishovite type(c)

To tal energy (e V/Ge O2unit)-980.8-981-981.2-981.4-981.6

Fig. 3 Total energy of GeO2 modelIt was found that, for GeO2, Stishovite type is the moststable. The obtained densities are 13.8 g/cm3 (Cristobalite type),
3.99 g/cm3 (Quartz type) and 2.24 g/cm3 (Stishovite type).

Total energy (eV/SiO2 unit)

Next, the relationship between the total energy and theisotropic strain between -5% and 5% for SiO2 is shown in Fig. 4.

-983.8-984-984.4-984.6

GeO2 (GPa)Cristobalite

165.8

157.0

Quartz

135.0

54.2

Stishovite

170.3

129.5

Cristobalite-984.8-985

4Quartz-985.2-6-5-4-3-2 -1012Strain (%/SiO2 unit)

3456Fig. 4 Total energy-strain diagram of SiO2 model

It was found that the change of total energy of Quartz typeis smaller than other models. So Quartz type can deform easierthan Cristobalite type and Stishovite type. When the strain with
±3% is applied to SiO2, the most stable structure shifts from
Cristobalite type to Quartz type.
The relationship between the total energy and the isotropic
strain between -5% and 5% for GeO2 is shown in Fig. 5.

-980-980.2-980.4

Cristobalite-980.6-980.8-981

Stishovite-981.2
Quartz-981.4-981.6-6-5 -4-3 -2 -1 0 1
2Strain (%/GeO 2 unit)

345Conclusion

Mechanical properties of SiO2 and GeO2 crystals wereanalysed by the first principles calculation. It was found that, inSiO2 model, Cristobalite type is the most stable structure. On theother hand, in GeO2 model, Stishovite type is the most stablestructure.
The calculated result of bulk modulus indicates that GeO2
crystal is softer than SiO2 crystal.

-985.4

Total energy (eV/GeO 2 unit)

SiO2 (GPa)

It was found that the bulk modulus of SiO2 is larger thanGeO2 in each structure.
The results obtained in this study indicates that GeO2
crystal is softer than SiO2 crystal.

Stishovite-984.2

Table 1 Calculated bulk modulus of SiO2 and GeO2.

6Fig. 5 Total energy-strain diagram of GeO2 model
It was found that the change of total energy of Quartz typeis smaller than other models. So Quartz type can deform easierthan Cristobalite type and Stishovite type. When the strain with
±4% is applied to GeO2, the most stable structure shifts from
Stishovite type to Quartz type.
The calculated bulk modulus of SiO2 and GeO2 issummarized in Table. 1.

References[1] C. Claeys and E. Simoen, Germanium-based Technologies:
From Materials to Devices, Elsevier, Amsterdam, 2007.
[2] The CASTEP code is available from Accelrys Software Inc.
[3] W. Kohn and L. J. Sham, “Self-consistent equations
including exchange and correlation effects,” PhysicalReview, vol. 140, no.4A, pp. A1133, 1965.
[4] D. Vanderbilt, “Soft self-consistent pseudopotentials in a
generalized eigenvalue formalism” Physical Review B,
vol.41, no. 11,pp. 7892,1990.
[5] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalizedgradient approximation made simple,” Physical Review
Letters, vol. 77, no. 18, pp.3865, 1996.
[6] G. Kresse and J. Furthmü ller, “Efficient iterative schemes
for ab initio total-energy calculations using a plane-wave
basis set,” Physical Review B, vol.54, no. 16, pp.
11169,1996.
[7] T. H. Fischer and J. Almlo ̈ f, “General methods forgeometry and wave function optimization,” Journal of
Physical Chemistry, vol. 96, no. 24, pp. 9768, 1992.