1P041
STRESS AND STRAIN in Si/HfO2 INTERFACES
Department of Chemical System Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo,Tokyo 113, Japan.*, Nano & Giga Solutions, Gilbert, AZ, 85296, USA **)O Giacomo Giorgi *, Anatoli Korkin **, Koichi Yamashita *INTRODUCTION
Scaling electronic devices nowadays is one of the most active research areas in microelectronics.
Transistor performance has to be maintained with scaling of its lateral dimensions to smaller size,
thus imposing the SiO2 gate oxide thickness to be reduced proportionally. The growing tunnelingcurrent limits SiO2 gate oxide shrinking to about 1 nm. To retain the current progress of CMOS
technology, SiO2 has to be replaced by another material with higher dielectric constant. Recentanalysis has revealed hafnium oxide (HfO2) as one of the most promising candidates, butinterface defects and mobility degradation remain the challenges to overcome. In our atomistic
DFT study we designed of HfO2/Si interfaces for a comparative study Si/SiO2 systems in order toreveal the important trends in stress and strain and their relation to the electric properties. We usecomparative thermodynamic analysis in order to estimate the local stress at the interface and toestimate its components, chemical (intermediate oxidation state) and local mechanical (bonddeviation from their optimal values) and polarization. In particular, we have built up andoptimized three interfaces Si-HfO2, consisting of 100, 116, and 120 atoms (see Fig 1a-1c).
COMPUTATIONAL DETAILSAll calculations have been performed using DFT methods implemented in SIESTA [1] andVASP [2] program, which have numerical atomic orbitals and plane wave basis sets, respectively.
Both GGA [3] and LDA [4] level of theory have been employed in our calculations; in particular,in SIESTA calculations, PBE (Perdew-Burke-Ernzerhof) [1] XC functional has been employed at
GGA level of theory calculations, while CA (Ceperley-Alder) [1] functional has been employedat LDA level of theory. LDA/CA and GGA/PW91 (Perdew-Wang91) [2] calculations have been
performed with VASP package.
RESULTS
Our analysis on the three optimized interfaces reveals a high amount of the stress energy, i.e. theextra energy associated to the difference between the energies of the supercells and those of theircomponents (Si, HfO2, and SiO2) as described in [5]. In particular, as reference systems we havechosen the 8-atom unit cell for Si, the 12-atom unit cell (4 Hf and 8 O atoms) for monoclinic
hafnia (m-{HfO2}). As the reference system for SiO2, α-quartz unit cell structure has beenchosen for calculations using NAO/GGA/PBE, NAO/LDA/CA, and PW/LDA/CA approaches.
First, we have calculated the stress energy deriving from each component (Si and HfO2) to thethree Supercells taking into account the starting structures from which the Supercells have been
built up; we have let the two subcells, Si and HfO2, relax keeping fixed the lateral dimensions.
To evaluate the components of the stress we used bulk Modulus (K) and its first derivative (K’=∂K/∂P) calculated from the Birch-Murnaghan’s formula at both PW/GGA/PW91 andPW/LDA/CA level of theory. We also estimated the stress components by comparing energies ofrelaxed and constrained HfO2 and Si cells implying the lateral parameters of HfO2/Si supercell tothe separate HfO2 and Si units.

Fig. 1aFig. 1bFig. 1c

REFERENCES:[1] J.M. Soler, et al. J. Phys.: Condens. Matter 14, 2745 (2002) and references therein.
[2] G. Kresse, J. Furthmuller, Phys. Rev. B 54, 11169 (1996) and references therein.
[3] J.P. Perdew, et al. Phys. Rev. B 46, 6671 (1992); J.P. Perdew, Y. Wang, Phys. Rev. B
45, 13244 (1992).
[4] J.P. Perdew, A. Zunger, Phys. Rev. B, 23, 5048 (1981).
[5] A. Korkin, J.C. Greer, G. Bersuker, V. Karasiev, R.J. Barlett, Phys. Rev. B.73, 165312 (2006)