Computer Simulation of Stress Distribution in Amorphous SiO 2 Thin Films
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ABSTRACT A molecular dynamics simulation of amorphous Si0 2 thin films has been made to investigate the structure and internal stress. The atomic configuration of the amorphous structure is investigated through the radial distribution function and the distribution of Si-O-Si bond angles. Distribution of internal stress through the specimen is evaluated from the volume and the shape of the Si0 4 tetrahedron, which is the elementally unit of amorphous Si0 2 . INTRODUCTION Thermal and elastic, and optical properties of glasses are known to show characteristic behaviors. The specific heat and the thermal conductivity are proportional to T and TV below 1 K, respectively, and the ultrasonic attenuation shows power dependence due to resonance absorption[1,2]. These phenomena have been attributed to the two level system (TLS) based on quantum mechanical tunneling, but the atomic structure responsible for the TLS is not so clear. Si0 2 glass is a representative materials for the study and various of investigations have been made. We have measured the internal friction of Ge-doped SiO 2 glass to investigate mechanical response of the glass structure[3,4]. On the other hand, amorphous SiO 2 thin films are important materials as an insulating materials in the electronics devises. The situation of the internal stress in the materials may closely related to the life time of the devises. One of the purposes of present paper is to investigate the distribution of the internal stresses in the material from the atomic configuration by the molecular dynamics computer simulation. METHOD OF SIMULATION A pair potential for Si0 2 developed by Tsuneyuki at al.[51 is used in the present simulation. The potential is based on ab initio cluster calculations, and is expressed by a simple function. 6 Ujq(r) = QQj 1/r + fo(b4 + bj) exp[(ag + aj - r)/(b 4 + bj)] - c-cj/r ,
(1)
where, r is the distance between atoms, ai is effective radius, and suffix i or j specifies the atom "Si" or "0". The RHS of the eq.(1) consists of a Coulomb interaction, a Born-Mayertype repulsion, and a dispersive interaction. The interaction energies between Si and 0, Si and Si, and 0 and 0 calculated from the potential are shown in Fig.1. 553 Mat. Res. Soc. Symp. Proc. Vol. 505 0 1998 Materials Research Society
Fig. 1
Atomic configuration of amorphous Si02
A model system consisting of 1000 Si-atoms and 2000 O-atoms was treated in the present simulation. As an initial condition, the atoms are arranged in the structure of the hightemperature phase cristobalite, because the density of the amorphous Si0 2 is close to the crystal. The shape of the model system is a cube, and the periodic boundary condition is adapted in x- and y-direction. The surface perpendicular to z-axis is set free to realize the thin film. Two model systems with the density p = 2.1 and 2.3g/cm3 are prepared and they are referred as "SI" and "S2" in this paper. Firstly, a particle velocity with random distribution was given to each atom. The mean kinetic energy of the atom corresponds to about 3000
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