Diffusion of Metals in Silicon Dioxide

The diffusion coefficient and solubilities of several metals (Ag, Cu, Au, Pd, and Ti) have been investigated by bias temperature stress (BTS) of metal / SiO 2 / Si (MOS) structures using the candidate metal as the electrode. Temperatures ranged from 250° to 600°C, and the electric fields ranged from +10 6 to −10 6 V/cm in ambients of vacuum (10 −6 torr), nitrogen ( N 2 ) , and forming gas ( N 2 H 2 ) . In dry N 2 ( < 3 ppm H 2 O ) , the activation energy for silver diffusion is found to be 1.24 eV in the temperature range of 275°–365°C. The diffusion coefficient for silver at 300°C in silicon dioxide is 4.5 × 10 − 13 cm 2 / s . Copper diffusion has an activation energy of 1.82 eV in the temperature range of 350°–450°C in a forming gas environment ( < 3 ppm H 2 O ) and a diffusion coefficient in SiO 2 at 450°C of 1.2 × 10 − 11 cm 2 / s . A thermodynamic model to predict the activation energy of the solid solubility of these metals in SiO 2 and an interstitial diffusion model, that includes both strain and electrostatic energies, which predicts the diffusion activation energy, have been developed. Diffusion coefficients are estimated from a closed form solution of the diffusion equation and the observed behavior of the metal in SiO 2 .