The diffusion and segregation coefficient of germanium in silica

Abstract

This research was instigated to study non-equilibrium segregation effects during the crystallization of a glass. The non-equilibrium segregation coefficient has been experimentally measured in a variety of alloys including silicon and it has been observed to increase by orders of magnitude as a function of growth rate. Monte Carlo modeling has successfully simulated this effect and has led to the analytical Jackson equation which describes it. Glass crystallization usually takes place far from equilibrium and glasses have the advantage that the glass-crystal interface does not move during quenching, and so the segregation effects can be evaluated at room temperature. The germanium in silica system was chosen for this study because germanium should substitute for the silicon and the glass matrix, and diffuse slowly enough in silica to permit evaluation of the non-equilibrium segregation. Samples were prepared by implanting silica glass with germanium, and then annealing to permit diffusion and to promote crystallization. The samples were analyzed with RBS before and after annealing to determine the distribution of germanium. Initially, the implanted germanium peak was observed to shift towards the surface which is attributed to ion drift in an electric field. This effect was eliminated with a pre-anneal which incorporated the germanium ions into the glass matrix. Since the non-equilibrium segregation depends on the dopant diffusion rate, the diffusion coefficient of germanium in amorphous and crystalline silica was measured. The diffusion coefficient in the silica glass was found to be DG=47exp(-5.8x 10⁴/T) cm²/s and the diffusion coefficient in the silica crystal was found to be DC=360exp(-(6.9x 10⁴/T)) cm²/s . The non-equilibrium segregation coefficient was evaluated based on the distribution of the dopant after crystallization, including the build-up of dopant at the crystal/glass interface. When fitted to the Jackson equation the equilibrium distribution coefficient was found to be k(eq) = 0.01. The non-equilibrium segregation coefficient increased with crystallization rate.