Evidence of a long-range density gradient inSiO2films on Si fromH2-permeability measurements

We describe a technique for the measurement of the diffusivity, solubility, and permeability of ${\mathrm{H}}_2$ through ${\mathrm{SiO}}_2$ thermally grown on Si substrates at room temperature. We have applied this technique to determine the dependence of the ${\mathrm{H}}_2$ permeability on oxide thickness and growth temperature. Since permeability depends strongly on density, these measurements provide a sensitive probe of the oxide density. Our results indicate that the ${\mathrm{H}}_2$ permeability is considerably less in ${\mathrm{SiO}}_2$ films thermally grown on Si substrates than through bulk ${\mathrm{SiO}}_2$, in agreement with previous works which had indicated that thermally grown oxides are denser than bulk ${\mathrm{SiO}}_2$. The permeability is found to decrease with oxide thickness, indicating that thinner oxides have larger densities than thicker oxides. Oxides grown at high temperatures are found to have higher permeabilities than oxides of similar thickness grown at lower temperatures. We present evidence that the dependence of permeability on oxide thickness results from a density gradient throughout the oxide rather than from a uniform reduction of the oxide density as the oxide becomes thicker.