Crystal growth rate limited by step length — the case of oxygen-deficient TiO2 exposed to oxygen

Abstract

We study how an oxygen-deficient crystal of TiO2 crystal grows when exposed to O2. While the O flux is external to the crystal, the Ti flux necessary for growth comes from internal (bulk) interstitials (Phys. Rev. Lett. 76 (1996) 791). We address where the reaction between O and Ti to form new crystal takes place in the regime of pure step flow (i.e., surface steps advancing without new-layers nucleating). The detailed partitioning of the growth flux among individual surface steps is studied using low-energy electron microscopy for two geometries on the (110) surface—an array of islands on a terrace and an island stack generated from a dislocation source. For both geometries, the areas of islands larger than the critical size grow at rates strictly proportional to their perimeter length, independent of the local step configuration. In addition, we find that the growth rate is proportional to the O2 pressure. The step flow represents a simple limiting case of crystal growth (Phil. Trans. R. Soc. A. 243 (1951) 299)—only the growth species near a step edge becomes incorporated into the crystal. That is, only Ti and O reactions near the step edge lead to crystal growth. This case is in marked contrast to crystal growth controlled by species attaching to terraces and diffusing to steps, for which the growth rates depend upon the local step environment. Indeed, simulating the island array as if the growth flux was partitioned among the individual islands by concentration gradients (i.e., diffusion-controlled growth) totally failed to reproduce the experimental rates.