Low temperature processing is necessary for the fabrication of thin-film transistors for electronics-on-glass applications, including active matrix flat-panel displays. One method to achieve this involves the use of pulsed excimer-laser annealing of an Amorphous silicon layer on top of an SiO2 layer. The intense UV laser is absorbed in the Amorphous silicon region, Maintaining a low average temperature. The thickness of the underlying SiO2 layer affects the solidification velocity and hence the grain size of the annealed layer. Previous work has concluded that the resultant grain size is small (<100 nm) and further work is needed in finding ways of increasing grain size. This paper describes how grain size is affected by varying the thickness of the SiO2 layer. Correlations will be discussed.between the solidification velocities and grain size as affected by the varying thickness of the SiO2 layer. The paper includes a comparison between experimental and theoretical results, using equations based on energy balance considerations.