  We present thermodynamic crystallization and melting models and calculate
phase change velocities in $Ge_2 Sb_2 Te_5$ based on kinetic and thermodynamic
parameters. The calculated phase change velocities are strong functions of
grain size, with smaller grains beginning to melt at lower temperatures. Phase
change velocities are continuous functions of temperature which determine
crystallization and melting rates. Hence, set and reset times as well as power
and peak current requirements for switching are strong functions of grain size.
Grain boundary amorphization can lead to a sufficient increase in cell
resistance for small-grain phase change materials even if the whole active
region does not completely amorphize. Isolated grains left in the amorphous
regions, the quenched-in nuclei, facilitate templated crystal growth and
significantly reduce set times for phase change memory cells. We demonstrate
the significance of heterogeneous melting through 2-D electrothermal
simulations coupled with a dynamic materials phase change model. Our results
show reset and set times on the order of ~1 ns for 30 nm wide confined
nanocrystalline (7.5 nm - 25 nm radius crystals) phase change memory cells.
