Master-equation approach to the study of phase-change processes in data storage media

We study the dynamics of crystallization in phase-change materials using a master-equation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed using the thermodynamics of the processes involved and representing the clusters of size two and greater as a continuum but clusters of size one (monomers) as a separate equation. We present some partial analytical results for the isothermal case and for large cluster sizes, but principally we use numerical simulations to investigate the model. We obtain results that are in good agreement with experimental data and the model appears to be useful for the fast simulation of reading and writing processes in phase-change optical and electrical memories.

Figure 1

(a) Crystallization behavior of GST during isothermal anneals. The solid denote simulation results and symbols are experimental data from Ref. 13 for $T=131°\mathrm{C}$; the dashed line shows $T=119°\mathrm{C}$ and the dotted line $T=140°\mathrm{C}$. (b) Dependence of incubation time on the annealing temperature. The line shows simulation result. Symbols are experimental data taken from Ref. 13.

Figure 2

Numerical solutions of the master equation (1). (a) Initial iterations for $T=140°\mathrm{C}$. (b) Final cluster size distribution profile for $T=140°\mathrm{C}$—the final profile is determined by the exhaustion of monomer.

Figure 3

Crystallized fraction of the GST material as a function of temperature during a ramped anneal with a heating rate $3°\mathrm{C}∕\min$ starting at 120 °C. The line shows the result of simulation using our model, while the squares are experimental data from Ref. 35.

Figure 4

(a) Crystallized fraction of the GST material and (b) distribution of crystal sizes for two different anneals; during $A$ to $B$ the material is subjected to 240 °C for 0.1 s while between $C$ and $D$ it is subjected to 500 °C for a very short time $\tau$ (see text).