Investigation of crystallization dynamics in phase-change material using the Master rate equation at ultrafast heating rates

Phase-change materials are widely used in non-volatile computer memories, and in arithmetic and logic processing applications. Phase-change based devices are also required to operate at different and high heating rates in response to electrical or optical excitations to achieve the required read-write rates. Crystallization is a fundamental and complex process involved in the phase transition operation in phase-change materials. It is sensitive to the nature of the phase-change material, its thermodynamic and kinetic parameters, geometric and interface effects, and thermal history. Thus, crystallization is the time limiting process in phase-change technologies. This work is concerned with theoretically understanding the crystallization dynamics of the Ge2Sb2Te5 (GST) phase-change material under different heating regimes and at the micro-structure level of the material to reduce crystallization times and increase the operating speed of phase-change devices and memories. A review and comparison of crystallization models was carried out to distinguish the more physically realistic Master rate equation method's ability to naturally trace both the nucleation and growth processes during crystallization, through the attachment and detachment of monomers to calculate the distribution of nano-cluster size distributions necessary to achieve the aims of this research. Full mathematical derivations and numerical implementation details of both the original discrete form of the Master rate equation and its approximate form were provided. Error analysis and computational experiments illustrated the limitations of the approximate form of the rate equation, and its detrimental sensitivity to the model parameters to justify the use of the discrete rate equation throughout this work. The crystallization rate is a strong function of the material's viscosity, and hence the physically realistic Mauro−Yue−Ellison−Gupta−Allan (MYEGA) model of the temperature dependence of viscosity was implemented in the Master rate equation. Crystallization simulations were carried out under ramped annealing conditions with heating rates from 50 K/s to 40,000 K/s to study the role of the viscosity model parameters (including the fragility index, glass transition temperature, and infinite temperature viscosity) on the crystallization dynamics. Those simulations showed, for high and low heating rates, the influence of the increasing fragility index on reducing the cluster nucleation time and increasing the crystallization speeds. Moreover, the increase of the glass transition temperature made a corresponding shift in crystallization temperature towards higher values. Furthermore, at low heating rates, infinite temperature viscosity parameter (i.e. extrapolated value of viscosity at temperature = ∞) has negligible effect on the crystallization dynamics while, at higher heating rates, smaller values of infinite temperature viscosity parameter increase the crystallization rate and final crystalline volume. Due to the relatively low computational cost of the Master rate equation method (compared to atomistic level computations), an iterative numerical algorithm was developed to fit Kissinger plots simulated with the Master rate equation system to experimental Kissinger plots from ultrafast calorimetry measurements at increasing heating rates. The simulations and analysis revealed the strong coupling between the glass transition temperature and fragility index, and highlighted the often ignored role of the dependence of the glass transition temperature on heating rate for the accurate estimation of the fragility index from analysis of experimental measurements. The extracted fragility indices in this work were lower than published values, highlighting the limitations of existing methods of extracting the viscosity parameters (using oversimplified analytical models with disparity in model parameters), and the importance of using detailed crystallization models for analysis of experimental measurements. Moreover, and for the first time, the variation of glass transition temperature with heating rate for GST was extracted from Kissinger measurements, in agreement with the values reported in the literature. The influence of the preparation conditions of amorphous GST on the crystallization dynamics was theoretically investigated using the Master rate equation by systematically implementing initial distributions of cluster sizes resulting from different thermal treatments such as melt-quenching and pre-annealing, and theoretical Gaussian initial cluster size distributions. Simulations of ramped pre-annealing to temperatures much lower than the crystallization temperature showed distributions of nano-clusters sizes of 2 - 8 nm in agreement with recently published high-resolution transmission electron microscopy measurements. Furthermore, the simulations explicitly showed the marked decrease in crystallization temperature (and therefore increase in crystallization speed) when there is predominately a narrow distribution of smaller crystalline clusters embedded in the initial amorphous phase.The Ministry of Higher Education of Iraq