A neural network potential for the phase change material gete: large scale molecular dynamics simulations with close to ab initio accuracy

Phase change materials based on chalcogenide alloys are attracting an increasing interest worldwide due to their ability to undergo reversible and fast transitions between the amorphous and crystalline phases upon heating. This property is exploited in rewritable optical media (CD, DVD, Blu-Ray Discs) and electronic nonvolatile memories of new concept, the Phase Change Memories (PCM). The strong optical and electronic contrast between the crystal and the amorphous allows discriminating between the two phases that correspond to the two bits of binary information zero and one. The material of choice for applications is the ternary compound Ge2Sb2Te5 (GST). However, the related binary alloy GeTe has also been thoroughly investigated because of its higher crystallization temperature and better data retention at high temperature with respect to GST. PCM devices, born thanks to the work of Ovshinsky in the late 1960s, offer extremely fast programming, extended cycling endurance, good reliability and inexpensive, easy integration. A PCM is essentially a resistor of a thin film of the chalcogenide alloy with a low field resistance that changes by several orders of magnitude across the phase change. In memory operations, cell read out is performed at low bias. Programming the memory requires instead a relatively large current to heat up the chalcogenide and induce the phase change, either the melting of the crystal and subsequent amorphization (RESET) or the recrystallization of the amorphous (SET). In the last few years, atomistic simulations based on density functional theory (DFT) have provided useful insights into the properties of phase change materials. However, several key issues such as the thermal conductivity at the nanoscale or the origin of the fast crystallization, just to name a few, are presently beyond the reach of ab initio simulations due to the high computational cost. In fact, first principles simulations can deal at most with 10^2 atoms on the timescale of 10^2 ps, while many properties like thermal conductivity or direct simulations of the crystallization process require at least 10^3 atoms on the timescale of 10^3 ps. The development of reliable classical interatomic potentials is a possible route to overcome the limitations in system size and time scale of ab initio molecular dynamics. However, traditional approaches based on the fitting of simple functional forms for the interatomic potentials are very challenging due to the complexity of the chemical bonding in the crystalline and amorphous phases revealed by the ab initio simulations. A possible solution has been proposed recently by Behler and Parrinello, who developed highdimensional interatomic potentials with close to ab initio accuracy employing artificial neural networks (NN). In this thesis work, we developed a classical interatomic potential for the bulk phases of GeTe employing this NN technique. The potential was validated by comparing results on the structural and dynamical properties of liquid, amorphous, and crystalline GeTe derived from NN-based simulations with the ab initio data obtained here and in previous works [10]. The NN potential displays an accuracy close to that of the underlying DFT framework at a much reduced computational load that scales linearly with the size of the system. It allows us to simulate several thousands of atoms for tens of ns, which is well beyond present-day capabilities of DFT MD. The development of a reliable interatomic potential with close to DFT accuracy is thus a breakthrough in the modeling of phase change materials. To date, we employed our NNP in order to investigate three issues: 1. the thermal conductivity of the amorphous phase 2. the viscosity and atomic mobility in the supercooled liquid and overheated amorphous phases 3. the dynamics of homogeneous crystallization of the liquid and amorphous phases Thermal conductivity is a key property for the PCM operation, as the phase changes corresponding to the memory writing/erasing processes strongly depend upon heat dissipation and transport. Moreover, thermal cross-talks among the different bits is a crucial reliability issue in PCM. Although experimental data on thermal conductivity are available for few materials in this class it is unclear whether the value measured in the bulk phase could also describe the behavior of the material in nanoscaled devices (10-20 nm) which might be smaller than the phonon mean free path. This is particularly relevant for PCM architectures based on nanostructures employing nanowires, colloidal nanoparticles, thin bridges and nanotubes. In fact, amorphous materials can also display propagating phonons with mean free path as long as 0.5 μm. This has been demonstrated for amorphous Si where propagating modes with long mean free path contribute to half of the total thermal conductivity. It is therefore of great technological relevance to assess whether similar propagating modes with long mean free path might be present in amorphous phase change materials as well. Atomistic simulations can provide crucial insights into the thermal transport properties of phase change materials suitable to aid a reliable modelling of the device operation. However, the calculation of the thermal conductivity in an amorphous system requires very long simulations (on the ns scale) of large models (thousands of atoms) that are presently beyond the reach of fully DFT simulations. The use of NN potentials allowed us to compute the mean free path of phonons in a-GeTe and to assess that ballistic transport is inhibited by disorder even at the nanoscale. The key property that makes some chalcogenide alloys suitable for applications in PCM is the high speed of the transformation which leads to full crystallization on the time scale of 10-100 ns upon Joule heating. What makes some compounds alloys so special in this respect and so different from most amorphous semiconductors is, however, still a matter of debate. The driving force for crystallization of the supercooled liquid is actually the free energy difference between the crystal and the supercooled liquid. However, the crystallization is controlled both by the driving force and by the atomic mobility. The driving force vanishes at melting and increases upon cooling. A large atomic mobility at high supercooling can thus boost the crystallization speed. These conditions can actually be met by fragile liquids. In fact, supercooled liquids are classified as fragile or strong on the basis of the temperature dependence of their viscosity [16]. An ideal strong liquid shows an Arrhenius behavior of the viscosity η from the melting temperature Tm down to the glass transition temperature Tg. On the contrary, in a fragile liquid η is very low down to a crossover temperature T∗, below which a steep rise of the viscosity (and thus a steep decrease in the mobility) is observed. If T∗ is sufficiently far from the melting temperature (Tm), high supercooling and large atomic mobility can be met at the same time. The question is thus whether phase change materials are fragile liquids or not. Due to the high crystallization speed it is unfortunately not possible to measure η below Tm experimentally. We have thus addressed this problem by MD simulations and we have demonstrated that indeed GeTe is a very fragile liquid (fragility index ∼ 100). Moreover a breakdown of the Stokes-Einstein relation between the viscosity and the diffusion coefficient is found, which further increase the atomic mobility down to temperatures very close to Tg. Hysteretic effects in the heating of the amorphous phase above Tg have been addressed as well. Finally, we have performed direct simulations of the homogeneous crystallization of the supercooled liquid and amorphous phases with 4000-atom models and simulation times of several ns. Although similar simulations have been previously performed by fully DFT simulations, the limitations in size (about 200 atoms) and time scale (500 ps) prevented a reliable estimate of the size of the critical nucleus and of the crystallization speed, which are instead accessible by our large scale simulations. This thesis is organised as follows: in the introductory chapter 1 I provide essential information about phase change materials and phase change memories. Chapter 2 is dedicated to theory and methods, while chapters 3,4,5 and 6 are devoted to the results on the thermal conductivity of the amorphous phase of GeTe, on the properties of its supercooled liquid phase and on the homogeneous crystallization from the melt and the overheated amorphous phase.