# Interplay of glass dynamics and crystallization kinetics in amorphous phase change materials

• Zusammenspiel von Glasdynamik und Kristallisationskinetik in amorphen Phasenwechselmaterialien

Aachen : RWTH Aachen University (2022)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2022

Abstract

In the pursuit for hardware implementations of artificial intelligence and brain-inspired neuromorphic computing, the utilization of phase change materials (PCMs) offers great potential. PCMs exhibit a large contrast in electrical resistivity and optical reflectivity between the amorphous and crystalline phase, data non-volatility as well as rapid phase switching. A phase switch is introduced either by amorphization via melt-quenching or by crystallization. While PCMs are already utilized successfully in ordinary binary data storage, synaptic weights are emulated by varying the crystalline volume fraction in a single multi-level memory cell. There are two challenges yet to overcome to increase the applicability of PCMs in future memory devices. First, the resistivity of amorphous PCMs drifts and continuously increases due to structural relaxation of the glassy phase, which compromises the unambiguous determination of the programmed multi-level state. Second, crystallization takes an order of magnitude longer than amorphization and therefore represents the rate limiting step that must be accelerated to maximize data processing ability. Finding solutions to minimize or even reverse the resistance drift requires a detailed understanding of the glassy phase, structural relaxation, and glass dynamics as well as about the influence of thermal treatment. To address the second challenge, the crystallization kinetics of amorphous PCMs must be well understood to allow an accurate prediction of the conditions that accelerate this process. The rate of crystallization is particularly dependent on whether PCMs crystallize from the (amorphous) unstable glassy phase or the (amorphous) meta-stable undercooled liquid (UCL), because their temperature dependence is inherently different. Crystallization is generally faster in the glassy phase due to the frozen-in, more open structure, while the glassy phase experiences a steady deceleration caused by structural relaxation that is absent in the UCL. However, the question of which phase PCMs crystallize from is currently debated in literature with arguments for both sides. This ambiguity is accompanied by a significant scatter in reported temperature values where the glass transition occurs. In contrast, literature on the resistance drift is quite clear that PCMs at low temperatures are in a glassy phase that relaxes structurally. To address both challenges, this work focuses on the correct determination, the qualitative and quantitative description of the amorphous phase that is crystallizing. Additionally, the identification of glass dynamics' features and its influence on physical properties is investigated for multiple PCMs and several non-PCM as reference. To identify the amorphous phase that is crystallizing in this work, the calorimetric response and the effect structural relaxation has on resistivity, viscosity and medium range order of fourteen amorphous chalcogenides including nine PCMs is measured and analyzed in considerable detail. From the calorimetric measurements, characteristic features of crystallization and glass dynamics such as enthalpy relaxation and the glass transition are determined. It is found that all PCMs, except for Ge$_{3}$Sb$_{6}$Te$_{5}$, crystallize during enthalpy relaxation before the glass transition takes place, which unambiguously demonstrates that they crystallize from the glassy phase. In contrast, all non-PCMs, except for Sb$_{2}$Se$_{3}$, crystallize after the glass transition was observed, indicating that here crystallization occurs from the UCL. Whenever there is a notable glass transition, the glass transition temperature $T_\mathrm{g}$ is found directly and unambiguously from calorimetric measurements. The fact that for most PCMs the glass transition is obscured by crystallization may cause the controversy regarding the amorphous phase that crystallizes and the large scatter in reported $T_\mathrm{g}$ values. Nevertheless, analyzing the exotherm of enthalpy relaxation and partly crystallizing tellurium in Ge$_{15}$Te$_{85}$ allowed for the determination of the glass transition temperature $T_\mathrm{g}$ of the three prominent PCMs Ag$_{4}$In$_{3}$Sb$_{67}$Te$_{26}$ (AIST), Ge$_{2}$Sb$_{2}$Te$_{5}$ and GeTe. $T_\mathrm{g}$ together with the parameter of fragility $m$ is needed to predict the temperature dependence of the viscosity in the UCL. Here, the fragility for several materials is found from fitting literature viscosity data and from the cooling rate dependence of the glass transition. The fragility measurements reveal a fragile-to-strong transition (FST) within the UCL in GeSe and Ge$_{3}$Sb$_{6}$Te$_{5}$. Such an FST is beneficial for amorphous phase stability at low temperature and high crystallization speed at high temperature. Contrary to GeSe, Ge$_{3}$Sb$_{6}$Te$_{5}$ shows PCM characteristics and therefore the presence of a FST further underlines its potential for memory applications. If resistance drift in amorphous chalcogenides is caused by structural relaxation of the glassy phase, resistance convergence and even drift inversion should be possible under appropriate conditions. These conditions are applied to a non-PCM and a PCM and indeed the drift convergence and the drift inversion are observed. Moreover, the relaxation can be described by conventional glass dynamics, so that a mathematical prediction of the resistance drift is possible. Furthermore, it is shown that the enthalpy relaxation can be described with the same model. The experimental proof and the mathematical description of resistance drift inversion is important for the integration of PCM-based multi-level data storage for brain-inspired novel calculation schemes for e.g. artificial intelligence or in-memory computing as it enables drift correction techniques. Besides a detailed investigation of glass dynamics, the crystallization is studied at various heating rates. Crystallization shows a maximum at the crystallization peak temperature $T_\mathrm{p}$, which follows an Arrhenius-like heating rate dependence when crystallized from the glassy phase and a curved super-Arrhenius-like heating rate dependence when crystallized from the UCL phase in Kissinger's analysis. This difference constitutes an additional criterion of judging at what applied heating rate and temperature a material crystallizes from the glassy phase or the UCL. The conclusion based on the $T_\mathrm{p}$ data confirms the distinction found from calorimetric data. When crystallized from the glassy phase, pre-annealing is observed to affect (hamper) this phase transition because of structural relaxation of the glassy phase while for the UCL, pre-annealing shows no significant effect on crystallization. Additionally, in PCMs identified to crystallize from the glassy phase, the activation energy of crystallization changes drastically when surpassing a critical heating rate $\vartheta_\mathrm{c}$, indicating a change in the crystallization mechanism. This drastic decrease in activation energy is explained by the emerging glass transition interfering with crystallization as the heating rate $\vartheta$ is increased. Support for that conclusion is obtained from numerical simulations. They confirm the experimental data including the decrease in activation energy by implementing an instantaneous glass transition. Thus, the critical heating rate marks the turning point from glassy phase to UCL crystallization. In conclusion, based on the observations obtained in this work, the amorphous phase that is crystallizing is identified unambiguously. This finding enables the correct prediction of crystallization in engineering PCM devices since the temperature dependence is now predictable as the developed numerical model shows. Additionally, the discovery and the successful mathematical description of the resistance drift inversion aids the implementation of multi-level data storage needed for advanced computational schemes.