In the era of information technology, the demand for data storage and processing is increasing exponentially. The global size of data sets generated by mobile elec-tronics, high- definition video devices, fundamental research and advanced technologies, including artificial intelligence (AI) and supercomputing, doubles every 2 years. The global data volume is estimated to reach 44 zettabytes by 2020 (ref.1) and will soon go beyond the capabilities of current computing and memory devices. To cope with the burden, changes in computing archi-tecture and hardware are urgently needed2,3. Today, computing devices use the von Neumann frame with separate processing and memory units; more specifi-cally, for every operation, data are sent to the central processing unit (CPU) for processing and then trans-ferred back to the memory units. In memory units, there is a complex hierarchy of speed and capacity (fig. 1a). This hierarchy comprises fast but volatile static and dynamic random access memories (SRAMs and DRAMs, respectively) and non- volatile but slow flash- based solid- state drives (SSDs) and magnetic- based hard disk drives (HDDs), on which data are stored even in the absence of supplied power. Frequently accessed data sets are loaded temporarily in SRAMs (cache mem-ory) and DRAMs (main memory), while the remaining data are kept in SSDs and HDDs for long- term storage. The shuffling of data between these units creates traffic jams, and it is unlikely that the overall computing effi-ciency can be increased by several orders of magnitude

by simply improving the performance of the computing and memory units separately.

Non- volatile memory4–9 and neuro- inspired comput-ing10–15 are promising technologies to overcome the data traffic bottleneck. Non- volatile memory devices com-bine the advantages of non- volatility and fast operation speed, thus making the distinction between data storage and memory obsolete. Neuro- inspired computing uni-fies computing with storage in a single cell, marking a shift to non- von Neumann computing architectures15. The goal is to construct neuro- inspired computing sys-tems using electronic devices, which are several orders of magnitude faster than standard devices and provide higher density and lower power consumption with long- term data retention. Candidates for non- volatile memory and neuro- inspired computing devices include phase- change materials (PCMs)16–19, resistive- switching oxides20–23, spintronic materials24–26, ferroelectric materials27,28, 2D and van der Waals materials29,30, carbon nanotubes31,32 and organic materials33,34.

Among emerging memory devices, PCM- based RAMs (PRAMs) are the most mature. Joint efforts by Intel and Micron, that is, Optane memories, which are based on a 3D crossbar array structure35 (fig. 1b), have entered the market as storage class memories (SCMs)36,37. These SCMs fill the performance gap between DRAMs and SSDs. On 31 May 2018, Intel announced their first persistent memory product based on the 3D XPoint technology — Optane DC Persistent Memory38.

Designing crystallization in phase- change materials for universal memory and neuro- inspired computingWei Zhang 1*, Riccardo Mazzarello 2, Matthias Wuttig 3,4 and Evan Ma5

Abstract | The global demand for data storage and processing has increased exponentially in recent decades. To respond to this demand, research efforts have been devoted to the development of non- volatile memory and neuro- inspired computing technologies. Chalcogenide phase- change materials (PCMs) are leading candidates for such applications, and they have become technologically mature with recently released competitive products. In this Review , we focus on the mechanisms of the crystallization dynamics of PCMs by discussing structural and kinetic experiments, as well as ab initio atomistic modelling and materials design. Based on the knowledge at the atomistic level, we depict routes to improve the parameters of phase- change devices for universal memory. Moreover, we discuss the role of crystallization in enabling neuro- inspired computing using PCMs. Finally , we present an outlook for future opportunities of PCMs, including all- photonic memories and processors, flexible displays with nanopixel resolution and nanoscale switches and controllers.

1Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, China.2Institute for Theoretical Solid- State Physics, JARA- FIT and JARA- HPC, RWTH Aachen University, Aachen, Germany.3Institute of Physics IA, JARA- FIT and JARA- HPC, RWTH Aachen University, Aachen, Germany.4Peter Grünberg Institute PGI-10, Forschungszentrum Jülich GmbH, Jülich, Germany.5Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD, USA.

*e- mail: wzhang0@ mail.xjtu.edu.cn

https://doi.org/10.1038/ s41578-018-0076-x

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This device is slightly slower than high- performance DRAMs but has a larger storage capability (512 GB) and non- volatile features. If these persistent memory devices are integrated with high- performance DRAMs, the computing efficiency of large servers and computing clusters will be improved by a few orders of magnitude38. This product is an important step towards the replace-ment of DRAMs and SSDs with a universal memory device based on PCMs, as proposed in 2005 (ref.39). Improvements on performance of PRAMs in terms of access time and storage density are still being pursued, as PCMs can achieve switching times of a few nano-seconds and even subnanosecond in memory cells of submicrometre dimensions40, and the size can be scaled down further to a few nanometres41. The subnanosec-ond speed extends the concept of universal memory to include SRAMs as well. In addition, the fabrication cost of PRAMs is shown to be competitive, as the cost per gigabyte is approximately 10–100 times less than that of DRAMs and SRAMs37 (fig. 1a). Therefore, phase- change

universal memory may lead to electronic devices with improved computing efficiency by simplifying the mem-ory hierarchy and eliminating the bus congestion, as a consequence of massive data transfer between SSDs, DRAMs and SRAMs.

To store data, PRAMs exploit the large contrast in electrical resistance between the amorphous state (0) and crystalline state (1) of PCMs42 (fig. 1c). This con-trast originates from differences in structural disorder, carrier concentration and bonding mechanism43–49. The fast and reversible phase transition between the two states at elevated temperatures and yet the good ther-mal stability at room temperature guarantee the speed and retention times required for non- volatile phase- change applications. In phase- change devices, the local temperature is controlled by the length and strength of the applied voltage pulse via Joule heating. The write or SET process is accomplished by crystallization at tem-peratures of ~500–600 K (ref.50), and the erase or RESET process is achieved by amorphization (fig. 1c) via melting

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Fig. 1 | Current and emerging computing units. a | The memory hierarchy of current computing devices can be categorized into the non- volatile data storage type — hard disk drives (HDDs) and solid- state drives (SSDs) — and the volatile memory type — dynamic random access memory (DRAM) and static RAM (SRAM). Faster operation speed is accompanied by a decrease in storage capability and an increase in fabrication cost. Phase- change materials (PCMs) have an ideal combination of fast speed, non- volatility , large storage density and medium fabrication cost. b | 3D XPoint setup35. Memory units (green) are covered by Ovonic threshold switching selectors (yellow) to prevent current leakage. These selectors employ the threshold switching effect of chalcogenide glass, such as As- doped Se–Ge–Si (ref.36). c | Phase- change principle. Large contrast in electrical resistance between the amorphous and crystalline phases of PCMs defines the two logic states as 0 and 1. Fast and reversible switching between the two states is achieved by crystallization (SET/write) and amorphization (RESET/erase). Panel a is adapted with permission from Fong, S. W. et al. Phase- change memory — towards a storage- class memory. IEEE Trans. Electron Devices 64, 4374–4385 (ref.37), © (2017) IEEE.

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at temperatures greater than ~1,000 K and subsequent rapid quenching5,51–53. The amorphization process can be as fast as tens of picoseconds54, while crystallization is the bottleneck, because it typically occurs in tens to hun-dreds of nanoseconds. Thus, understanding the micro-scopic origin of crystallization kinetics with the aim to improve the SET speed is a major goal in the field5,51–53.

Neuro- inspired computing has been demonstrated with phase- change devices that exploit the accumula-tion mode of the crystallization kinetics of PCMs to emulate the behaviour of biological neurons, includ-ing the integrate- and-fire functionality17,55 and the synaptic learning rules56,57. Instead of crystallizing the amorphous component completely with a single voltage pulse, it is possible to crystallize it cumulatively using multiple short pulses. During this process, the electrical resistance of the memory cell changes in a nonlinear manner and is dependent on the previous excitation58,59. This analogue behaviour can be classi-fied as memristive, and PCMs have also been termed as memristors59–62.

In this Review, we focus on the crystallization kinet-ics of PCMs. First, we introduce the material compo-sition and structural features of PCMs and discuss the relationship between structure and the mode of crys-tallization. Second, we discuss the atomistic origin of nucleation and highlight the role of ab initio materi-als design in suppressing the stochasticity for ultrafast incubation. Third, the crystal growth of PCMs from nuclei as well as from planar crystalline–amorphous interfaces is reviewed, and the underlying microscopic mechanisms are elucidated. Fourth, we discuss the strong temperature dependence of the liquid dynamics enabling phase- change data storage and explain how this property can be rationalized in terms of the large fragility of PCMs. Finally, we outline a future perspec-tive in terms of materials design and device engineer-ing to realize universal memory and neuro- inspired computing devices.

Material compositionThe first phase- change chalcogenide — Ge10Si12As30Te48 — with reversible resistive- switching characteristics was synthesized in the 1960s42, but its slow crystalli-zation and limited cycling endurance hindered its applications. PCMs became popular in the late 1980s after the discovery of the binary GeTe (ref.63) and the ternary GeSbTe compounds along the pseudobinary GeTe–Sb2Te3 tie line64, such as Ge2Sb2Te5, Ge1Sb2Te4 and Ge8Sb2Te11. As a consequence of their fast crystalliza-tion and good optical contrast, these compounds led to the development of rewritable optical storage products, including rewritable compact discs, digital versatile discs and Blu- ray discs. A few years later, doped Sb2Te and doped Sb compounds were identified as candidates for rewritable optical applications65,66. One alloy in the doped Sb2Te class, with a composition close to that of Ag4In3Sb67Te26 (AIST), has been widely used. The three classes of PCMs are shown in the Ge–Sb–Te ternary diagram (fig. 2a). At a later stage, more sophisticated maps67 enabling a systematic search for PCMs were devel-oped. These maps are based on bonding characteristics

and exploit the fact that the crystalline state of PCMs shows an unconventional bonding mechanism, called metavalent or resonant bonding, characterized by pronounced electron delocalization48,68–70.

Parallel to the development of the phase-change optical data storage industry, many companies and research institutions renewed their interests in electro-nic phase- change memories in the 2000s. In 2005, short programming times (<50 ns) were achieved using phase-change devices16, which indicated the creation of universal memory using PCMs39. The three classes of PCMs were tested in memory devices, and the GeSbTe compounds (in particular, Ge2Sb2Te5 (GST)) became the materials of choice because of their higher cyclability and were subsequently used in commercialized pro-ducts36. However, to improve the speed and energy consumption of phase-change devices for universal memory, studies of the fundamental properties of PCMs are needed.

Growth versus nucleationThe crystallization kinetics of PCMs at elevated temperatures are either nucleation driven or growth driven71 (fig. 2b). For growth- driven (slow nuclea-tion) PCMs, crystallization of an amorphous region surrounded by a crystalline matrix proceeds rapidly at the crystalline–amorphous interface, and no size-able and robust crystalline seeds form during the short timescale involved in the growth process. In situ trans-mission electron microscopy (TEM) studies confirm that AIST is a growth- driven PCM72. The recrystal-lized phase forms a single crystallite, because there is no obvious contrast between the recrystallized region and the surrounding crystals (fig. 2b, right panels). In nucleation- driven (fast nucleation) PCMs, crystal-lization occurs via the stochastic formation of critical nuclei and their subsequent growth. The recrystallized region is polycrystalline, with grains of different orien-tations. The size of the grains depends on the temper-ature and ranges from several nanometres to several tens of nanometres. TEM experiments on GST indi-cate that its crystallization is nucleation driven72. In the TEM image of GST (fig. 2b, left panels), the central recrystallized region contrasts with the surrounding GST crystals because of the difference in the size and orientation of the grains.

The crystallization modes of GST and AIST differ because of the large variation in their nucleation rates. Nucleation is a stochastic process mediated by thermal fluctuations. Two competing effects, the driving force (volume effect) and the interfacial energy (surface effect), determine the height of the free- energy barrier for nucleation. According to classical nucleation theory, the free energy of the system rises as atoms are added to a subcritical nucleus, because of the interface penalty. This free energy starts to decrease when the nucleus reaches a critical size. The build- up of the critical- sized nuclei requires an incubation period73. The larger the driving force and/or the lower the interfacial energy, the smaller the size of the critical nucleus. The critical size varies with temperature, because the driving force and the interfacial energy are temperature- dependent

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(with typical interfacial energies on the order of 35 meV per atom at 800 K (refs74,75)). In classical nucleation the-ory, the nucleation rate exhibits a well- defined maxi-mum at a temperature determined by two factors acting in opposition to each other: with decreasing temper-ature, the driving force increases (reducing the size of the critical nucleus), but the atomic jump rate also decreases (reducing the rate of atomic attachment to the nuclei)73. However, such approximation is inadequate to describe ultrafast nucleation processes in PCMs as a consequence of the non- isothermal condition and non- equilibrium dynamics in phase- change devices.

The incubation process at elevated temperatures takes a few nanoseconds in GST76, while the process takes >20 μs in AIST77. In both cases, films were ~30 nm

thick and capped with suitable materials to suppress boundary- assisted crystal growth (and to prevent oxi-dation). Structural characterization experiments and ab initio simulations on the crystalline phase and the amorphous phase have shed light on the large difference in nucleation rate between GST and AIST, as discussed in the next section.

Structural propertiesUpon nanosecond switching, GST crystallizes in a cubic rocksalt phase with a Te sublattice and the other sublattice randomly occupied by 40% Ge, 40% Sb and 20% atomic vacancies64,78. Recrystallized AIST forms an A7 structure, with a statistical distribution of the four elements79. Hence, the crystalline states obtained

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Fig. 2 | Prototypical phase- change materials. a | The important classes of phase- change materials (PCMs) are found in the Ge–Sb–Te ternary diagram, including GeSbTe compounds along the GeTe–Sb2Te3 pseudobinary line, doped Sb2Te and doped Sb compounds. b | The modes of crystallization in PCMs are either nucleation driven (for example, Ge2Sb2Te5 (GST)) or growth driven (for example, Ag4In3Sb67Te26 (AIST)). The transmission electron microscope (TEM) images show the crystallized states upon heating (marked by the red circles). The TEM images show the outcome of a recrystallization experiment. The region marked by the red circles corresponds to the recrystallized PCM upon heating. In the case of GST, this region displays a clear contrast with its crystalline surrounding owing to the difference in grain size and orientation, showing that crystallization was driven by nucleation. By contrast, AIST exhibits no contrast, indicating a smooth crystal growth from the boundary , yielding a single- crystalline state. The distributions of primitive rings of different size in amorphous GST and AIST are shown in panels c and d. c | Fourfold primitive rings are the dominant structural fragments in amorphous GST. The inset shows an amorphous model of GST, with two ABAB squares and a cube (A = Ge or Sb, B = Te) highlighted. d | In amorphous AIST, the distribution of primitive rings is broad, with fivefold primitive rings being the most abundant structural fragments. The inset shows an amorphous model of AIST, in which some fivefold primitive rings are highlighted. Ge, Sb, Te, Ag and In atoms are rendered in grey , yellow , blue, orange and purple, respectively. The TEM images in panel b are reproduced from ref.72, CC- BY-3.0.

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in phase- change devices are highly disordered, in terms of compositional randomness and structural distortion. In particular, most of the atoms display distorted and/or defective octahedral coordination (fig. 1c).

For many years, the structures of GST and the par-ent compound GeTe in the amorphous phase were under debate. Early experiments using extended X- ray absorption fine- structure spectroscopy suggested that the majority of Ge atoms were tetrahedrally coor-dinated, and an umbrella flip model was proposed to explain the fast crystallization18. This view was chal-lenged by ab initio molecular dynamics (AIMD) simu-lations based on density functional theory80,81, which yielded amorphous models containing only one- third Ge atoms in a tetrahedral coordination. The majority of Ge atoms were in a defective octahedral coordina-tion82–86. As revealed by local energy and bonding analy-sis, these tetrahedral Ge units are stabilized locally by the quenched- in homopolar Ge–Ge bonds87 and should disappear during the spontaneous structural relaxation of the glass46,47 accompanied by a reinforced bond distor-tion. This ageing model is in line with X- ray absorption near- edge structure measurements88 and is supported by TEM measurements combined with local reverse Monte Carlo simulations, in which Ge atoms in amor-phous GST are found in an octahedral coordination but with more pronounced bond distortion than their crystalline counterparts89.

Further analyses of the short- range and medium- range order of the amorphous network through primitive rings topology79,83 provide insights into the crystallization behaviour of GST and AIST. In amor-phous GST, fourfold primitive rings are the most abun-dant structural fragments (fig. 2c), and more than 80% of these fourfold primitive rings have the form ABAB (A = Ge or Sb, B = Te), as supported by AIMD calcula-tions82,83 and reverse Monte Carlo simulations based on synchrotron- radiation X- ray diffraction data90. These ABAB squares are the smallest structural units in rock-salt GST, and two ABAB squares can combine to form a cube (fig. 2c, inset). Hence, these squares are considered the key structures for fast nucleation in GST83,90. By con-trast, amorphous AIST shows a broader distribution of primitive rings from threefold to sevenfold, with fivefold primitive rings being the most numerous (fig. 2d). These structural fragments deviate from the local octahedral environment in crystalline AIST, presumably resulting in a lower nucleation rate79.

Origin of nucleationIntrinsic stochastic nature. Direct dynamical simula-tions of the crystallization process of PCMs are desir-able to test the proposed link between nucleation rate at elevated temperatures and local structural motifs in the amorphous phase at room temperature. To this end, AIMD simulations are typically used, because they yield quantum mechanical accuracy and, thus, are capable of describing complex and rapidly changing chemical con-figurations. The very small timescales and length scales relevant to the crystallization process in ultrascaled PCM memory cells are accessible with AIMD simula-tions at an acceptable computational cost: for example,

a 0.5 ns AIMD trajectory for a model of GST containing 460 atoms (corresponding to a size of ~2.4 × 2.4 × 2.4 nm3) can be obtained in several months of computing time on a parallel computing cluster using accelerating meth-ods91 and efficient AIMD codes92,93. The first AIMD crystallization simulation of GST was accomplished for a 72-atom model during quenching from the liquid state94. This simulation revealed the fast crystallization tendency in GST, partly because of strong finite- size effects as a result of periodic boundary conditions. For GST models containing 180–460 atoms, the spurious finite- size effects are reduced. The simulations at 600 K showed that the crystallization time fluctuated between 0.12 ns and 8 ns, reflecting the stochastic nature of the nucleation process95–101. This stochasticity is related to the fact that the crystalline precursors, that is, ABAB squares and cubes, which are found in amorphous GST at room temperature, are not stable at elevated tempera-tures97–99. The ABAB squares break and reform rapidly98,102 (fig. 3a) at 600 K, with an average lifetime of ~5 ps (ref.40), and even an embedded crystalline seed containing 58 atoms in a 460-atom GST model disappears quickly at this temperature99. Therefore, these simulations suggest that the stochastic nature of nucleation prevents further optimization of the memory writing time for pure GST.

Bypassing incubation via pre- programming. Although GST nucleates rapidly, the rate is not sufficient to increase the operation speed to compete with fast DRAMs and SRAMs, which require subnanosecond switching times (fig. 1a). Furthermore, a strategy must be devised to increase the crystallization speed at ele-vated temperatures while not significantly affecting the long- term data retention at room temperature. To overcome the bottleneck caused by stochastic incu-bation, a pre- programming strategy was developed76: in this strategy, a constant low- voltage pulse was applied for 10 ns to an ~30 nm- thick pore- like memory cell, and a SET time of 0.5 ns was achieved76, which is an order of magnitude faster than that of GST devices of simi-lar size with single- pulse switching103. The explanation for this finding was a structural pre- ordering process induced by the constant voltage pulse, which induces pre- seeding of nuclei inside the amorphous matrix. As a result, the memory cell is quickly switched to the crystalline state through crystal growth from multiple nuclei76. However, this pre- programming strategy is not suitable for the high- frequency data access required for DRAM and SRAM replacements, as the time needed for each SET operation, including the pretreatment stage, exceeds 10 ns.

Reducing stochasticity by materials design. To achieve subnanosecond writing in the absence of pre- programming, an ab initio materials design strategy was developed to reduce the intrinsic stochasticity of incubation: stabilize the crystalline precursors with marginal changes to the amorphous network40. To avoid the structural complexity stemming from tetrahedral structures, Sb2Te3 was chosen as the host compound. Sb2Te3 forms a metastable cubic rocksalt phase104 upon fast crystallization; moreover, the material displays only

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defective octahedral coordination in the amorphous phase105,106, which resembles the crystalline phase. Amorphous Sb2Te3 crystallizes more rapidly than GST at high temperatures but has poor thermal stability at room temperature104. A small percentage of dopants improves the stability of the amorphous phase107,108, but the choice of dopants is important so as not to alter the amorphous network. Therefore, the materials design needs to identify dopant atoms that can promote the formation of ABAB squares and cubes with higher bonding strength than the crystalline precursors of the host material.

Transition metals are good dopants because their tellurides have high melting points. A screening of transition- metal tellurides (fig. 3b) reveals six com-pounds — Sc2Te3, YTe, MnTe, ZnTe, CdTe and HgTe — that pass the geometry criterion, because they form cubic structures with bond lengths close to 3.0 Å (the average length of Sb–Te bonds in cubic Sb2Te3).

This geometrical conformability should reduce the interface energy and consequently the nucleation bar-rier, facilitating crystallization. Further cohesive energy calculations and quantum chemistry bonding analyses by the crystal orbital Hamilton population109–112 method identified Sc as the optimal alloying element, as it forms stronger chemical bonds with Te than with Sb (ref.40). The stabilized crystalline precursors effectively increase the nucleation site density, shifting the peak in the tem-perature–time–transformation diagram to speed up the crystallization.

Subnanosecond crystallization. Subsequent experiments indicated that an ~4% concentration of Sc atoms, corresponding to Sc0.2Sb2Te3 (SST), is optimal and that SST crystallizes in the cubic rocksalt phase in a temperature window similar to that of GST. The resistance contrast between the amorphous phase and rocksalt phase was over two orders of magnitude,

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Fig. 3 | Nucleation rate by materials design. a | The evolution of a potential Ge2Sb2Te5 (GST) nucleus at ~600 K from ab initio molecular dynamics (AIMD) simulations, in which ABAB squares and cubes break and reform rapidly. b | Material screening over transition- metal tellurides. Blue squares marked with black outlines are the tellurides that have the cubic rocksalt phase, compatible with rocksalt Sb2Te3 (top- right corner). All transition- metal tellurides except gold telluride have a higher melting temperature than rocksalt Sb2Te3. The calculated formation energy and chemical bonding features indicate that rocksalt Sc2Te3 is more robust than rocksalt Sb2Te3(ref.40). c | Primitive ring analysis showing that a small addition of Sc in Sb2Te3 does not alter the amorphous structural patterns for fast nucleation. The inset shows an amorphous model of Sc0.2Sb2Te3 (SST), in which two ABAB squares and a cube (A = Sc or Sb, B = Te) are highlighted. d | AIMD simulations of SST with an embedded crystalline seed at ~600 K. The ScTe squares and cubes stay intact against thermal fluctuations and serve as the centres for crystal growth. The model is crystallized to a large extent within 600 ps. Sc, Sb and Te atoms are rendered in red, yellow and blue, respectively. CN, coordination number. Panel a is adapted with permission from ref.98, APS. Panels b and d are adapted with permission from ref.40, AAAS.

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thereby confirming that SST is suitable for PRAM applications40. Remarkably, the amorphous structure of SST generated through AIMD simulations was found to consist predominantly of fourfold primitive rings (fig. 3c), and all the Sc atoms were involved in ABAB squares (A = Sc or Sb, B = Te). The robust Sc–Te bonds and cubes remained intact for at least 50 ps during AIMD simulations at 600 K: the high stability of these crystalline precursors against thermal fluctuations because of the stronger Sc–Te bonds increases the prob-ability of forming sizeable seeds. In fact, unlike GST, crystalline seeds containing ~50 atoms could withstand thermal fluctuations in SST at 600 K, serving as stable centres for fast crystal growth. One such seed led to rapid crystallization within 600 ps in a 428-atom SST model40 (fig. 3d), indicating that SST could crystallize much faster than GST at high temperatures. Although it was not feasible to quantitatively determine the crit-ical nucleus size from AIMD simulations, because of insufficient statistical sampling, the simulations indi-cated that the critical size of the nucleus is smaller in SST than in GST, corresponding to a higher density

of nucleation sites in SST. The prediction of superior crystallization was demonstrated by SST- based phase- change devices, which showed a real subnanosecond (0.7 ns) write time even in large conventional memory cells40, reaching speed levels of SRAM. To conclude, the abundance of dynamically robust crystalline precursors is the key to the ultrafast incubation of PCMs.

Crystal growth at atomic scaleEven if the stochastic incubation stage is suppressed, rapid crystallization cannot be accomplished unless the crystal growth speed is fast. For instance, the maximum crystal growth speed from liquid SiO2 is only ~10−9 m s−1, despite the abundance and robustness of crystalline pre-cursors113,114, namely, the tetrahedral SiO4 motifs in the amorphous network. This slow speed corresponds to a SET time on the order of seconds in a nanostructured memory cell, which is too long for memory or data storage applications. Clearly, both GST and SST must have very fast crystal growth speed, as the SET process is finished within 1 ns (excluding the pretreatment time for GST).

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Fig. 4 | Crystal growth from atomistic simulations. a | Crystallization snapshots of a Ge2Sb2Te5 (GST) model (containing 180 atoms) during an ab initio molecular dynamics (AIMD) simulation at ~600 K. b | The evolution of the effective radius (Reff) of the crystalline clusters extracted from two independent crystallization trajectories of GST. The slope in region III determines the growth rate, indicating an average speed of ~5 m s−1. c | AIMD simulations of crystal growth from crystalline–amorphous boundaries in Ag4In3Sb67Te26 (AIST) (containing 810 atoms) at ~585 K. No sizable crystalline clusters are formed during the interface growth process. d | Number of crystalline- like (cryst.) atoms formed during interface growth: the estimated growth rate is ~7.8 m s−1. e | The profile of the bond order parameter (Q4

dot) for the snapshot at the initial stage of crystallization, indicating a narrow interface of less than 1 nm. f | The diffusion coefficients along the growth direction (Dx) show a subnanometre narrow interface, corresponding to a rapid reduction in atomic mobility from the amorphous region to the crystalline front. g | The calculated growth speed of GeTe from 500 K to 675 K. Single and multiple growth centres are found at 675 K and 500 K , respectively. These crystallization simulations (containing 4,096 GeTe atoms) were made by employing neural network potential- based molecular dynamics simulations. Panels a and b are reproduced with permission from ref.95, APS. Panels c–f are adapted from ref.120, CC- BY-4.0. Panel g is adapted with permission from ref.123, ACS.

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Growth from nucleus. In AIMD simulations of the crys-tallization of GST, fast crystal growth from the nucleus (fig. 4a,b) was observed in 180-atom models (in an ~1.8 × 1.8 × 1.8 nm3 supercell) at 600 K (ref.95). The extrapolation of the change in the effective radii with time (fig. 4b) indicates a growth rate of ~5 m s−1, which is larger than the experimental value in this tempera-ture window50,115. This discrepancy is partly a conse-quence of finite- size effects. Larger models containing 400–900 atoms were considered to reduce these spurious effects97–99,116,117. An enhanced sampling method118 was used to accelerate the formation of a critical nucleus and to reduce the computational cost116,117. A bond order cor-relation parameter119 that distinguished amorphous- like atoms from the crystalline part was used to compute the growth rate. An average of three 460-atom models gave a growth rate of ~1.2 m s−1 at ~600 K (ref.116), which is reduced to ~0.5 m s−1 in a 900-atom model117. These values are compatible with experimental data50,115.

Growth from planar interface. To quantitatively investigate the crystal growth processes, the geometry of the crystalline–amorphous interface should be sim-plified. For example, a growth- driven material, AIST, with a growth orientation along the [0001] direction of the crystal was considered120. By fixing two adja-cent crystalline layers during the melt- quenching pro-cess, a large amorphous slab (>4.2 nm) containing two smooth crystalline–amorphous interfaces (because of the periodic boundary conditions) was created (fig. 4c). In total, the model contained 810 atoms with the stoi-chiometry Ag4In3Sb67Te26, corresponding to a size of ~2.2 × 2.1 × 5.1 nm3. Upon heating at ~585 K, crystal-lization proceeded quickly through the two interfaces (fig. 4c), and no sizeable crystalline seeds were observed in the disordered regions, confirming a pure boundary- assisted growth process. By calculating the change in fraction of crystalline- like atoms with time, an estimate for the growth rate of ~7.8 m s−1 along the [0001] growth orientation was obtained (fig. 4d). This high value is in line with experimental values in this temperature win-dow72. Similar simulations were carried out for GST along the [111] direction of the cubic phase, for which a growth rate of ~1 m s−1 was obtained116, again compatible with experimental values115. Note that if the surround-ing materials promote boundary- assisted crystal growth, even GST- based memory cells could become growth driven, owing to the high crystal growth rate of GST. For example, amorphous GST only a few nanometres thick can crystallize via boundary growth before the stochastic incubation process occurs116,121.

Growth mechanisms. The fast crystal growth of AIST and GST is explained by the high mobility, the narrow interface and the effective atomic attaching process (because of the deep undercooling and, thus, large driving force)45. The calculated bulk diffusivity was 5.0 × 10−10 m2 s−1 at 585 K for AIST and 1.6 × 10−10 m2 s−1 at 600 K for GST. The profiles of the bond order parameter and the diffusivity along the growth direction revealed a narrow interface of <0.8 nm in both systems (fig. 4e,f), which guaranteed fast and frequent impinging of atoms

onto the crystalline boundary. The attaching coefficients determine the probability of an atom that visits the crys-talline sites at the interface sticking permanently to the crystal. These parameters at 600 K were calculated to be 0.38 and 0.20 for AIST and GST, respectively, indicating an effective attaching process116,120.

Challenges in AIMD simulationsDespite the insights on nucleation and interface growth gained from AIMD simulations, challenges remain. For example, strong deviations of the crystal growth rate and atomic diffusivity of AIST between simulations and experiments are observed at ≤ 500 K (ref.120). The issue was attributed to the too fast cooling rate used in the simulations but requires clarification. In addition, the size of the critical nuclei as a function of temperature remains to be determined. The AIMD simulations per-formed to date suffer from insufficient statistical sam-pling. To fully describe memory cells, simulations over larger timescales and length scales need to be performed. Furthermore, the presence of interfaces between the PCM and other materials should be taken into account because such interfaces could significantly alter the activation barrier for crystallization.

The development of classical neural network inter-atomic potentials122–125 and augmented Tersoff- based potential126,127 have enabled large- scale molecular dynamics simulations of GeTe. In particular, neural network potentials allow an accuracy comparable to that of ab initio simulations122–125. Interatomic potentials generated from neural networks were used to study the crystallization kinetics in models of GeTe containing 4,096 atoms, thus enabling a thorough investigation of finite- size effects, incubation times and crystal growth rates at elevated temperatures. Growth rates were deter-mined to be on the order of a few metres per second123 (fig. 4 g), similar to those of GST. In the neural network potential framework, surface and interface effects can be modelled by a proper training of the network for inves-tigations of structural transitions in GeTe nanowires128. Neural network potentials or other advanced machine- learning potentials129–132 could be trained for ternary GST compounds133 and to include more complex envi-ronmental effects. Using these potentials in combination with enhanced sampling methods could enable a more accurate estimate of the critical nucleus size and the free- energy barrier for nucleation, in principle.

FragilityAn appealing feature of PRAMs is the combination of fast switching time at elevated temperatures with good data retention at room temperature. This combina-tion requires nanosecond crystallization at ~600 K but robust amorphous stability for decades at ~300 K. This enormous difference in dynamics in a narrow temper-ature range (fig. 5a) has been elucidated recently, and the fragile nature of PCMs was identified to be the key50,72,115,134–137. Kinetic fragility describes the change in dynamics, for example, viscosity η, as a function of temperature. If the logarithm of the viscosity of the supercooled liquid state varies linearly as a function of 1/T from the glass transition temperature Tg up to the

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melting temperature Tm, indicating Arrhenius behaviour, the system is defined to be a strong liquid, for example, SiO2 (ref.138). For fragile liquids, a high activation energy Ea for viscous flow is typically observed near Tg, while Ea decreases markedly as temperature increases. Hence, fragile liquids — for example, o- terphenyl — display super- Arrhenius behaviour138. Fragility is defined by the slope of the viscosity η in an Angell plot139 (fig. 5b) upon approaching Tg, m = [d(log10η)/d(Tg/T)]T=Tg. The larger the fragility, the stronger the deviation from Arrhenius behaviour139,140. The fragility of SiO2 is ~20, correspond-ing to a strong liquid, while the fragility of glycerol is ~80, corresponding to a fragile liquid.

Large fragility. GST was first determined to be a highly fragile liquid115 in ultrafast differential scanning cal-orimetry (DSC) measurements on amorphous thin films obtained by magnetron sputtering (as- deposited).

Ultrafast DSC allows rapid heating at rates over 104 K s−1 to bring the amorphous phase to elevated temperatures and measure the growth rate in this temperature win-dow. At ~400 K, the growth rate of GST is on the order of 10−9 m s−1, but it increases rapidly when the temperature is raised to ~500 K. At higher temperatures, the growth rate continues to increase, reaching ~2.8 m s−1 close to ~650 K (fig. 5b). The growth rate decreases upon further increasing the temperature to approach the melting temperature of GST (900 K). This trend is in contrast with Si and SiO2, for which the growth rates increase approximately in a simple Arrhenius manner from their Tg to Tm (ref.114) (fig. 5a). The viscosity of GST is derived from the measured growth rate and is included in an Angell plot (fig. 5b, solid green line). The extrapolation of the derived viscosity (fig. 5b, dashed green line) does not reach the expected value (1012 Pa s) at Tg (taken as 383 K), indicating a decoupling of crystal growth and

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Fig. 5 | temperature- dependent dynamics of phase- change materials. a | The measured growth rate of Ge2Sb2Te5 (GST) between 450 K and 650 K from ultrafast differential scanning calorimetry experiments. GST shows a much faster growth rate than Si and SiO2, as well as a large bending of the growth rate curve as a function of temperature (T). b | Angell plot including GST and other typical strong and fragile liquids. The viscosity (η) data for GST are derived from the growth rate values. A clear fragile behaviour is observed for GST. c | The measured growth rate of melt- quenched Ag4In3Sb67Te26 (AIST) between 418 K and 555 K from laser- based time- resolved reflectivity experiments and at 383 K from in situ transmission electron microscopy experiments (red points). The growth rate of as- deposited AIST obtained from atomic force microscopy measurements (blue points) is much slower than the growth rate of the melt- quenched AIST. d | Angell plot including AIST and GST data. A fragile- to-strong crossover is estimated to occur at ~650 K on the basis of directly measured viscosity data of liquid AIST above 820 K and the derived viscosity data of as- deposited AIST below 500 K. µmax, maximum crystal growth velocity ; kB, Boltzmann constant; Tg, glass transition temperature; Tm, melting temperature. Panel a is reproduced from ref.114, Springer Nature Limited. Panel b is reproduced from ref.115, Springer Nature Limited. Panel c is reproduced from ref.72, CC- BY-3.0. Panel d is reproduced with permission from ref.144, Wiley- VCH.

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viscous flow in supercooled liquid GST. If the viscosity value at Tg is taken as 1012 Pa s for GST, the extrapolation (fig. 5b, dashed blue line) leads to m ≈ 90. The large fra-gility of GST guarantees the high mobility of atoms at elevated temperatures for rapid crystallization, yet the large viscosity at low temperatures ensures stability of the amorphous phase.

This picture was further supported by high- temperature kinetic measurements on melt-quenched amorphous GST in real device setups50,134. Non- Arrhenius behaviour was observed, corresponding to a large change in activation energy for crystallization from ~3 eV near Tg to ~1.3 eV (isothermal heating) or ~0.5 eV (non- isothermal heating) above 500 K (ref.50). However, another experiment performed in simi-lar memory cells showed Arrhenius behaviour, with Ea = 3.0 eV between ~420 K and ~530 K (ref.135). In this experiment, GST was doped with other elements. Although no specific material composition was given, it is known that N or C dopants can stabilize amorphous GST for better data retention. However, these dopants can also lead to a reduction in crystallization capabi-lity at elevated temperatures, for example, the SET time can be increased by 2–3 orders of magnitude with >10% nitrogen dopants141. A plausible rationale for this behav-iour is that the strong but geometrically mismatched chemical bonds formed by nitrogen atoms could increase the stochasticity of incubation and slow down the diffusion kinetics141,142, preventing fast crystallization at intermediate temperatures. The Arrhenius behaviour of doped GST in a large temperature range may indicate a reduced fragility143. Nevertheless, the fragility should remain high, and a strong change in the growth rate should eventually occur, albeit at higher temperatures.

Fragile- to-strong crossover. The crystallization dynamics of AIST between 400 K and 550 K also shows Arrhenius behaviour72 (fig. 5c). In this study, growth rates were obtained from time- resolved reflectivity measurements of laser- melted and quenched AIST. At ~550 K, the growth rate was >3 m s−1. Extrapolating to higher temperatures, the growth velocity would exceed the speed of sound in AIST (~1,000 m s−1) at around 625 K, which is obviously not possible. Hence, a strong change in growth rate must occur at temperatures above 550 K.

The Arrhenius dependence was interpreted as a sign of glassy behaviour, implying a Tg > 550 K. This high value of Tg was attributed to the high quenching rates (1010 K s−1). Moreover, a very large fragility m > 100 was estimated by fitting the viscosity curve for the liquid data above Tm and by constraining the curve to con-nect to the glass data72. This interpretation was later challenged because the estimated values of Tg and the activation energy for viscosity deviate significantly from DSC data144. The extrapolation of η at the DSC value at 380 K (the suggested value of Tg) would be orders of magnitude larger than the viscosity value tradition-ally used to define a glass, that is, log10η = 12 (fig. 5d). Therefore, it was suggested that a fragile- to-strong crossover occurs in AIST144. The high- temperature fragility145 m’ was estimated to be around 74, while a

low- temperature fragility m = 37 was derived on the basis of the as- deposited data144–147. These developments raise the question of whether the Arrhenius behaviour of crystallization observed in memory cells containing doped GST could also be ascribed to a fragile- to-strong transition. This point deserves investigation, for which accurate measurements of Tg are necessary.

Kinetic crossover. For phase- change applications, the presence of a kinetic crossover is essential. Kinetic cross-over is defined as a large change in activation energy for diffusion and viscosity, and thereby in crystal growth rate, as a function of temperature. This kinetic crosso-ver must occur in the intermediate temperature window, for example, 0.5–0.8 Tm, where the driving force term is large enough to guarantee effective atomic attaching for fast crystal growth. Below the crossover region, the kinetics are suppressed because of the dramatic increase in viscosity, thus enabling good data retention.

An improved understanding of the fragility and glass formation in PCMs is required. For example, fra-gility is reduced by doping N into GST143; however, an increase in fragility was observed by doping Ge into Sb (ref.148). In addition, it was observed that fragility is size- dependent and can be altered with confinement149. As mentioned above, the determination of Tg of PCMs is still under debate because of experimental challenges144. Doping143,148,150, synthetic methods72,147, cooling rate120 and ageing46 could strongly affect the Tg value. Studies are needed to understand the effect of the decoupling between diffusivity and viscosity115,124, which has been shown to occur in some PCMs. Elucidation of these phe-nomena in PCMs could shed light on other classes of fragile materials140,151–153.

Phase- change universal memoryA universal memory device would optimize the mem-ory hierarchy and thereby significantly reduce the time delay and power consumption caused by data shuffling. Replacing DRAM and flash memory with PCMs was first envisioned in 2005 (ref.39). Ten years later, rele-vant commercial products have been released36,38. The aspects that need to be improved to develop universal memory include switching speed, data retention, cycling endurance, power consumption and storage capacity. Optimization strategies in terms of materials design and device engineering are discussed in this section.

Switching speed. To make a universal memory device, fast switching speed is important. The insufficient switching speed of commercialized GST- based PRAMs is limited by the stochasticity of nucleation. In a conven-tional memory cell (150 nm- thick and in contact with a 190 nm- diameter bottom electrode (fig. 6a, inset)), the minimum SET time is >10 ns using GST. However, if SST is the active material, the minimum SET time is 0.7 ns (fig. 6a). AIMD simulations suggest a Sc- assisted crys-tallization process, which is corroborated by comparing the performance of SST and Sb2Te3 devices of the same size. Sb2Te3 devices show a minimum SET time of 6 ns, which is an order of magnitude longer than the mini-mum SET time for the SST devices, because of the lower

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stability of Sb–Te bonds than of Sc–Te bonds40. Other transition- metal dopants, such as Ti, were also shown to improve the SET time107; however, this time saturated at 4 ns as the voltage bias increased. Moreover, at high pro-gramming temperatures, phase segregation into hexag-onal TiTe2 occurs108. These drawbacks are related to the fact that the stable phase of TiTe2 is hexagonal instead of cubic rocksalt.

The RESET operation of SST devices can be achieved with the same width of pulses as for the SET operation (fig. 6b), suggesting subnanosecond phase- change opera-tions using this material. Fine- tuning of the SST compo-sition may lead to faster crystallization, but the room for adding Sc is limited. The addition of too much Sc would slow down atomic diffusion, and thus the crystal growth process, and would increase the RESET energy, as the melting temperature of Sc2Te3 is much higher than that of Sb2Te3. Scaling down the cell size is known to reduce the SET time154. When the thickness of the PCM layer is reduced to ≤20 nm, interface- assisted crystal growth at the crystalline–amorphous boundary (fig. 6a, inset, red

region) may play a leading role, and a PCM with a fast crystal growth speed could enable SET operations within a few nanoseconds (ref.154). If this boundary- assisted growth can be combined with enhanced nucleation in SST, the record SET time (currently 0.7 ns (ref.40)) may not be the ultimate limit. Note that nucleation should become necessary again in the drastically miniaturized memory cell of only a few nanometres, where the bound-aries between the amorphous region and the crystalline surroundings are not likely to be present155.

Data retention. It is difficult to combine the ultrafast crystallization and good thermal stability of PCMs in a narrow temperature window, because increasing crys-tallization speed usually weakens amorphous stability. For example, pure Sb is a fast transformer, but it forms a poor glass at room temperature, at which spontaneous crystallization occurs156,157. Interestingly, this trade- off was not observed in the newly designed SST material. Despite its subnanosecond crystallization capability at ~600 K, amorphous SST shows good thermal stability

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at room temperature. The extrapolated temperature for failure (resistance falls to half of its initial value) after 10 years is 87 °C in SST, which is slightly higher than that of GST40 (fig. 6c).

The good thermal stability of SST is sufficient for most non- volatile applications. However, for certain embedded applications, for example, in the automo-tive industry, a 10-year failure temperature >100 °C is desirable. An improved thermal stability of glass can be achieved by exploiting nanosize effects158. It was shown that the capping layers can, in some cases, increase the activation barrier of crystallization to improve the thermal stability of the amorphous phase by many tens of degrees Celsius159–164. It is even possible to stabi-lize pure amorphous Sb for PRAM applications41. In this work, ultrascaled Sb films (~3 nm) were confined with SiO2 capping layers, which enabled the formation of melt- quenched glassy Sb, and the lifetime of this phase reached 50.8 hours at 20 °C despite the extreme proneness to crystallization of the bulk phase41,165. Heterogeneous nucleation from the confinement layers must be avoided to retain the amorphous phase.

Cycling endurance. With high- quality device fabrica-tion, PRAMs can support 108–109 cycles, outperform-ing SSDs, which have 105–106 cycles4. However, the cycling endurance needs to be improved to 1017 cycles for memory applications166. By scaling down the cell size to <30 nm with proper confinement, GST devices showed an improved endurance of 1011–1012 cycles167,168. Large voids are typically formed near electrodes after >1010 cycles, which is a consequence of the pronounced density change upon crystallization. Typically, crystal-lization is accompanied by an increase in density of 5–9%. This density difference between the two phases causes mechanical stresses, but these stresses are smaller (by at least a factor of ten) than expected for a purely elastic model. Hence, there must be significant plastic flow in the amorphous phase to reduce stress build- up169. This observation raises the question of how plastic flow is accomplished under reduced dimensions, such as in small cells, or on very short timescales. A self- healing prop-erty was recently observed in phase- change devices170. By reversing the polarity of the voltage pulse, the elec-tromigration of Sb was controlled and exploited to anni-hilate these large voids170. Another way to prevent the formation of large voids is to reduce the density con-trast by increasing the atomic packing efficiency of the amorphous phase171.

Phase segregation also affects cycling endurance, because GST is a ternary compound and tends to sepa-rate into its parent compounds GeTe and Sb2Te3 or pure elemental clusters after extensive cycling. It is possible to overcome this issue via a full liquifying process above the melting temperature of all possible materials made of the three elements172. The failure mechanism of SST has not yet been thoroughly studied, and the endurance of 105–107 cycles40 (fig. 6b) is primarily limited by device fabrication quality, as GST does not perform better in the same device setting. We speculate that SST has the potential for a superior cyclability compared with GST, because the two parent compounds in this case are Sc2Te3

and Sb2Te3, and they have better geometrical conforma-bility than GeTe and Sb2Te3. Clearly phase segregation is avoided if one element, for example, pure Sb, is used for PRAMs41,165. Together with some advances in device fab-rication and programming strategies, almost unlimited cycling endurance was speculated for PRAMs172.

Power consumption. Reducing power consumption is another step towards practical applications. To some extent, this reduction can be achieved by shortening the SET operation time. Nevertheless, RESET is the more power- consuming operation because it involves melt-ing of the crystalline state and, thus, an increase in local temperature above the melting temperature (~900 K for GST). Scaling down the cell size51,167 and improving the thermal insulation173,174 are effective methods for saving energy. The RESET energy was reduced down to ~80 fJ (refs175–177) in cell setups with carbon nanotube (CNT)-based electrodes. The reason for this reduction was mainly attributed to the miniaturized switching volume of GST in the setup.

As well as optimizing the device design, it is pos-sible to reduce the RESET energy by engineering the core materials. SST films show an order of magnitude reduction in RESET energy with respect to GST films in the same device setting (fig. 6d). This energy gain was speculated to be a consequence of the higher vacancy concentration in rocksalt SST (~16%) than in rocksalt GST (~10%), which might increase the possibility to accommodate energetically unfavourable Te–Te anti-bonding states at high temperatures, leading to larger distortions and thus easier disordering40. The pulse width employed in the GST–CNT setup was ~30 ns, and the RESET energy was speculated to reach a few femtojoules by using subnanosecond pulses175–177. By replacing GST with SST in the same setup, another tenfold decrease in RESET energy is anticipated, reaching the subfem-tojoule level, superior to that of DRAMs177. Moreover, the good data retention of PRAMs does not require fre-quent and periodic refreshes to retain data as in DRAMs (approximately every 64 ms), thus saving power.

Storage capacity. 3D stacking is an effective route to improve storage capacity. Breakthroughs in the commer-cialization of PRAMs are a consequence of this strategy. With the 3D crossbar structure (fig. 1b), multiple mem-ory sheets can be integrated along the vertical direction, which increases the storage capacity compared with conventional 2D devices. However, 3D stacking causes the sneak path issue to arise, where some memory units are switched because of unwanted current leakage, because all the units share the same word lines or bit lines. In the 3D XPoint setup, selector layers are implemented above memory layers and act as a gate that turns on and off the flow of electric current through the memory layers. Chalcogenide glasses, such as As- doped Se–Ge–Si, are typically used as selectors36. The working mechanism exploits the Ovonic threshold switching effect178,179, according to which the resistance value of chalcogenide glasses is very large for low- voltage biases but suddenly decreases by orders of magnitude when the voltage bias reaches a threshold value180–182. This process can be as

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fast as a few picoseconds but is volatile, and the resis-tance returns to the initial value as soon as the voltage is removed. For practical use, the high on- to-off ratio of resistance and the high threshold voltage value are key parameters, although the fundamental physics remains to be elucidated.

The Ovonic threshold switching effect also plays a role in PCM memory cells, because it enables the flow of current through the amorphous state and thus the Joule heating that triggers crystallization for sufficiently high voltage. Ovonic threshold switching is a generic phenomenon that has been consistently observed in amorphous PCMs and other amorphous alloys178. Even single- element amorphous Sb exhibits clear threshold switching features41,165. Further efforts are required to elucidate the origin of this phenomenon and to optimize the material composition for use as selectors.

The use of multilevel storage is a second route to improve storage capacity. PCMs allow multiple logic states to exist in a single memory cell, resulting in an exponential increase in storage capability with respect to standard binary storage51. The multiple logic states are implemented by partially melting the PCM in the memory cell to have different crystalline–amorphous ratios. Owing to the large electrical contrast (over 2–3 orders of magnitude) between the amorphous and crys-talline states, many intermediate resistance states can be obtained. The challenge that prevents ultradense multi-level data storage over a long time is the resistance drift phenomenon observed in amorphous PCMs at room temperature183. More specifically, the electrical resistance value increases slowly but steadily with time, indicating a structural transition path towards an ideal or ultrasta-ble glass state184, in contrast with the crystallization path at elevated temperatures. In Ge- rich PCMs, the ageing phenomenon has been attributed to the disappearance of homopolar bonds and tetrahedrally coordinated Ge (refs46,47,88), as well as to a reinforcement of bond dis-tortions46. The latter mechanism was speculated to be more generic46, because ageing also occurs in Ge- free PCMs. Even pure amorphous Sb shows a remarkable resistance drift process at 100 K with a drift coefficient similar to that of GST at room temperature41,165. When in contact with metals or dielectric materials in certain device settings, amorphous PCMs display smaller drift coefficients185,186. This behaviour is not understood, and the ageing path of amorphous PCMs in these devices needs investigation.

Phase- change neuro- inspired computingIt has been estimated that up to 40% of the power consumed in computing devices is a consequence of data transfer among the various computing, memory and storage units, wasting a huge amount of energy. The data buses interconnecting these components are also bandwidth- limited, which strongly affects the overall computing speed. The use of universal mem-ory devices would improve the computing efficiency greatly. However, a fundamental change in the com-puting architecture, for example, to non- von Neumann computing schemes, is necessary to increase computing efficiency. In fact, the human brain offers an intriguing

computing scheme in this regard. Our brain consumes only a few tens of Watts of power and takes less than 2 litres of space. Both are orders of magnitude smaller than the state- of-the- art supercomputers. Moreover, the human brain outperforms supercomputers on complex tasks, such as pattern recognition and language transla-tion. The remarkable computing efficiency of the brain may stem from the massively parallel computing archi-tecture consisting of ~1011 neurons and ~1015 neuron interconnections — the synapses (fig. 7a, top).

A deeper understanding of the human brain has inspired the realization of new hardware and algorithms. On the algorithmic side, deep neural networks have ena-bled successes in pattern recognition. However, these networks are frequently implemented in traditional von Neumann computers, which are not efficient for such tasks3. Hence, in recent years, dedicated hardware has been developed187. Even more ambitious is the reali-zation of neuro- inspired hardware. The conventional route to make such hardware is to exploit silicon- transistor-based circuits, but it is difficult to scale these circuits down, because more than ten silicon transistors are needed to emulate a single synapse56.

By contrast, PCMs offer simple implementations of synapses (fig. 7a, bottom) and neurons (fig. 7b), as mul-tiple logic states with a continuous change in electrical resistance can be achieved in a single memory cell. More specifically, multiple RESET states can be obtained by partial amorphization of the cell, while the gradual SET operation can be completed by applying multiple short medium- level voltage pulses, corresponding to a step-wise crystallization process of the amorphous phase. During these operations, the resistance value of the current state depends on its excitation history in a sin-gle phase- change device and can be employed to build complex and deep neural networks based on a massive array of phase- change devices188. Neural networks that consider the emulation of the synaptic learning rules56,57 and the integrate- and-fire functionality17,55 of biological neurons are termed spiking neural networks188.

Phase- change synapses. To emulate biological syn-apses, the primary focus is to realize Hebbian learning189, which describes the connection strength between pre-synaptic and postsynaptic neurons. This theory proposes an explanation for the adaptation of neurons during the learning process in the human brain. More specifically, it hypothesizes that the synaptic weight between pre-synaptic and postsynaptic neurons is enhanced if they activate simultaneously but decreases if they activate separately. For neuro- inspired computing applications, the weights between artificial neurons must be altered according to this learning principle. Spike- timing- dependent plasticity (STDP), a form of Hebbian learn-ing, was implemented with a single PCM cell per syn-apse56, and these artificial synaptic dynamics closely resembled the biological synapse (fig. 7c).

In this setup, the GST- based PCM cell receives a stream of pre- spike pulses with high bias but narrow width: if these pulses overlap with the low- intensity but long post- spike pulses, the combined heating effect becomes sufficient to induce melt- quenching or

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crystallization, resulting in a decrease (depression) or an increase (potentiation) in the conductance (synap-tic weight) of the PCM cell. The correlation between the amplitude, length and spacing of voltage pulses thus determines the different characteristic responses of electronic synapses to the input signals. The nano-scale physical size (a few hundred nanometres) and low power consumption (picojoule level) of PCM- based synapses are steps forward in reaching compact and energy- efficient neuro- inspired computational devices. Large- scale neural networks187,190,191 and spiking neu-ral networks192 based on GST synapses have enabled breakthroughs in complex visual pattern extraction

and recognition with much reduced power consump-tion. For instance, a mixed hardware–software neural network implementation, involving more than 0.2 mil-lion GST synapses, could achieve equivalent accuracy in classifying complex collections of images as software- based training methods using supercomputers, but with an improvement of two orders of magnitude in energy efficiency187.

Despite these successful applications, the micro-scopic details of crystallization under complex pulsing conditions, in particular, the nonlinear change in elec-trical resistance, remain to be explored. AIMD simula-tions using partially crystallized 180-atom GST models

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Fig. 7 | Phase- change neuro- inspired computing. a | A comparison of schematics of biological neurons (top) and phase- change devices (bottom). A synapse that connects two neurons can be emulated with a single phase- change device. Potentiation and depression of the synapse can be emulated by crystallization and amorphization of Ge2Sb2Te5 (GST) via a series of medium- level and high- level voltage pulses. b | The construction of a biological neuron using phase- change devices. The electronic neuron is divided into three parts: dendrites (input), neuron soma (processing unit) and axon (output). The neuronal membrane in the neuron soma can be emulated by a single phase- change device, with the membrane potential stored by the phase configuration of the device (the potential in biological neurons is maintained by a lipid bilayer). The dendrites can be emulated with an array of plastic synapses or phase- change synapses. c | Spike- timing-dependent plasticity learning rule emulated with phase- change devices. The conduction of phase- change devices represents the synaptic weight. d | The neuronal integrate- and-fire functionality emulated by the progressive crystallization dynamics of a single phase- change device. The conductance of the device changes nonlinearly as a function of the number of pulses. e | The number of excitations needed to trigger neuronal firing depends on the amplitude and width of voltage pulses. The larger the amplitude (still weaker than the melting pulse) and/or the longer the voltage pulse, the fewer excitations needed for the phase- change neuron to fire. Detailed pulse settings are (1) 20 ns and 2 V, (2) 20 ns and 4 V, (3) 50 ns and 2 V and (4) 50 ns and 4 V. PCM, phase- change material. Panels a and c are adapted with permission from ref.56, ACS. Panels b, d and e are adapted from ref.17, Springer Nature Limited.

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revealed changes in the number of fourfold primitive rings in response to heat pulses193. However, the varia-tions in structural order were small and did not affect the electronic structure. This discrepancy was attributed to the limited system size employed in the simulations. Large- scale ab initio simulations and in situ multifield experiments are needed to gain a deeper understand-ing of the dynamics in devices. In addition, the crys-tallization dynamics could be largely affected by the confinement materials as the cell size reduces to a few nanometres, and it is yet to be explored whether mul-tiple states can be obtained within this limit. To further enhance the performance of PCM neural networks, it is crucial to explore the device physics as well as the material properties in complex environments.

Phase- change neurons. An important step towards neuro- inspired computing systems is to build artifi-cial neurons, which requires the emulation of neuronal dynamics, including maintenance of the membrane potential, the transient dynamics and the process of neu-rotransmission. In biological neurons, the membrane potential is maintained by ion pumps and ion channels in the membrane lipid bilayer. This potential can be altered by excitatory or inhibitory postsynaptic potentials from dendrites of the neuron. Upon sufficient excitation in the neuron soma (integrate), an action potential is generated (fire or spike). Then, the action poten-tial travels along the axon (fig. 7a, top). Neuronal fir-ing strongly depends on the history of excitations. In phase- change neurons (fig. 7b), the low conductance (high resistance) of the amorphous state can be viewed as the neuronal membrane potential. The integrate- and-fire functionality can be emulated by the progres-sive crystallization process of PCMs under a series of input voltage pulses17. The neuron fires when the con-ductance reaches a threshold value, corresponding to a largely recrystallized phase (fig. 7d). After firing, the neuron is RESET by a melting voltage pulse. By corre-lating the amplitude, width and time interval of multiple voltage pulses, the firing rate of phase- change neurons is manipulated (fig. 7e). In combination with plastic synapses, even one such neuron can carry out complex computational tasks, such as the detection of temporal correlations in parallel data streams17,55.

The intrinsic stochastic nature of phase- change neu-rons stems from crystallization (in particular, nuclea-tion) processes. This stochasticity has a key role in signal encoding and transmission17 and can be tuned by altering the amorphous topology as well as the strength of chemical bonds. Using GST as a reference, stronger stochastic behaviour can be obtained by doping with chemically strong but geometrically mismatched dopants, such as nitrogen or carbon. Conversely, sto-chasticity can be suppressed by reducing the concentra-tion of GeTe towards the stoichiometry Sb2Te3. In this way, the abundance of crystalline precursors remains unchanged, but the structural complexity because of Ge is reduced, improving the nucleation rate. Adding Sc into Sb2Te3 suppresses the stochasticity and yields a higher nucleation rate, because the strong Sc–Te bonds hold the crystalline precursors in place against thermal

fluctuations at elevated temperatures. This materi-als design strategy tunes the crystallization time from subnanosecond to submillisecond and should alter the firing rate of phase- change neurons by orders of mag-nitude under the same pulsing program. Furthermore, each spike of phase- change neurons corresponds to a RESET pulse, which is different to phase- change syn-apses, where each spike is correlated to partial SET pulses. Thus, the failure mechanisms of phase- change neurons and phase- change synapses upon extensive cycling could be quite different.

The accumulation mode of crystallization of PCMs can be used to perform basic arithmetic calculations194 as well as complex vector–matrix multiplications195 using massive parallelized arrays of devices, termed as in- memory computing or memcomputing188. The strategy of designing crystallization kinetics should also lead to improvement in this regard. Overall, phase- change neuro- inspired computing and in- memory computing have a similar set of requirements to that of phase- change universal memory, including reduced stochasticity, smaller drift, faster speed, lower power consumption and longer endurance.

OutlookOver the past two decades, phase- change memory has become a mature technology capable of increasing the computing efficiency of electronic devices. The goal is to develop universal memory to cope with the data explosion crisis. To achieve this goal, it is important to project the understanding of materials properties of PCMs to more complex situations occurring in devices, in which interface effects, stoichiometric variation, ageing, stress relaxation, extensive cycling, nanosize effects, complex pulsing schemes and non- isothermal and non- equilibrium conditions must be taken into account. Future studies are anticipated to explore the capabilities of the crystallization dynamics in accumu-lation mode and in miniaturized PCM cells for phase- change neuro- inspired computing and in- memory computation. Ultrafast and ultrasmall energy- efficient, neuro- inspired phase- change electronic chips with the ability to solve complex computational tasks are envi-sioned in the near future, providing support to AI and data- intensive applications based on non- von Neumann computing hardware.

In addition to the electrical resistance contrast, a pronounced change in the optical property also occurs in PCMs during the fast and reversible SET/RESET operations. The refractive index, extinction coefficient and reflectance change by several tens of percent upon crystallization, because of a change from covalent to metavalent bonding48,68–70. This optical contrast enabled PCM- based rewriteable optical data storage in the 1990s. Now, the integration of PCMs with waveguides opens up the possibility of on- chip photonic phase- change memory applications196–198. Similar to its electronic ana-logue, photonic phase- change memory is non- volatile but is superior in terms of bandwidth for data transfer. Both binary and multilevel data storage were achieved by detecting the change in transmission of the waveguide under short optical pulses198,199.

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Photonic phase- change devices have also been shown to emulate synaptic learning rules200. Similar to electronic phase- change synapses, depression and potentiation can be obtained by partial amorphization and progressive crystallization but under optical excita-tions. By combining multiple optical pulses with various amplitudes, widths and time intervals, the STDP rule can be implemented. In addition, phase- change arith-metic computations can be achieved by all- optical methods201. Further development of all- optical devices will benefit from the ongoing computational and exper-imental investigations on the dynamical properties of PCMs and their links with the optical changes. It would also be interesting to explore the use of recently discov-ered PCMs such as Sc0.2Sb2Te3 (refs40,102) and pure Sb (refs41,165) for these applications.

Phase transitions in PCMs are driven by either elec-trical or optical pulses and are accompanied by signif-icant changes in electrical and optical properties. Such features have led to the development of optoelectronic applications, such as colour rendering and nanopixel displays202. An optical cavity based on a thin GST film sandwiched between two transparent, conducting indium tin oxide (ITO) electrodes was fabricated and shown to produce stable and bright colours with a wide colour range. Colour can be tuned by either varying the thickness of the bottom ITO layer or by triggering phase

transitions in GST using electric pulses. Using electric pulses, it is possible to construct pixel sizes of 50 nm and below, much smaller than the diffraction limit of light. Greyscale pixels are possible with partial amorphization of the GST layer, analogously to multilevel phase- change memories. Furthermore, such thin films can be depos-ited on any substrate, including flexible ones, because the processing temperature is quite low. This processability opens up the possibility of PCM- based flexible and rol-lable displays with nanopixel resolution202. In addition to GST, growth- driven AIST was also exploited in some non- volatile photonic applications201,203.

Last but not least, we note that the easy- to-integrate properties could make PCMs suitable components for other applications. For example, the crystallization of PCMs can be used to control the surface plasmon res-onance204, to confine surface phonon polaritons205 and to create metamaterials206. In addition, PCMs can be integrated with 2D materials207,208 or doped with mag-netic impurities209–212, yielding electronic and magnetic characteristics that can be tuned by switching the PCMs. The rapid phase transitions together with a strong prop-erty contrast between different solid states make PCMs a great base for future nanoelectronic and nanophotonic applications, as well as nanoscale switches and controllers.

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AcknowledgementsThe authors acknowledge Y.-X. Zhou and J.-J. Wang for their help with figure preparations and R. Feng for useful discus-sions. W.Z. thanks the support of the National Natural Science Foundation of China (61774123 and 51621063), 111 Project 2.0 (BP2018008), the Youth Thousand Talents Program of China, the Young Talent Support Plan, Xi’an Jiaotong University and the International Joint Laboratory

for Micro/Nano Manufacturing and Measurement Technologies. R.M. and M.W. acknowledge funding from Deutsche Forschungsgemeinschaft within SFB 917 ‘Nanoswitches’. E.M. is supported at Johns Hopkins University by the US Department of Energy, Office of Basic Energy Sciences, Department of Materials Sciences and Engineer ing (DOE- BES-DMSE) under grant DE- FG02-13ER46056.

Author contributionsW.Z. researched the data and wrote the manuscript. R.M., M.W. and E.M. edited the manuscript. All authors made a substantial contribution to the discussion of content.

Competing interestsThe authors declare no competing interests.

Publisher’s noteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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