Highly tunable β-relaxation enables the tailoring of crystallization in phase-change materials

In glasses, secondary (β-) relaxations are the predominant source of atomic dynamics. Recently, they have been discovered in covalently bonded glasses, i.e., amorphous phase-change materials (PCMs). However, it is unclear what the mechanism of β-relaxations is in covalent systems and how they are related to crystallization behaviors of PCMs that are crucial properties for non-volatile memories and neuromorphic applications. Here we show direct evidence that crystallization is strongly linked to β-relaxations. We find that the β-relaxation in Ge15Sb85 possesses a high tunability, which enables a manipulation of crystallization kinetics by an order of magnitude. In-situ synchrotron X-ray scattering, dielectric functions, and ab-initio calculations indicate that the weakened β-relaxation intensity stems from a local reinforcement of Peierls-like distortions, which increases the rigidity of the bonding network and decreases the dynamic heterogeneity. Our findings offer a conceptually new approach to tuning the crystallization of PCMs based on manipulating the β-relaxations.


Supplementary Figures
. Full scans of the Ge15Sb85 powder samples using powder mechanical spectroscopy. (a) Storage modulus E' (black symbols) and loss modulus E″ (red symbols) of the as-deposited sample. (b) The annealed samples at 458 K (~0.92•Tα) for 3 hours and (c) for 6 hours. A constant frequency of 1 Hz and heating rate of 3 K/min were used, and a temperature calibration of -18 K is applied to all measurements. Storage modulus E' and loss modulus E″ are represented by black and red symbols, respectively.
A constant frequency of 1 Hz and heating rate of 3 K/min were used, and a temperature calibration of -18 K is applied to all measurements. Supplementary Fig. 3. The probability of crystallization during a fine-pulse duration scan at a constant power of 40 mW for of as-deposited, 3 hours and 6 hours annealed Ge15Sb85, respectively. The fitting for minimum crystallization time is based on the Gompertz function, which is a sigmoid function that depicts the growth mode being slowest at the start and saturated for a relatively long time. The asymptote parameter a is confined to 100 as the success rate should be no larger than 100%. The standard deviation of Y-axis (probability of crystallization), Sy, can be evaluated by the equation: . The calculated standard deviation of as-deposited, annealed at 185℃ for 3h and 185℃ for 6h films are 3.52%, 1.85% and 3.51%, respectively.
Supplementary Fig. 4. The repeated measurements of the PTE diagram. To ensure the replicability, we carried out independent measurements of amorphous Ge15Sb85 samples with a relatively low resolution (30*30 points). The results are in good agreement with the PTE diagram shown in the main text (Fig. 2a).
Supplementary Fig. 5. DSC scans of Ge15Sb85 at different heating rates from 3 to 60 K/min for (a) as-deposited, (b) 3hr-annealed at 458 K and (c) 6 hr-annealed at 458 K. Supplementary Fig. 6. Flash DSC scans of Ge15Sb85 at the heating rates from 100 to 30000 K/s for (a) as-deposited, (b) 3hr-annealed at 458 K and (c) 6hr-annealed at 458 K. Note that the curves are vertically shifted for clarity and the lowest curve corresponds to 100 K/s with a lower signal-to-noise ratio. 6hr-annealed Ge15Te85. Note that due to the low melting point, a heating rate above 3000 K/s shifts the Tp into the melt, partially bypassing the crystallization. Supplementary Fig. 9. (a) The zoom-in of the first S(q) peaks of Ge15Sb85 upon isothermal annealing at 458 K for 6 hours. (b) The difference plot ΔS(q)=S(q,t)-S(q,t=0hr). The trend of the peak sharpening is observed upon annealing.
Supplementary Fig. 10. The reduced pair distribution functions G(r) during the isothermal annealing of the amorphous Ge15Sb85 at 458 K up to 6 hours. The spectra are vertically shifted for an easy view. Inset: the zoom-in of the peak intensity and full-width-halfmaximum (FWHM) of the first main peak of G(r). Only the 0hr-annealed and 6hr-annealed curves are shown in the insets.
Supplementary Fig. 11. The calculated partial and total pair distributions of amorphous Ge15Sb85. The plots are obtained from AIMD simulations employing the PBE exchange correlation function. Plotted for a direct comparison are the total and partial G(r) of the nonannealed sample, of a sample kept at ~458 K for 1 ns and 2 ns before re-quenched to ~285 K. Simulated S(q) of Ge15Sb85 for X-ray scattering (XRD) compared with the experimental XRD data (red curve). The agreement is satisfactory for a qualitative interpretation, as all the main features are reproduced in the simulation. (c) Simulated g(r) functions are compared with the experimental g(r) (red curve) converted from G(r). Note that the number density ρ0 upon annealing at 458 K is needed to convert G(r) to g(r) via g(r)=G(r)/4πρ0+1. Unfortunately, we do not have this density information and thus assumed ρ0 is roughly equal to the value of roomtemperature density. The level of agreement is in line with previous computational work on PCMs employing standard PBE functionals.
Supplementary Fig. 13. The analysis of angular limited three-body correlation (ALTBC) concerns triples of atoms. Within a given maximum angle θlim between two inter-particle vectors rAB and rBC, the statistics of two inter-particle distances rAB and rBC will be determined. Thus, the 2D distribution (contour plot) of (rAB, rBC)-values indicates the chain-like three-body correlations. If the peaks in the contour plot are off the diagonal rAB = rBC, it indicates a chain of alternating short and long bonds and Peierls-like distortions (73). Supplementary Fig. 15. The cross-section plots along r=2.85-3.05 Å of the Sb-centered ALTBC. Three Ge15Sb85 samples are included, i.e., the melt-quenched sample and samples annealed at ~458 K for 1 ns and 2ns before re-quenched to ~285 K. The 2D ALTBC contours of two samples are also given here. Note that the increase in peak height in cross-section plots is consistent with the trend in total ALTBC; therefore, the Sb-centered contribution dominates the total ALTBC due to its high atomic percentage in the alloy.
Supplementary Fig. 16. The cross-section plots along r=2.85-3.05 Å of the Ge-centered ALTBC. Three Ge15Sb85 samples are included, i.e., the melt-quenched sample and samples annealed at ~458 K for 1 ns and 2 ns before re-quenched to ~285 K. The 2D ALTBC contours of two samples are also given. The change in peak height does not show a clear trend as observed in total ALTBC. Thus, Ge-centered ALTBC does not appear to dominate the total ALTBC. Supplementary Fig. 17. Total nearest-neighbor distribution of amorphous Ge15Sb85. The centers of the histograms shift to higher distances with increasing nearest neighbor order, and the overlaps between histograms of different nearest neighbor orders are also obvious. The peaks of the orders 1, 2, 3, and 4 show a slight but clear enhancement to higher intensity, which is dominated by Sb-centered nearest neighbor distribution, see Supplementary Fig. 18-21. On the contrary, fifth and sixth order peaks reveal weaker values after annealing.
Supplementary Fig. 22. The drift of the potential and total energy along the isothermal annealing at 300 K and 458 K for 2 ns. At 300 K, the drift is of the order of 4×10 -3 eV/ns per atom. The similar trend in the drift appears at 458 K despite a larger uncertainty. The drifts stem from genuine relaxation of the amorphous state. Supplementary Fig. 23. Reflectance spectra of amorphous Ge15Sb85 as measured by FTIR at room temperature. Black solid line is as-deposited Ge15Sb85, while blue and red solid lines are amorphous Ge15Sb85 annealed at 458 K for 3 and 6 hours, respectively. The corresponding dashed lines represent the fitting results employing Tauc-Lorentz model. Supplementary Fig. 24. Illustration for the suppression of b-relaxation and its influence on crystallization kinetics in Ge15Sb85. The shadow region represents the upper and lower boundary of Tb as a function of Q. Tb crosses Tp at the heating rate around which the effect of suppressing b-relaxation starts to show up in crystallization.

Supplementary Table
Supplementary Table S1 Standard deviations of Tp in the FDSC measurements for asdeposited (SDasd), 3 hours annealed (SD3hr) and 6 (SD6hr) hours annealed Ge15Sb85 samples. The standard deviation values are calculated from the average of 10 measurements for each heating rate.

Supplementary Notes
The timescales of b-relaxation and crystallization At the low heat rates Q~1-50 K/s, which is within the typical range of conventional DSC, the suppression of the b-relaxation has little impact on the Tp values. In this regime, the temperature of the b-relaxation Tb occurs well below that of the crystallization. Both occur at the relatively low temperatures, where the overall dynamics are slow. Although the atomic mobility in some local regions, corresponding to the b-relaxation, is higher than that of the slow a-processes in the surrounding matrix, it is apparently not sufficient to affect the crystallization behavior, probably because the overall mobility is still not enough for nucleation and growth of crystals at this temperature. Therefore, the vanishing of b-relaxation with low heating rates barely causes any changes in Tp.
With the increasing heating rate, both Tb and Tp are shifted to higher temperatures. However, their heating-rate dependences differ due to their different activation energies. Using the data in Fig. 1a, we can estimate the peak temperature of b-relaxations Tb as a function of the heating rate Q. According to Ref. (25), Tb is related to the testing frequency f of DMA (PMS in our case) measurement via the equation f = f0·exp(-Eb/RTb), where Eβ is the activation energy of brelaxations, R is the gas constant, and f0 is a pre-factor. It has been shown that Eβ can be expressed by an universal relation with the standard Tg (Tg at 20 K/min in a DSC measurement) of the materials, Eb = (26±2)·RTg where the pre-factor 26 is a fitted parameter for a range of glassy materials (e.g., metallic, polymeric, molecular and oxide glasses) (74, 75). As demonstrated in Ref. (76), the testing frequency f and the heating rate Q are linked by a linear relation ns·f = Q, where ns is the shift factor ns. As shown in our previous work, after temperature calibration, Ta measured at 1 Hz in PMS is approximately equal to the standard Tg measured in DSC with a heating rate of Q = 20 K/min. This results in a ns of 1/3 K. If we assume Tg = Ta = 500 K and Tb is located in the range from 440 K to 490 K at the frequency of 1 Hz, with a known shift factor ns between the PMS frequency and the heating rate, we can identify the prefactor f0 (6.78×10 12 Hz when Tb = 440 K; 3.33×10 11 Hz when Tb = 490 K), Eb (108 kJ/mol) and ) if we assume Tb = 440 K. Note the value of f0 will be different if a different Tb is used. The estimated range of Tb at different heating rates is sketched by the shadow region in Supplementary Fig. 24, together with the crystallization peak temperature Tp. Note the determination of Tb at 1 Hz is not trivial, as the peak of b-relaxation has partially merged into the α-relaxation peak due to the coupling of the two relaxation processes. Therefore, the range of Tb at 1 Hz is estimated using an upper and a lower boundary temperature, 440 K < Tb < 490 K. As shown in Supplementary Fig. 24, the Tb is shifted to higher temperatures with larger heating rates and crosses Tp in the range of ~530 K-550 K at the heating rate of about 50 to 10 2 K/s. At this crossover temperature, the timescales of the crystallization and the b-relaxation become comparable. As shown in Fig. 3c, at almost the same rate, the effect of thermal annealing on crystallization becomes pronounced. This is hardly a coincidence and implies that b-relaxation starts to dominate the crystallization when the timescales of both processes are comparable.