Fig. 1A shows the X-ray diffraction (XRD) intensity of a-GST under various pressures, in the P range before inducing crystallization into bcc-GST at P > 28 GPa (6, 8, 9, 11). We also performed ab initio molecular dynamics (AIMD) simulations, which will be used in the following to extract the P-induced local structural evolution on the atomic level. The scattering intensities of the AIMD models at various pressures are compared in Fig. 1A with the experimental data. The minor disagreement between the simulations and experiments is acceptable, considering the spatiotemporal limitation of AIMD simulations (discussed in Methods) and the possible variants of the as-sputtered amorphous structures. The equation of states (P-V relation) derived from the AIMD models is plotted in Fig. 1B.

(A) Experimentally measured (solid lines, Exp.) and simulated (dotted lines, Sim.) scattering intensities in arbitrary (arb.) units, from in situ XRD and AIMD models in the pressure range of 0–28 GPa, exhibit similar trend. The black arrow marks where 8 GPa is reached. The XRD experiment was conducted in a DAC, filled with silicone oil as the pressure-transmitting medium. (B) Simulated equation of states (EOS, i.e., P-V relation) of a-GST models under various pressures (up to 28 GPa, before it transforms to bcc-GST in experiments). (C) The resistivity—pressure relation of a-GST (the red arrows indicate the unloading and loading sequence experienced; see text). Inset displays an optical micrograph of the a-GST sample in DAC with four Pt probes.

In the P range of 0 to 20 GPa, the electrical resistivity ρ has been measured in situ, as shown in Fig. 1C. The loading to high P during the first cycle ensured intimate contact between the powder particles, so the data are reported for the unloading part, together with those for the loading part of the second cycle. The ρ of the a-GST is approximately 20 Ωcm near ambient pressure (below 1 GPa) but drops dramatically with increasing P. Beyond P = approximately 6 GPa, the decrease levels off and ρ eventually saturates at the level of approximately 10-3 Ωcm, exceeding the low end of the typical range for semiconductors (17). Fig. 1C exhibits a hysteresis loop, presumably due to some kinetic constraints and obstacles associated with the internal structural rearrangements (see below).

An inevitable residual pressure exists in the diamond anvil cell at the starting and final points of the pressure cycle, but by extrapolating the curves to P = 0 GPa the ρ of a-GST at ambient pressure can be estimated. The extrapolation suggests a value around 102–103 Ωcm, consistent with previous measurements (18, 19). More loading–unloading cycles extending to higher P produced similar ρ-P loops. These observations confirm the intimate contact between sample powders and the probes.

Pressure Compresses the Low-Electron-Density (LED) Regions in a-GST to Induce High Electrical Conductivity.

We first focus on the lower P regime (0 to approximately 8 GPa), in which the electrical resistivity (ρ) change in a-GST is the most dramatic. The decrease of ρ by approximately four orders of magnitude is comparable to the potential range achievable by thermal-annealing-induced phase transitions and in fact more pronounced than that in the particular a-GST to rs-GST phase transition used in memory devices (compare Fig. 1C with the change of ρ as a function of annealing temperature, for example, the reported curve in ref. 3 and ref. 19).

An understanding of this P-induced precipitous ρ drop from the evolution of the underlying glass structure is of course highly important before this phenomenon can be used for applications or for guiding searches of other high-contrast memory materials. In general terms, pressure increases the mass density of the glass, and barring a phase transition, pressure-induced conductivity rise for semiconductors is often associated with the broadening and eventual overlap of the valence and conduction bands (20, 21), due to the shortening and rotation of bonds (changes in bond lengths and bond angles). To assess changes in the atomic configurations and relevant structural features (in terms of local coordination), our AIMD model configurations have been analyzed. Plotted in Fig. 2 are the partial pair correlation functions (PCFs, Fig. 2A), the bond-angle distribution (Fig. 2B), and the coordination numbers (CN ELF , Fig. 2C) as determined based on the electron localization function (ELF) approach (13). Apparently, none of these characteristic structural parameters change significantly within the P = 0 to 8 GPa range (the changes at higher pressures will be analyzed in the next section). For example, the Ge-Te and Sb-Te bond lengths, which can be obtained from the first peaks in the respective PCF, remain largely unchanged. Even the Te-Te pair distance, and the bond-angle distribution (Fig. 2B), are observed to have experienced only minor changes in this pressure range.

Fig. 2. Structural data extracted from the molecular dynamics models in the 0 to 28 GPa pressure regime. (A) Partial PCFs of Ge-Te, Sb-Te, and Te-Te. The dashed line marks the first peak at approximately 2.8/3.0 Å for the Ge-Te/Sb-Te bond lengths, and the initial/finial distance of approximately 4.2/3.1 Å for Te-Te pairs. The black arrows indicate the pressure around 8 GPa, where the structural transition is evolving from the first stage (the fast compression of LED regions) to the second stage (prominent increase of CN and decrease of bond angle) (B) The bond-angle distribution. The dashed line marks the 90° peak position expected for perfect octahedral coordination. (C) The CNs based on ELFs threshold (CN ELF ) surrounding each species in the low-pressure regime.

We note here that the CNs by ELF criterion only count the covalently bonded neighbors with a sufficient degree of electron localization in between. This is different from the distance cutoff method, which determines CNs solely by interatomic distances. The advantages of the ELF criterion have been discussed before (3, 13). The minor change of CN ELF again suggests that the average local order and bonding in a-GST have not changed a great deal in the P = 0 to 8 GPa regime.

As such, in terms of the structural origin it is quite challenging to provide a quantitative explanation to the large ρ variations observed. The changes in the normally used structural parameters are rather small and difficult to quantify and monitor, as displayed in Fig. 2. In the following, we set out to identify an effective structural indicator to reflect/summarize the gradually changing local chemical environments, rather than dwelling on the subtle details of the complicated local structure that often involve ambiguity or arbitrary cutoffs.

To this end, we notice that intrinsically the a-GST at ambient pressure possesses a relatively loose structure with the presence of a significant fraction of LED regions. These regions have been previously characterized as voids/cavities by geometric criteria and proposed to be an important feature in the structure of a-GST (22, 23). They are analogous to the vacancies in rs-GST, the role of which in facilitating phase transition has been discussed by several authors (8, 10, 24). Here we examine, from the charge density perspective, the LED regions in amorphous state and their effects on the electrical resistivity. The compression-induced volume reduction of these LED regions at increasing P can be the primary reason for the density increase in this amorphous material, correlating with the rapid ρ drop.

Different from geometric tessellation that can isolate cavity-like voids from the networking atoms (22, 25), here we identify LED regions, which can be as small as atomic scale, by mapping out volumes that have electron charge density lower than a critical level. The LED regions defined as such can be visualized, as in Fig. 3, to observe the distribution of (percolated) LED regions in space. Specifically, we employed the normalized electron density ( ), which is the absolute electron density observed at any given location in the ab initio model, normalized by the average valence electron density of the whole system. This is necessary for a meaningful comparison of a-GST under different pressure, with different mass/atomic density, as plotted in Fig. 3A. The LED regions are those enclosed by the isosurface of at a threshold value. To determine this threshold, we used a “standard”: The rs-GST is a defect-ridden crystal known to contain 10 at.% vacancies (or 20% on the Ge/Sb sublattice sites) (14, 26⇓–28). In this case, we determine the threshold to be the level that results in a total vacant region amounting to 10% of the entire crystal volume (Fig. 3B). The same threshold is then applied to a-GST (dashed line in Fig. 3A). The LED regions (corresponding to the left-hand side of the dashed line) determined this way can thus be reasonably designated as “vacant” or “vacancy-like,” and their fraction can be compared among different systems (at different pressures).

Fig. 3. (A) The distribution of (the absolute electron density normalized by the average electron density) in a-GST under various pressures. The threshold (the dashed line) to separate the vacant area is set to be 0.22, at which the volume fraction of vacancy in rs-GST is 10%; see the rs-GST reference in B. (C)–(E) Visualization of LED regions (The light areas with ) at different P. (F) The fraction of LED regions decreases rapidly with increasing pressure in the P < approximately 8 GPa regime, correlating with the fast resistivity reduction.

The LED regions in a-GST concentrate to form vacancy-like or void-like entities of various sizes (see scale markers in Fig. 3), randomly distributed inside the glass. With increasing pressure, we clearly observe a marked decrease of their volume fraction (F LED ) in the system, as shown in Fig. 3 C–E. At ambient pressure, it is known that a-GST is approximately 6.5% less dense than the rs-GST (29), and F LED starts out at approximately 16% in our a-GST (6% more than that in the calculated rs-GST). F LED turns out to be a strong function of pressure, as the electron charge density redistributes and the local motifs rearrange to arrive at different contents of the LED regions, reaching a much lower level of approximately 4% at P = 6 GPa.

To recap, in situ experiments have revealed that moderate pressures (0–8 GPa) on a-GST can reduce the electrical resistivity (ρ) of a-GST (Fig. 1C) by orders of magnitude, not possible in dense glasses such as metallic glasses (30), and to the extent similar to what is achieved via temperature-induced crystallization of a-GST (a first-order phase transition to rs-GST). Interestingly, in this pressure regime where the ρ changes most precipitously (Fig. 3), the changes in local order are neither pronounced nor easily quantifiable. Instead, the concurrent decrease in the volume fraction of the LED regions (F LED ) is rapid and highly noticeable, suggesting a strong correlation of the latter with ρ. This correlation, when explicitly plotted as in Fig. 3F, is obvious.

This correlation prompts us to take the F LED as a useful indicator to effectively reflect the overall changes in local structures, in explaining the large resistivity contrast. In fact, LED regions themselves are a meaningful structural feature that is worthy of studying, complementary to the tracking of atoms, their configurations, and bonding details. Here we note that whereas the average structure, as reflected by the PCFs in Fig. 2A, does not change much, the local structures around the LED regions may have experienced more changes. In other words, the structural change that governs the resistivity behavior is believed to be inhomogeneous and concentrated locally around the LED regions. Because F LED can be unambiguously defined and changes continuously, the reduction of LED volumes serves as a simple and yet revealing signature to summarize/represent the evolving atomic-level structure, the latter being the ultimate structural origin of property variations in glass.

To substantiate the important role of F LED on ρ in this P regime, we consider an amorphous semiconductor with localized states in its band gap and the Fermi energy (E F ) lying in the middle of the gap (see the energy band diagram for a-GST in refs. 3 and 4). The electronic transport can be understood as having two possible mechanisms: (1) the trap-limited Poole–Frenkel conduction, for which the resistivity follows (4, 31) [1]where E C is the mobility edge in the conduction band. In this mechanism, localized electrons are thermally activated to become extended electrons, contributing to the electrical conduction (32, 33). In addition, some extended electrons can be trapped by the unoccupied localized states near E C , and the release of these trapped electrons to the extended state, or the thermally assisted hopping to a nearby unoccupied localized state, has a field dependence, giving rise to a field-dependent term, Δϕ field (this term is estimated to be orders of magnitude smaller than E C -E F in our experiment). (2) the variable-range hopping (34), which refers to phonon-assisted tunneling of electrons from one localized state to another near the Fermi level. The logarithm of the electrical conductivity governed by this mechanism has a T-1/4 dependence on temperature, whereas that due to Poole-Frenkel conduction is expected to scale with T-1 (see 1 above). Based on the different temperature dependence, previous studies have concluded that variable-range hopping does not play a significant role in a-GST (4, 31, 35). Therefore, the electrical conductivity of a-GST should scale exponentially with E C -E F . The dependence of the latter on pressure, as explained in the following, holds the key to understanding the precipitous ρ drop (by several orders of magnitude). First of all, the band gap (the “optical gap” between the bottom of the conduction band and the top of the valence band) of a-GST is expected to decrease with increasing pressure. An obvious reason that can lead to a reduced band gap is that the fewer the (originally abundant) LED regions, the stronger the interactions between the local structural motifs or “clusters,” leading to broadened energy bands (35, 36). Our ab initio energy band calculation indeed supports this proposition, as indicated by the density of states (DOS) under different P plotted in Fig. 4A. The band gap obtained may not be accurate in absolute values (37), but the trend is clear for the broadening of the valence band and the shrinking of the band gap.

Fig. 4. (A) The electron DOS of a-GST in the low pressure regime. The red dashed lines in A show the broadening of the valence band and narrowing of the band gap. (B) The average value of the ELFs in the bonding areas, decreasing with the volume reduction of LED regions.

Note that to confirm the controlling role of LED regions, we also preformed ab initio calculations on another set of a-GST models, in which the atomic density changes and the same range of pressure (0 to 8 GPa) are generated solely by scaling the bond lengths, without structural relaxation that diminishes the LED regions in the original models. These unrelaxed models did not exhibit major band gap changes in the same P regime. This result can be understood by considering the two factors that affect the band gap: (1) the compressed bond length increases the bonding–antibonding splitting (in contrast to the relaxed model, where this splitting is not changed due to near-constant bond length); (2) The reduction of LED volumes (though far less significant as the relaxed models) enhances the interactions between local clusters, expanding the band width. The two contributions largely cancel out, leading to little change in the band gap (35).

Second, in addition to calculating the change in band gap, we use ELF to provide evidence that some localized electrons in a-GST become more delocalized with diminishing LED regions. The average ELF calculated for the bonding electrons is shown in Fig. 4B. Electrons with ELF toward 1 are more localized than those with ELF toward lower values (38). Fig. 4B suggests a trend that some originally trapped electrons become less localized at high P, signifying a shift of the mobility edges and narrowing of the band tails (34). This, taken together with the reduced band gap, indicates that the mobility gap is effectively reduced. E C -E F is thus expected to decrease, resulting in the exponential increase of the charge carrier density and hence of the conductivity. This is a different approach in tuning the electrical resistivity compared to the annealing-induced disorder–order transition (17).

An important implication of our discussion is that the LED regions may also play an important role in the resistivity contrast between a-GST and rs-GST (which we use in today’s devices), given that a-GST has 6% more LED fraction than rs-GST. We have shown that by tuning the volume fraction of often-localized LED regions in the glassy state itself (or vacancies in the crystal), large resistivity contrast can result. This is a desirable feature for applications in memory devices (18, 19). Also, GST in real devices is likely to work under certain level of pressure [e.g., several hundred MPa either from the confinement or due to the density change upon phase transition (29)]; understanding the P-sensitivity of ρ and its structural origin would therefore be of practical importance. The use of either one of the two thermodynamic variables, P or T (e.g., heat treatment to crystallize a-GST into rs-GST), when reducing the LED/vacancies to the same level, may produce similar ρ. Of course, different from P, the thermal crystallization of a-GST will include other types of structural changes, e.g., the bonding nature (the resonant bonding and the long-range order mentioned earlier upon phase change to rs-GST) (39⇓–41). Nevertheless, Fig. 3 suggest that shrinking LED regions should play an important role in inducing, or contributing to, the large resistivity contrast relative to the as-prepared a-GST. Indeed, heat treatment can further reduce the vacancy content in the rs-GST crystal when it is transformed to the stable phase trigonal-GST (t-GST). This t-GST also has local structures similar to rs-GST (42), but its resistivity is even lower (i.e., becoming a degenerate semiconductor) (17).