Glass Transitions, Semiconductor-Metal Transitions, and Fragilities in $\mathrm{Ge}\text{−}V\text{−}\mathrm{Te}$ ($V=\mathrm{As}$, Sb) Liquid Alloys: The Difference One Element Can Make

Glass-transition temperatures ($T_g$) and liquid fragilities are measured along a line of constant Ge content in the system Ge-As-Te, and contrasted with the lack of glass-forming ability in the twin system Ge-Sb-Te at the same Ge content. The one composition established as free of crystal contamination in the latter system shows a behavior opposite to that of a more covalent system. The comparison of $T_g$ vs bond density in the three systems Ge-As-chalcogen differing in chalcogen, i.e., S, Se, or Te, shows that as the chalcogen becomes more metallic, i.e., in the order $\mathrm{S}<\mathrm{Se}<\mathrm{Te}$, the bond-density effect on $T_g$ becomes systematically weaker, with a crossover at $⟨r⟩=2.3$. When the more metallic Sb replaces As at $⟨r⟩$ greater than 2.3, incipient metallicity rather than directional bond covalency apparently gains control of the physics. This observation leads us to an examination of the electronic conductivity and then semiconductor-to-metal (SC-$M$) transitions, with their associated thermodynamic manifestations in relevant liquid alloys. The thermodynamic components, as seen previously, control liquid fragility and cause fragile-to-strong transitions during cooling. We tentatively conclude that liquid-state behavior in phase-change materials is controlled by liquid-liquid (LL) and SC-$M$ transitions that have become submerged below the liquidus surface. In the case of the Ge-Te binary, a crude extrapolation to GeTe stoichiometry indicates that the SC-$M$ transition lies about 20% below the melting point, suggesting a parallel with the intensely researched “hidden liquid-liquid transition” in supercooled water. In the water case, superfast crystallization initiates in the high-fragility domain some 4% above the LL transition temperature (${\mathrm{T}}_{\mathrm{LL}}$) which is located at approximately 15% below the (ambient pressure) melting point.

Figure 1

Ternary phase diagrams of Ge-As-Te and Ge-Sb-Te with common Ge-Te boundary. In the Ge-As-Te ternary diagram (right triangle), the arrows indicate the composition line of ${\mathrm{Ge}}_{15}{\mathrm{As}}_x{\mathrm{Te}}_{85-x}$ alloys studied in this work. The black shaded area is the glass-forming domain determined by the water-quenching method according to Ref. [27]. In the Ge-Sb-Te ternary diagram (left triangle), the orange dots and lines mark typical compositions of phase-change materials according to Ref. [2]. The thin orange arrow indicates the corresponding compositions in the Ge-Sb-Te system that we explore, with only limited success due to fast crystallization.

Figure 2

DSC heat flow of ${\mathrm{Ge}}_{15}{\mathrm{Sb}}_2{\mathrm{Te}}_{83}$ measured upon heating at various rates $q_h$ after previous cooling ($q_c$) from supercooled liquid at the same rate $q_c=q_h$. The onset temperatures of the glass transitions are determined by tangent line constructions as illustrated for $q_h=3\mathrm{K}{\min }^{-1}$. The curves are vertically shifted for clarity.

Figure 3

DSC heat flow upon heating at $20\mathrm{K}{\min }^{-1}$ for as-quenched samples of ${\mathrm{Ge}}_{15}{\mathrm{As}}_x{\mathrm{Te}}_{85-x}$ and ${\mathrm{Ge}}_{15}{\mathrm{Sb}}_2{\mathrm{Te}}_{83}$. Solid and open triangles indicate the glass-transition temperatures $T_g$ and crystallization onset temperature $T_x$, respectively. The arrows point to the onset ($T_e$) and the end ($T_L$) of melting. The composition As30 apparently belongs to a different phase field. The excess heat flow for the binary (starting) composition ${\mathrm{Ge}}_{15}{\mathrm{Te}}_{85}$ and ${\mathrm{Sb}}_2$ seen on the high-temperature side of the eutectic temperatures is due to the residuum of the liquid-state $C_p$ anomaly, which is the focus of our previous article [23]. The composition line under study appears to be closely following a eutectic valley from ${\mathrm{Ge}}_{15}{\mathrm{Te}}_{85}$ down to a ternary eutectic near 20% As (in Fig. 1).

Figure 4

(a) Glass transition $T_g$, melting onset (or eutectic) $T_e$, and liquidus $T_L$ temperatures of ${\mathrm{Ge}}_{15}{\mathrm{As}}_x{\mathrm{Te}}_{85-x}$ as a function of $x$ values. The open diamonds represent $T_g$ for as-quenched glasses measured at $20\mathrm{K}{\min }^{-1}$, while dots (inside diamonds) are standard $T_g$ values under the constraint $q_h=q_c=20\mathrm{K}{\min }^{-1}$. (b) The Turnbull parameter $t_{rg}$ (solid squares) and the width of the supercooled region $\mathrm{\Delta }{T}_{x-g}$ (open diamonds). Uncertainties on the individual points are comparable with the symbol sizes.

Figure 5

The natural logarithm of scanning rate $\ln (q)$, where $q=q_h=q_c$ holds, is plotted against $1/T_f$ for ${\mathrm{Ge}}_{15}{\mathrm{As}}_x{\mathrm{Te}}_{85-x}$ ($x=30$, 20, 15, 10, 5) and ${\mathrm{Ge}}_{15}{\mathrm{Sb}}_2{\mathrm{Te}}_{83}$. The slope of the fitted line is equal to $-E_a/R$, which is related to fragility by $m=E_a/(2.303R{T}_g)$, where $T_g$ is the glass-transition temperature measured under a standard DSC scan, $q_h=q_c=20\mathrm{K}{\min }^{-1}$. Note that the same $m$ values can be also obtained by constructing a $\ln (q)/q_s$ vs $T_f^s/T_f$ plot (see details in Refs. [23, 30]).

Figure 6

The fragility $m$ of ${\mathrm{Ge}}_{15}{\mathrm{As}}_x{\mathrm{Te}}_{85-x}$ (solid circles) liquids as a function of $x$ in at. % As. $m$ ranges from intermediate to strong with increasing As content. For ${\mathrm{Ge}}_{15}{\mathrm{Sb}}_x{\mathrm{Te}}_{85-x}$, fragility data are only available for $x=2$ (solid diamonds). The open diamond represents the fragility $m\sim 90$ for $x=28$ (approximately GST124; see text for details) by assuming that GST124 has a similar fragility to that of GST225 ($m\sim 90$) estimated by Orava et al. [4].

Figure 7

Glass-transition temperature $T_g$ as a function of bond density $⟨r⟩$ for ${\mathrm{Ge}}_{15}{\mathrm{As}}_x{\mathrm{Te}}_{85-x}$ (this work), Ge-As-Se (Tatsumisago et al. [20] and Wang et al. [21]), and Ge-As-S (Yang et al. [22]). The linear variation is a good approximation up to $⟨r⟩$ values of 2.4. Beyond $⟨r⟩=2.4$, composition-specific effects are found [20, 22], causing the spread of data points. More scattered data for Ge-As-Te glasses from early work by Savage [33] and additional data from Lucas et al. [34] (not shown) support the present findings at slightly lower $T_g$ values. For Te- based glasses with $⟨r⟩$ increased by Sb instead of As (thus, entering the fast-crystallizing PCM domain), the behavior becomes uncertain and confusing. Some estimates imply weak positive dependence of $T_g$ on $⟨r⟩$, while others require decreases, as we discuss in the text. Inset: The glass-transition temperature of ${\mathrm{Se}}_{100-x}{\mathrm{Te}}_x$ alloys [35]. The gray square is the extrapolated $T_g=350\mathrm{K}$ of pure Te and is consistent with the value extrapolated from the data in the main panel.

Figure 8

(a) Electronic conductivity of liquid ${\mathrm{As}}_2{\mathrm{Se}}_3\text{−}{\mathrm{As}}_2{\mathrm{Te}}_3$ alloys (upper panel) and the apparent activation energy $E_a$ for conductivity (lower panel) (adapted from Ref. [46]). The dashed lines mark the temperatures of the maximum $E_a$, i.e., the SC-$M$ transition temperature $T_{\mathrm{SC}\text{−}\mathit{M}}$. The arrow points to the temperature $T({C_p}^{\max })$ of the heat capacity anomaly of ${\mathrm{As}}_2{\mathrm{Te}}_3$ (780 K) [47]. (b) Upper panel: Densities of liquid ${\mathrm{As}}_2{\mathrm{Se}}_3$ at various pressures showing density anomalies. The phase-transition temperature is where the minimum in $\alpha (T)$ occurs. Lower panel: Optical band gap of liquid ${\mathrm{As}}_2{\mathrm{Se}}_3$ closes at approximately 1250 K and that of ${\mathrm{As}}_2{\mathrm{S}}_3$ closes at a higher temperature. Data taken from Refs. [48, 49]. (c) Electronic conductivities for a variety of liquid chalcogenide and two glasses (data reproduced from Refs. [46, 50, 61]). Note that the conductivities approach a plateau of the order of magnitude approximately ${10}^3{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ (the Mott minimum metallic conductivity) by a SC-$M$ transition.

Figure 9

Preliminary estimate of the SC-$M$ transition temperature $T_{\mathrm{SC}\text{−}\mathit{M}}$ in a phase-change material GeTe on the binary Ge-Te phase diagram [59]. An extrapolation to approximately 800 K for GeTe is based on the temperatures of liquid $C_p(\max )$ (red solid circles) [60, 61]. $T_g$ are represented by solid blue circles (${\mathrm{Ge}}_{15}{\mathrm{Te}}_{85}$ [23], ${\mathrm{Ge}}_{10}{\mathrm{Te}}_{90}$ [62], and Te, 350 K from Fig. 7).