Article pubs.acs.org/cm
Specific Heat of (GeTe)x(Sb2Te3)1−x Phase-Change Materials: The Impact of Disorder and Anharmonicity Peter Zalden,*,† Karl Simon Siegert,† Stéphane Rols,‡ Henry E. Fischer,‡ Franziska Schlich,† Te Hu,§ and Matthias Wuttig*,†,∥ †
I. Physikalisches Institut (IA), RWTH Aachen University, 52056 Aachen, Germany Institut Laue-Langevin, 6 rue Jules Horowitz, B.P. 156, 38042 Grenoble cedex 9, France § SLAC, Stanford Institute for Materials and Energy Sciences, 2575 Sand Hill Road, Stanford, California 94025, United States ∥ JARA − Fundamentals of Future Information Technology, RWTH Aachen University, 52056 Aachen, Germany ‡
S Supporting Information *
ABSTRACT: Phase-change materials (PCM) are bad glass formers, and their rapid crystallization is accompanied by a drastic change in optical and electrical properties, which opens opportunities for novel nonvolatile data storage devices. Many of these materials are located on the pseudobinary line between GeTe and Sb2Te3 and form a metastable rock-salt-like atomic arrangement in which Te atoms occupy one of the two sublattices and the other is randomly filled with Ge and Sb atoms as well as vacancies. The resulting disorder has profound impact on, for example, transport properties, causing disorder-induced localization of charge carriers. Here we discuss the impact of disorder on thermal properties. We have investigated several PCMs from the pseudobinary line between GeTe and Sb2Te3. A significant enhancement of the specific heat is found for the disordered rock-salt-like phase compared with the ordered trigonal phase, in which Ge and Sb atoms occupy separate layers. The magnitude of this enhancement is correlated with the fraction of stoichiometric vacancies in the Ge/Sb sublattice. The additional contribution to the specific heat is shown to consist of a reversible fraction and an irreversible fraction, which are attributed to anharmonic lattice dynamics and irreversible vacancy ordering, respectively. These findings underline the prominent role of vacancy ordering in electrical and thermal transport.
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crystallization (e.g., by laser heating in optical rewritable discs)8 or by annealing in a furnace some number of kelvins above the crystallization temperature.9 The resulting phase is semiconducting. If sufficiently high annealing temperatures are applied, Ge and Sb atoms as well as vacancies arrange on separate layers.6 This leads to a loss of the cubic symmetry (giving the lattice trigonal symmetry), and at sufficiently high temperatures it even results in metallic properties. The present study focuses on a peculiar behavior of the specific heat of crystalline GST compounds that is related to the existence of disordered vacancies. The resulting data confirm that a continuous ordering of vacancies takes place, which reduces the pronounced anharmonicity of the material. Anharmonic effects in the metastable phase lead to phonon scattering and hence influence the thermal conductivity.9,10 Tuning the thermal conductivity might provide opportunities for the application of PCMs in thermoelectric devices. At the same time, the heat capacity is an important parameter in thermal
INTRODUCTION Phase-change materials (PCMs) possess a remarkable property portfolio that enables their application in nonvolatile data storage devices: they can be cycled repeatedly between two phases, an amorphous phase and a crystalline phase. This transformation is accompanied by a significant change in properties upon switching.1−3 For many PCMs located on the pseudobinary line between GeTe and Sb2Te3 (GST), recently a continuous transition within the crystalline phase from insulating to metallic behavior with increasing annealing temperature has been observed.4 This transition has been attributed to a disorder−order phase transition. Subsequent density functional theory (DFT) calculations have identified vacancy ordering as the main cause responsible for the metal− insulator transition (MIT).5 The atoms in the initially disordered rock salt (RS) phase (Fm3̅m) occupy two sublattices, with the Te atoms on the anionic sublattice and a random distribution of Ge and Sb on the cationic sublattice.6 The stoichiometric imbalance of atoms on the two sublattices goes along with a large concentration of vacancies on the cationic sublattice,7 which reaches 29% in GeSb4Te7. This chemically disordered phase is obtained either after rapid © 2014 American Chemical Society
Received: January 16, 2014 Revised: February 27, 2014 Published: February 28, 2014 2307
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Figure 1. Phase-change materials from the pseudobinary line between GeTe and Sb2Te3 have a specific heat at constant pressure (cp) that systematically exceeds the Dulong−Petit limit (24.9 J mol−1 K−1) upon heating. The samples were initially in the AD amorphous phase and were heated over the given temperature range, in which crystallization (at Tc < 480 K) and the irreversible cubic RS → trigonal transition (only for x ≤ 0.75, cf. vertical markers) or the reversible rhombohedral RS-like → cubic (only for x ≥ 0.89, cf. vertical markers) took place. One data set for a measurement of the stable phase upon cooling is shown (blue triangles) and represents the behavior of all samples with x ≤ 0.75. It is clearly seen that the large additional specific heat of the just-crystallized phase (around 450 K) of all samples scales with the initial concentration of stoichiometric vacancies. power necessary to apply a temperature sequence to two empty pans (made of aluminum). The temperature sequence consisted of isotherms (1 min each) and temperature scans for 1 min with a heating/cooling rate of 10 K/min, resulting in a temperature change of ΔT = 10 K. In a second scan to determine Psample(t), one of the pans was filled with about 30−50 mg of the specimen, and the same temperature program was applied to these pans. In a third scan to measure Pref,2 (t), the sample pan was replaced by a new empty pan of known weight, and the measurement was repeated. During an isotherm and in the absence of chemical reactions it holds that P(t) = 0, and the power necessary to maintain a specific temperature does not depend upon the specific heat of the mounted pan. At temperatures in a [−20 K:+10 K] interval relative to the crystallization temperature, the latter condition is not fulfilled, and therefore, these data points were not treated further. The power required to heat/cool the specimen, ΔP(t), can be calculated as
modeling of phase-change memory devices, which is essential for the improvement of device performance in terms of operating speed and power consumption. Several compounds along the (GeTe)x(Sb2Te3)1−x pseudobinary line were investigated in order to reveal the influence of vacancies on the specific heat. As-deposited (AD) amorphous specimens with 0.33 < x < 1.0 crystallize in an RS or RS-like phase and possess a vacancy concentration of nominally (1 − x)/(6 − 4x) of the total lattice sites.11 This expression takes into account only the intrinsic vacancies due to stoichiometry but does not include the comparably small number of excess vacancies necessary to shift the Fermi level into the valence band.4 Materials with x < 0.33 have a higher tendency to crystallize directly into a stable trigonal (ST) phase in which the vacancies do not occupy lattice sites. Therefore, only materials with an RS or RS-like phase (i.e., with 0.33 < x < 1.0) were investigated here.
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ΔP(t ) = Psample(t ) −
where ΔCp,Al(T) is the difference of the heat capacities of the empty pans used for sample and reference measurements. P0 is chosen in such a way that the condition ΔP = 0 is fulfilled during an isotherm. Deviations from P0 = 0 are due to drifting effects in the calorimeter.13 The heat capacity of the specimen can then be determined using Cp(T) = ∫ ΔP(t)/ΔT dt. Finally, we derive an intrinsic quantity, the specific heat at constant pressure, through the relationship cp = Cp⟨u⟩/ m, where m is the mass of the specimen and ⟨u⟩ is the average molar mass (e.g., 114.1 g/mol in the case of Ge2Sb2Te5). In an ideal metal at high temperature, the specific heat at constant volume approaches the well-known Dulong−Petit limit, cV ≈ 3R ≈ 24.9 J mol−1 K−1. The difference between the two limits for the specific heat can be calculated from14
METHODS
The implications of this large concentration of vacancies were investigated by probing the vibrational properties and the anharmonicity through measurements of the density of vibrational states and the specific heat. The material’s charge carrier concentration at room temperature was found to be less than 1% of the lattice sites4 even after applying the highest annealing temperatures. Therefore, the electronic specific heat,12 CV ≈
1 ·[Pref,1(t ) + Pref,2(t )] − ΔC p,Al(T )·Ṫ + P0 2
π2 D(E F)kB2T 3
is below 0.08 J mol−1 K−1 (using values from the literature4), which is significantly smaller than the magnitude of the effects discussed here (>2 J mol−1 K−1). Hence, it is safe to assume that the heat capacity is dominated by lattice contributions. The specific heat was measured using a power-compensated differential scanning calorimeter (DSC) (PerkinElmer Diamond-DSC). It was calibrated using the melting temperature and melting enthalpy of indium and the specific heat of pure antimony powder. The measurements were performed employing a protocol described in the following (and sometimes called the “dual step” method13): First was the measurement of Pref,1(t), the differential
cp − cV =
α 2⟨u⟩ T κTρ
where α is the coefficient of thermal volume expansion (cf. later), κT is the compressibility [i.e., the inverse bulk modulus of 40(3) GPa15,16], and ρ = 6.3 g/cm317 is the mass density. Under ambient conditions at around 300 K, this difference leads to an excess in cp over cV of 1.22 J mol−1 K−1 (i.e., 5% of the Dulong−Petit limit). 2308
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It is worth mentioning that Kuwahara et al.21 also indicated that the specific heat during the initial scan of a crystalline sample deviates from that of the stable phase, although they did not show data or provide an explanation. Here we will present an explanation of this effect based on lattice anharmonicity. However, before we can proceed, we need to derive the average value associated with the distribution of force constants of the disordered bonds in the amorphous and crystalline phases. To date, these values have been presented in the literature for amorphous and crystalline GeSb2Te4 only for the contributions of Sb and Te,23 whose optical modes soften upon crystallization, although the sample hardens elastically. However, it is known that the change in interatomic distances upon crystallization is most pronounced around the Ge atoms.24 Therefore, we measured the full density of vibrational states by means of INS under ambient conditions. The resulting densities of vibrational states, g(ω), for AD amorphous and metastable crystalline Ge2Sb2Te5, normalized as ∫ −∞ 0 g(ω) dω = 1, are depicted in Figure 2.
The density of vibrational states was measured at instrument IN4 at Institut Laue-Langevin, Grenoble, by inelastic neutron scattering (INS).18 About 1 g of specimen was prepared for each phase of Ge2Sb2Te5 and was filled into pouches made of aluminum, where it homogeneously covered the cross section of the incident beam. The experiment was performed at ambient temperature in time-of-flight geometry on the anti-Stokes side with an incident neutron wavelength of 2.4 Å. The scattered neutrons were detected and integrated over an angular range from 13 to 120°, which for elastic scattering corresponds to a momentum transfer between 0.59 and 4.54 Å−1. The data treatment was performed using the Large Array Manipulation Program (LAMP),19 where in particular a measurement of an empty aluminum pouch was subtracted from the data. Additional multiphonon excitations were subtracted according to the procedure described by Reichardt.20 Samples were prepared by sputter deposition from stoichiometric targets onto substrates of borosilicate glass or stainless steel. After deposition of films of sufficient thickness (about 1.5 μm), the material can be removed by gentle scratching with a spatula or by bending the substrate. The resulting specimens were ground and subsequently confirmed to be in an AD amorphous phase via X-ray diffraction (XRD). A fraction of the powder was then annealed under an Ar atmosphere for 30 min at 185(5) °C in order to crystallize the metastable RS-like phase for neutron scattering experiments. All of the XRD measurements were performed using an X’Pert diffractometer with Cu Kα radiation in grazing-incidence geometry with a 2° angle of incidence. The scattered radiation was detected by a proportional counter behind a parallel plate collimator. Temperature-dependent measurements were carried out in an Anton-Paar furnace under an inert gas atmosphere.
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RESULTS The specific heat was measured for several compounds along the (GeTe)x(Sb2Te3)1−x pseudobinary line between elevated ambient temperature (330 K) and up to 100 K above each transition to the stable phase. Data points close to the crystallization temperature were discarded as explained earlier. The specific heats of these samples are shown in Figure 1, with the Dulong−Petit limit of 24.9 J mol−1 K−1 as the lower limit of the vertical axis range. Vertical marks in the topmost area of the figure indicate the individual transition temperatures from the RS to the stable phase (where applicable) or another reversible feature that produces a peak in the heat capacity and is associated with the change in entropy during the ferroelectric transition [at 680(10) K in GeTe]. Most of the data points represent heat capacities upon heating, whereas one additional curve (blue triangles and thin black line) depicts the universal cooling behavior of all samples with 0.33 < x < 0.85 in the trigonal phase. These data are in good agreement with an earlier calorimetric measurement of the specific heat for the stable trigonal phase of Ge2Sb2Te5.21 The specific heats of samples with x > 0.85, on the other hand, are strongly influenced by the reversible ferroelectric transition22 and therefore deviate at higher temperatures (cf. Figure S1 in the Supporting Information). Three important observations are evident from the data in Figure 1: (i) The specific heat is significantly larger upon heating (in the RS phase) than upon cooling. (ii) Even upon cooling (in the stable trigonal phase), the heat capacity exceeds the Dulong−Petit limit. (iii) The additional contribution to the specific heat observed during the first heating at around 468 K, where all samples are in the disordered RS-like phase, is correlated with the fraction of vacancies (cf. inset).
Figure 2. Densities of vibrational states of AD amorphous and metastable crystalline (RS phase, annealed at 170 °C) Ge2Sb2Te5 were measured by INS at ambient temperatures and are compared as raw data (thin lines with error bars) and without the multiphonon background (thick lines). Vibrational softening of the optical modes occurs upon crystallization, whereas the acoustic modes harden. These acoustic modes were fitted using a Debye model, which confirmed the acoustic hardening (solid green line for the crystalline state compared with the dashed green line for the amorphous state).
A first visual inspection confirms that the acoustic modes harden while the optical modes soften upon crystallization when the Ge-based states are taken into account as well. Around ambient temperature, the specific heat of all phases corresponds well to the Dulong−Petit limit, as illustrated in Figure 1. This indicates that at T < 300 K, the vibrational properties can be treated reasonably well with a harmonic model as the starting point for our analysis. Therefore, Debyelike behavior, g (ω) = 3
ℏ3ω 2 (kBθD)3
was fitted to the data for the acoustic modes of the AD amorphous and metastable crystalline phases in order to derive the Debye temperature θD (cf. Figure 2). It should be stressed that because of the limited spectral resolution of the neutrons, the amorphous phase might contain additional modes at lower energies that are hidden by the elastic scattering signal. Thus, the calculated Debye temperature of the amorphous phase has to be considered as an upper limit. The resulting values are 2309
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shown in Table 1 together with the force constants F derived by integration over all vibrational modes. F reflects a harmonic
lead to the stronger increase in the specific heat of crystalline Ge2Sb2Te5 at around 50 K. To our knowledge, no lowtemperature measurements of the specific heat of PCMs (Ge2Sb2Te5 in particular) that could confirm this conclusion have been reported to date. Figure 3 also provides a comparison with experimental data for the specific heat above ambient conditions. This comparison clearly reveals a large deviation from the harmonic model for all three phases, AD, RS, and ST. The data for the stable phase correspond to the universal cooling curve shown in Figure 1 and reveal the magnitude of the inherent anharmonic nature of the distorted octahedral bonds in these materials without the influence of disordered vacancies. Even larger deviations from the Dulong−Petit limit occur in the RS phase [observation (i)] depending on the annealing conditions, which will be discussed in more detail in the following. Before this deviation of the specific heat in the RS phase can be explained, the reversibility of the experimental data has to be probed. Since the transition from the RS to the stable phase is irreversible and could take place over a wide (∼50 K) temperature range, it is important to distinguish between the influence of this irreversible transformation (during which the specific heat is a thermodynamically ill-defined quantity) and additional reversible effects. It is possible to differentiate these by performing an annealing series during which the temperature is sequentially cycled between room temperature and 150, 200, 250, and 300 °C (annealing temperatures are always given in °C for consistency with earlier studies). If the specific heat curves upon heating and cooling match, the change in cp can be considered a reversible effect, whereas additional contributions to cp that occur only upon heating must be related to an irreversible transformation. Such data are presented in Figure 4 for GeTe, GeSb2Te4, and Ge2Sb2Te5. Red upward-pointing triangles symbolize data points measured upon heating, and blue downward-pointing triangles represent the specific heat upon cooling. Figure 4 clearly reveals that for ternary materials cp is composed of irreversible and reversible contributions. The latter can be explained on the basis of anharmonic properties of the lattice. The irreversible contribution, which occurs only upon heating, indicates relaxation processes in the material that cannot be described by equilibrium thermodynamics. The data
Table 1. Elastic and Vibrational Properties of Ge2Sb2Te5 at Ambient Temperaturesa amorphous (as-deposited) crystalline (metastable)
θD (K)
F (N/m)
