Phase-change-induced martensitic deformation and slip system in GeSbTe

Abstract

Films with a newly observed monoclinic phase of Ge₂Sb₂Te₅ (GST) were analyzed by high-resolution transmission electron microscopy (HRTEM) analysis and ab initio calculations. After an annealing treatment at 220 °C, the amorphous GST films were partly crystallized to an unknown monoclinic crystal structure. The transformation of the face-centered cubic (FCC) phase to monoclinic phases resulted from crystallization-induced stress caused by volume change during FCC formation. The crystallization-induced stress at the amorphous-FCC boundary was estimated to be 1.18 GPa. The volume per atom in the monoclinic phase was about 7.3% greater than that in the FCC phase. The stress value measured in situ was much smaller than the zx stress tensor (shear stress) calculated ab initio because the stress in the actual film was minimized by plastic deformation of the GST itself. Moreover, there is an activation stress barrier to deformation; this barrier corresponds to a deformation angle (γ) of approximately 78°. Slip of the (111) plane along the [110] direction also occurs in the FCC phase during annealing treatment. Based on the calculated total energy difference per atom in GST, the martensitic deformation as well as the slip system can occur at deformation angles as low as 70°.

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Introduction

The GeSbTe ternary alloy has been widely investigated for use in next-generation non-volatile memory (NVM) because of its ability to rapidly change phase, as well as its acceptable resistance margin, low power consumption, and good retention characteristics.^1–3 The metastable face-centered cubic (FCC) structure of GST, which has a distorted lattice containing 20% vacancies in the 4(b) site (Ge, Sb), can quickly (>20 ns) and reversibly change to an amorphous phase. On the other hand, the stable hexagonal GST phase does not contribute to the rapid phase-change behavior.^4,5 The phase transition between laser-melted amorphous GST and the FCC structure of GST demonstrates that some portion of Ge atoms change in Ge–Te symmetry from an octahedral to a tetrahedral structure during the melt-quenching process.⁶ However, the model for phase changes in materials such as GST is still disputed.^7,8 In amorphous GST, the sp³ hybridized bonds are reportedly destabilized and converted into p bonds by valence alternation between Ge and Te, leading to bond angles of about 90° around the Ge atoms.⁸ In addition, the interplay between the resonant bonding character and the Peierls distorted structure of the FCC GST has been suggested for phase-change behavior.⁹ Therefore, because the phase-change mechanism has been suggested with the atomic scale structure, it is important to observe the evolution of GST crystalline phases at the atomic scale to understand the behaviors of devices with nanoscale features.^10,11

To observe the origin of the phase change in GST at the atomic level, numerous studies have included the use of HRTEM analysis to investigate GST's crystalline microstructure. In collecting HRTEM images, damage from the high-energy electron beam becomes a crucial problem when a 10 nm-thick silicon nitride membrane used as a substrate enters the path of the electron beam.¹² Kim et al. reported the formation of GST with a metastable (FCC) and a stable (hexagonal close-packed) structure using HRTEM along with simulation code.¹³ However, samples prepared by mechanical polishing and Ar⁺ ion milling can undergo undesirable crystallization. Hence, to investigate the crystalline structure on the atomic scale without adding any extrinsic factors, HRTEM analysis should be carried out on undamaged samples that are free of contamination.

In this study, we prepared undamaged and contamination-free GST samples for HRTEM analysis. An unknown crystalline phase with a distorted monoclinic structure was generated during the transition of the GST film from an amorphous phase to an FCC phase. This distorted phase can be generated by plastic deformation during the phase transition. The experimentally measured stress during the annealing treatment was significantly less than the calculated value because of this relaxation due to deformation. To investigate the origin of these differences in stress values, we performed ab initio geometrical relaxations using the Vienna ab initio simulation package (VASP), calculating the relaxations for monoclinic phases with various deformation angles and observing their differences in stress. Ab initio calculations have been widely used to investigate the nature of chemical bonds in GeSbTe materials and the mechanical properties of chalcogenide materials.^3,8,14–18 The ab initio calculated hydrostatic pressures in the monoclinic phase were negligibly low, while the zx stress component (shear stress) in the [100] direction acting on the (001) plane was high relative to the ab initio calculated stress. That is, a stress barrier hinders GST deformation, indicating that plastic formation of the monoclinic phase begins when the stress is higher than the stress barrier. In addition, for deformation angles less than 70° (i.e., strain greater than 0.35), the slip system becomes active as its total energy per atom becomes less than that of the monoclinic deformation; around 70°, slip of the (111) plane in the FCC phase along the [110] direction occurs simultaneously with the monoclinic deformation.

Results and discussion

No crystalline regions were apparent in HRTEM images of the as-grown film deposited at room temperature (Fig. S1†); to investigate the structural changes in detail after annealing at 220 °C, we focused on changes at the boundaries between the crystalline and amorphous structures. A new crystalline phase, which was neither FCC nor hexagonal, was observed at the FCC-amorphous boundary in the GST films after annealing at 220 °C (Fig. 1(a)). This crystal structure has an angle between the two axes that deviated from that of the FCC phase. Although this crystalline phase had almost the same lattice spacing as the FCC phase along the two axes (3.02 and 3.05 Å, respectively), the angle between the [010] and [100] axes (about 73.4°) differed from those of the FCC and hexagonal phases of GST. This unknown phase was identified using information from HRTEM images and data on lattice spacing and angles between the axes. As we will discuss later, X-ray diffraction (XRD) analysis showed that the lattice spacing of the crystal in the GST thin film, in the normal direction of the film, was identical to the FCC crystal lattice spacing. Accordingly, we assumed in our calculations that this new phase had the same lattice spacing in the normal direction of the film (the c-axis) as that of the FCC. Using VASP simulation, we constructed a monoclinic phase with typical lattice parameters of a = 6.27 Å, b = 6.27 Å, and c = 6.01 Å, and angles of α = 90°, β = 90°, and γ = 73.4°; the constructed structure also consisted of Te, Ge, and Sb, with 20% of the vacancies located at the Ge and Sb sites, as in the FCC phase; a 2a × 2b × 2c example of this structure is shown in Fig. 1(b). The simulated atomic image for the monoclinic phase (green box in Fig. 1(a) produced using the NCEMSS code agreed with the crystalline phase.

Fig. 1 (a) HRTEM image of a GST film annealed at 220 °C; a simulated image of the monoclinic phase is shown in the green box. (b) Estimated 2 × 2 × 2 structure of a conventional monoclinic cell containing vacancies. (c) FFT diffraction patterns of (a) with a deformation angle of 73.9° and monoclinic (200) and (020) lattice spacings.

To obtain more general information regarding the monoclinic phase, a Fourier-transformed diffraction pattern was obtained; γ of 73.9° was observed in this pattern (Fig. 1(c)), which differed slightly from the 73.4° angle calculated from HRTEM images. This indicated that this angle varies among unit cells due to local differences in stress within the monoclinic phase. The interplanar spacings of M(200) and M(020) were 3.08 and 3.05 Å, respectively, indicating that the monoclinic phase was locally distorted and had a structure slightly different from a FCC structure, as indicated in Table 1. In ab initio calculations, varying γ in this phase led to slight variations in the resulting interplanar spacings.

Table 1 Crystal structures, stress tensors, and hydrostatic pressures for various values of γ

	Optimized crystal structure					Stress tensors and hydrostatic pressure [GPa]						Hydrostatic pressure
	γ	α, β	a [Å]	b [Å]	c [Å]	xx	yy	zz	xy	yz	zx
1	90	90	5.99	6.00	5.99	0.021	0.033	0.005	−0.001	−0.002	0.003	−0.020
2	86	90	6.01	6.01	5.99	0.069	0.083	0.107	−0.066	0.009	1.136	−0.087
3	82	90	6.07	6.09	5.96	0.031	0.029	−0.044	−0.025	−0.016	1.832	−0.005
4	78	90	6.11	6.20	5.96	0.036	−0.029	−0.016	0.021	−0.028	1.981	0.003
5	74	90	6.25	6.19	5.96	−0.021	0.084	0.007	0.087	0.061	1.295	−0.023
6	70	90	6.22	6.19	6.04	0.022	0.015	−0.032	−0.094	0.084	1.284	−0.002
7	66	90	6.52	6.63	5.90	0.056	0.07	0.042	0.105	−0.006	1.357	−0.056

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The decrease in volume upon crystallization from the amorphous to the FCC phase during annealing induces high tensile stress in the direction of the film plane, which can generate a deformed structure.¹⁹ The increased bond length observed in the plane direction provided evidence for this transformation. The Ge–Te bond, which was 3.136 Å long (Fig. 1(b)), was stretched due to tensile stress in the direction of the film plane; for comparison, the same bond in the FCC phase was 3.005 Å. The formation of a new crystalline phase by shear stress, with slight atomic rearrangement, indicates that this structural change can arise from martensitic transformation without any diffusion of atoms.²⁰ A previous study predicted martensitic transformations in GeSbTe materials;²¹ although that study was concerned with the transformation from the FCC phase to a hexagonal phase in GeSbTe materials, it suggests that GeSbTe materials can be deformed via diffusionless transformation.

The volume of the monoclinic phase was almost 7.3% greater than that of the FCC phase if, similar to the FCC phase, the monoclinic phase contained 20% vacancies in the Ge and Sb sites. As a result, the volume of the FCC structure was 30.15 ų per atom, whereas the volume of the monoclinic phase was 32.36 ų per atom. This volume expansion of the monoclinic phase is closely related to the tensile stress during the phase change from the amorphous to the FCC phase. As a result, this tensile stress generates a transformation from the FCC to the monoclinic phase with various angles. Another monoclinic phase was observed in a HRTEM micrograph of a sample that had undergone annealing at 220 °C (Fig. 2(a)); corresponding fast Fourier transform (FFT) diffraction data indicated a smaller angle of 69.2° between the monoclinic (200) and (020) axes than the corresponding 73.4° angle observed in the unannealed sample, showing that there was more tensile stress acting on this region of the annealed GST film. In a previous report on the crystalline phase transition in GeSb₂Te₄ film, scanning tunneling microscopy showed that a structure without threefold symmetry, which is slightly different from the FCC (111) structure, is formed after annealing.²² This result suggests that the structural difference is caused by resonance bonding of GST. On the other hand, in our HRTEM images, the distortion structure was observed only in the boundary region between the amorphous and crystalline phases, indicating that tensile stress in the GST film due to shrinkage of the FCC phase was responsible for this distortion. We also observed another type of monoclinic phase in HRTEM images and in FFT diffraction patterns obtained from these images (Fig. 2(c) and (d)): the lattice spacings of the monoclinic (200) and (020) phases were 3.02 and 3.01 Å, respectively, while the deformation angle γ was 85.1°, which is slightly smaller than the 90° angle of the FCC structure. Although we tried to find a single FCC phase at the crystalline-amorphous boundary in the GST films, we failed to detect a perfect FCC phase with an exact 90° angle in the direction of the plane. Instead, we readily found that the deformation angle γ varied between 80 and 88° throughout the monoclinic structures (Fig. S2 and S3†). Also, the diffraction patterns of those phases (Fig. S2(b) and (d) and Fig. S3(b) and (d)†) showed almost the same lattice spacing as that of the distorted monoclinic phases (Fig. 1(a) and 2(a)). The distorted monoclinic phases showed two deformation angle ranges that will be discussed in detail later: one from 70 to 74° and another from 81 to 88°.

Fig. 2 (a) HRTEM images of a monoclinic phase after annealing at 220 °C. (b) FFT diffraction patterns in this region with a γ angle of 69.2° and monoclinic (200) and (020) lattice spacings; γ here differs from the 73.4° angle observed in (a) because of a difference in local stress. (c) HRTEM image of the monoclinic phase, showing an FCC angle of 90°. (d) FFT diffraction patterns obtained from (c) with γ of 85.1° and monoclinic (200) and (020) lattice spacings of 3.02 and 3.01 Å, respectively.

The lattice parameters of crystals in the normal direction of the film surface were obtained by X-ray diffraction data collected in thin film mode using a fixed incident angle of 0.4° (Fig. 3(a)). The strongest peak at 29.7° agreed exactly with the FCC (200) lattice spacing of 3.005 Å. This result clearly indicates that the lattice spacing remains nearly constant in the normal direction of the film surface. Therefore, we assume that the c-axis of the monoclinic crystal did not change significantly, as described in Fig. 1(b). In addition, to analyze crystals in the plane of the thin film, selected area electron diffraction (SAED) was performed; the strongest ring (consisting of spots) in this analysis corresponded showed a lattice spacing of about 3 Å (Fig. 3(b)). Some spots had slightly different scattering vectors because of differences in the lattice spacing in the plane of the thin film, whereas no variation was observed in the normal direction of the film. To verify this observation, the diffraction pattern intensity profile and polar profile were analyzed; many spots had slightly different lattice spacings from the 3.005 Å spacing of FCC (200) (Fig. 3(c)). This result strongly supports the conclusion that various monoclinic crystals were present, with various lattice spacings depending on the tensile stress.

Fig. 3 (a) X-ray diffraction data from a GST film after annealing at 220 °C, collected using a fixed incident angle of 0.4° in thin film mode. The strongest peak is from the 3.005 Å lattice spacing, which is identical to FCC (200) in the normal direction of the film. (b) SAED pattern of the GST film collected by TEM after annealing at 220 °C. The strongest ring, which consists of many spots, has a lattice spacing of around 3 Å. (c) Diffraction pattern intensity profile obtained from (b), including a polar profile that contains individual scattering vectors of spots, as indicated by green arrows.

We attempted to estimate the stress caused by volume shrinkage of the FCC phase during GST crystallization when crystallization proceeds isotropically with a spherical shape, as shown in Fig. S4† (see Methods section). Previously, the density of the FCC phase was reported to be about 6.8% larger than that of the amorphous phase, which is equivalent to a 7.3% volume change.²³ By using eqn (4) in the Methods section, and using a shear modulus (μ) of 12.17 GPa,²³ we calculated that a large stress of about 1.18 GPa (caused by crystallization) was generated in the crystalline FCC phase. However, the actual stress change in the GST film during the phase change was significantly smaller than the calculated value (see black line in Fig. 4(a)). This phenomenon was also described in a previous report, which indicated that plastic deformation induces relatively little stress in GST films.²⁴ During plastic deformation, the calculated stress is much larger than the observed stress, which strongly suggests that the diffusionless transformation induced by plastic deformation can be applied to the GST system.²⁵ Therefore, a plastic deformation generates the monoclinic phase in GST films, thereby reducing the stress of the amorphous-FCC phase transition.

Fig. 4 (a) Stress–temperature relationship of the GST film on a Si substrate during heating to 320 °C (black line) and subsequent cooling to room temperature (red circles). (b) zx stress tensor values, hydrostatic pressures (right axis), and volume per unit atom (left axis) as a function of the angle between a and b (γ) in the GST structures, as simulated using VASP for various values of γ. The angle γ corresponding to the greatest zx stress tensor is about 78°, which acts as a stress barrier to the plastic deformation. A range of angles that were not observable is indicated by the cyan box; the regions governed by plasticity and by elasticity are indicated by colored arrows. (c)–(e) Geometrically optimized 4a × 4b × 4c GST crystal structures obtained from VASP ab initio calculations with γ of (c) 90°, (d) 82°, and (e) 70°; red dashed boxes correspond to a 2a × 2b conventional unit cell of GST, and the (001) plane of the structure is in the plane of the figure. The shear stress, which originated from the zx stress tensor, is indicated by an arrow in (d) and (e). (f) Total energy differences per atom as a function of strain in the monoclinic deformation and the slip in the FCC (111) plane along the [1̄10] direction. In the strain range from 0.0 to 0.35 (γ from 90 to 70°), monoclinic deformation has lower energy difference while the slip has lower energy difference for strain greater than 0.35.

To investigate in detail the mechanism whereby the monoclinic phase is formed, we carried out ab initio calculations to optimize the deformed structure of GST for various angles γ; Fig. 4(b) shows the volume per atom and the two stress values of the zx stress tensor and the hydrostatic pressure after geometrical optimization of the monoclinic structure; Table 1 gives detailed crystalline properties and stress tensors. Interestingly, the volume per atom of the deformed martensitic structure increased abruptly to 32.14 ų as γ was decreased below 70°. This volume change originated from the structural change from the FCC to the martensitic GST structure. Moreover, the zx stress in the [100] direction acting on the (001) plane increased to 1.981 GPa at 78° as the GST structure was deformed. As the deformation increased, the stress tensor plateaued at about 1.3 GPa between 74 and 66°. This stress variation simply indicated that there was a stress barrier to deformation corresponding to γ of about 70°. Based on the calculation data, we checked the deformation angles using HRTEM; γ angles from 73.4 to 69.2° were observed in the deformed monoclinic structure, whereas γ angles from 73.4 to 81° were not. This result is consistent with the maximum shear stress (see blue box in Fig. 4(b)). For deformation angles from 81 to 88°, GST behaves elastically because the local tensile stress in this regime does not overcome the stress barrier (Fig. 4(b)). However, at other angles (69.2–73.4°), GST behaves plastically. The stress barrier of 1.981 GPa was greater than the calculated stress value of 1.18 GPa originating from the volume change of the FCC phase; thus, this barrier prevented plastic transformation. As a result, transformation to the low-angle monoclinic phase (69.2–73.4°) occurred in only a few regions in which the stress barrier was overcome, allowing plastic deformation to proceed. Hydrostatic pressures were nearly 0 GPa throughout the 66–90° range, indicating low stresses in these experimental ranges (Fig. 4(a)). Generally, plasticity can be confirmed based on a stress–strain curve, as shown in a previous experiment dealing with tensile stress, similar to the stress–deformation angle curve in Fig. 4(b).²⁶ Fig. 4(c)–(e) show the 4a × 4b × 4c crystal structure of GST after the ab initio optimization with γ values of 90, 82, and 70°, respectively; Fig. S5† shows crystal structures simulated based on other angles. As mentioned previously, the zx stress tensor (along [100]) is high in the case of deformation, whereas the other stress tensors are negligibly low (Table 1). Therefore, the shear stress acts in the [100] direction (Fig. 4(d) and (e)). This stress can cause the GST FCC crystal to transform into an elastic, high-angle monoclinic phase or a plastic, low-angle monoclinic phase.²⁴ The deformation of the GST crystal structure was confirmed using HRTEM images of GST annealed at 220 °C. However, there is also a possibility that slip systems are present whereby the crystal can undergo plastic dislocation motion. In general, a FCC crystal is allowed to have a slip system along the close-packed plane; thus, slip can occur in the FCC (111) plane along the [1̄10] direction. To verify the existence of the slip system in FCC, we calculated the total energy difference per atom in the monoclinic deformation and in the slip system as a function of strain (i.e., deformation angle); in this analysis, the energy difference per atom in the monoclinic transformation was clearly much lower than that of FCC (111) slip over the range of strain of 0.0 to 0.35, which corresponds to the range of γ from 90 to 70° (Fig. 4(f)). However, for greater strains, the total energy difference became much lower in the slip system. Thus, the monoclinic transformation is only available up to the strain value of 0.35 (γ > 70°), while the slip system governs the deformation for strains greater than 0.35. This agrees with the previous observation of plastic deformation of the monoclinic phase starting with the deformation angle of 69.2°. With greater strain, slip by plastic deformation occurs (Fig. S6(a)†). Fourier-transformed diffraction patterns show the FCC crystal in this region (Fig. S6(b)†). Fig. S6(c)† schematically describes the successive atomic motion in the slip system of FCC (111) along the [1̄10] direction.

In the case of the martensitic deformation, many atoms in the martensitic structure were slightly distorted after optimization, indicating that the monoclinic phase was distorted because there were many vacancies in the original crystal structure (Fig. 4(e)). The local structures and bonds, however, still had a cubic form, which is crucial for monoclinic transformation because the shear stress slightly distorts the structure without diffusion. This behavior was also determined from the bond angle distribution around the Ge of GST with various deformation angles (γ), which are plotted in Fig. 5(a)–(f). Even with a γ of 66°, most bond angles were distributed between 80 and 100° (Fig. 5(f)). That is to say, most local bonds retained angles near 90°, even after enormous plastic deformation of the GST, suggesting that the local bonds remain stable throughout the deformation. This clearly indicates the existence of a certain stress barrier preventing transformation to a monoclinic phase, and suggests that, when GST materials are used in devices, their stress should be controlled during the switching process. That is to say, if a GST phase change memory device containing both amorphous and crystalline structures undergoes shear stress in excess of the stress barrier, a monoclinic phase could form, affecting device properties such as the retention and the resistance margin.

Fig. 5 (a)–(f) Bond angle distributions of the GST structure in Ge atoms for various values of γ, as obtained in VASP simulations. Most of the bonds are between 80 and 100°, clearly indicating that the bond angles are not significantly deformed, even after formation of the monoclinic phase of γ = 66°.

Characterizing the monoclinic phase in terms of deformation angle using ab initio density of states (DOS) calculations is also crucial to elucidate and precisely predict the atomistic behavior and device properties of GST materials. Accordingly, we also performed total DOS calculations using VASP, which yielded Gaussian widths of 0.1 eV; at the angle of 90°, a small gap was present below the Fermi level (Fig. S7†). This property corresponds to the DOS of semimetal materials, which will not be discussed here.^27–30 Instead, we focused on the absence of a gap after deformation. In most deformed GST structures, an absence of gap is clearly recognizable. This result suggests that the deformed GST structure can have different electrical conduction characteristics because the gapless DOS may induce metallic conduction behavior. Realistically, the deformed region can act as a conducting path in phase-change memory devices if some stresses remain inside the device. Considering that the martensitic transformation propagates at the speed of sound, about 340.29 nm ns⁻¹,^20,31,32 a deformed structure can be generated right after nanosecond pulsed switching in a phase-change device.

Conclusions

The crystalline phases of GST films were investigated by HRTEM analysis in conjunction with stress calculations using the ab initio method. A monoclinic phase having a different structure than the FCC phase was observed in annealed GST films. The calculated volumes of the monoclinic and FCC phases indicated that the stress due to the phase change process during annealing is critical for the monoclinic transformation. The calculated stress was significantly greater than the measured stress because in the actual samples, a monoclinic deformation originating from deformation of the GST film occurs during the amorphous-FCC phase transition. In addition, from the optimization performed by applying ab initio calculations, we found a stable region in which the zx stress tensors plateaued in terms of plasticity, corresponding to deformation angles γ of less than 74° but greater than 70°. Moreover, there was a stress barrier of about 1.9 GPa at 78° for the plastic deformation. Therefore, deformations occurring between 90 and 78° originated from elasticity. With higher strain of 0.35 (deformation angle lower than 70°), slip of FCC became active.

Methods

To produce a contamination-free GST microstructure, GST was deposited on a silicon nitride membrane in combination with in situ SiO₂ capping. Thirty-nanometer-thick silicon nitride membranes (Norcada Inc.) were used as substrates to minimize damage from the high-energy electron beam during the HRTEM observations. The membranes were produced by etching one side of a Si wafer containing silicon nitride. A 20 nm-thick layer of GST was deposited on the membrane by ion beam sputtering deposition (IBSD).³³ After GST deposition, a 10 nm-thick SiO₂ capping layer was deposited in vacuo to prevent further contamination by air exposure. Annealing was conducted for 20 minutes in a N₂ atmosphere at 220 °C to produce an FCC structure. In a previous report on annealing of GST/SiO₂ multilayers, we performed HRTEM to confirm an interaction between two layers with nano-scale sublayer thicknesses.³⁴ Based on the results, we concluded that there were no interactions or diffusion between sublayers, provided that the GST and SiO₂ sublayers were thicker than 10 nm. HRTEM observations were performed using a Tecnai G2 30 (FEI Inc.) instrument with a field-emission gun at an operating voltage of 300 kV. Atomic-resolution HRTEM images of the crystalline phases were confirmed using the National Center for Electron Microscopy Simulation System (NCEMSS) code.³⁵ SAED patterns were analyzed with a diffraction ring profiler, which was developed to identify phases in complex microstructures.³⁶ FFT diffraction patterns of selected areas in the HRTEM images were also obtained to identify crystalline phases.

We estimated stress based on the volume shrinkage of the FCC phase in GST crystallization with isotropic crystal growth and a spherical shape. Here, a spherical volume of radius R_a was assumed to be crystallized in an amorphous matrix of radius R_b, undergoing a volume shrinkage δv. The crystallization-induced stress (σ_rr) was determined in spherical coordinates by applying the boundary condition of σ_rr = 0 at r = R_b:³⁷

where μ denotes the shear modulus of GST.

The volume shrinkage (δv) can be written as

δv = (4/3)πR_a³e^T, (2)

where e^T is the dilatational strain due to the crystallization.

Combining eqn (1) and (2) yields the following relation.

After crystallization, R_a is much less than R_b, and eqn (3) can be reduced to the following.

The dilatational strain (e^T) induced by crystallization can be calculated as follows:

where V_amorphous and V_FCC denote the atomic volumes of the amorphous and FCC phases, respectively.

To confirm the average stress change of GST films during the phase transition, in situ stress was measured based on the change in curvature of the film's surface. The film stress can be expressed using Stoney's equation as follows:³⁸

where σ_f is the biaxial film stress, Y_s is the biaxial modulus of the substrate, K is the curvature of the film, and t_f and t_s are the respective thicknesses of the film and substrate. One hundred-nanometer-thick GST films were deposited on stress-released 200 μm-thick Si substrates. Film curvature was measured using a laser-scanning system with a heated stage; samples were heated from room temperature to 320 °C at the rate of 3 °C min⁻¹, and were then cooled in a N₂ atmosphere.

The ab initio geometry of FCC GST and that of monoclinic GST were optimized by using the Vienna ab initio simulation package (VASP) code, using the generalized gradient approximation (GGA) and the PBEsol approximation.³⁹ Some parameters in Perdew–Burke–Ernzerhof (PBE) were revised in PBEsol to obtain precise information about a solid under intense compression.⁴⁰ Projected Augmented Wave (PAW) pseudopotentials were used with a plane wave basis set cutoff of 500 eV without spin polarization.^15,41 The primitive unit cell used in the calculations comprised 58 total atoms (Ge₁₃Sb₁₃Te₃₂:Ge₂Sb₂Te_4.97), chosen on the basis of the lowest energy configuration with a layered structure of Sb normal to the [111] direction of the FCC structure.⁴² In this model, six vacancy sites with the lowest energy were randomly distributed. The structure with an ordered vacancy layer had the highest total energy. A 3 × 3 × 3 k point mesh generated by the Monkhorst–Pack scheme was used for numerical integrations over the Brillouin zone. The atomic positions in the supercell were optimized by a conjugate gradient, which is the default scheme for standard structure relaxations to minimize forces and energy and to locate a local minimum of the total energy surface. The forces on each atom were relaxed to less than 0.02 eV Å⁻¹. The stress tensor and hydrostatic pressure were obtained in a monoclinic system with various angles (ranging from 66 to 90°) between the a and b lattices (i.e., various angles of γ). Realistically, because the GST thin film has a confined geometry, tensile stress acts on GST during annealing treatment. Therefore, thin film behavior is reflected as shear stress (zx) on the GST structure in VASP calculations, as indicated in Table 1. Consequently, optimized crystal structures in VASP calculations with a non-90° angle γ (from 86° to 66°) exhibit high stress values in the zx direction as shear stress.

Author contributions

M.H.J. developed the design of the experiments and the ab initio simulations. M.H.J., S.J.P., and S.J.P. carried out the thin-film deposition process. M.H.J. analyzed the HRTEM images. M.H.J. and J.Y.S. calculated the stress. K.S.J. performed the ab initio simulations. J.Y.S. measured the in situ stress. S.J.P. carried out the XRD measurement. M.H.J., K.S.J., and M.-H.C. analyzed the results. M.H.J., S.J.P., and M.-H.C. wrote the manuscript.

Acknowledgements

HRTEM measurements were performed at the Korea Basic Science Institute in Seoul. XRD measurements were performed at the 10C beamline in the Pohang Light Source. This research was supported by the National Research Project under the name “Phase-Change Random Access Memory Development”, sponsored by the Ministry of Knowledge Economy of Korea, and by the Korea Research Institute of Standards and Science under the Metrology Research Center project.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra16946h

‡ Current address: Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, USA.

§ M.H.J. and K.S.J. contributed equally to this work.

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