Interface-Driven Phase Transition of Phase-Change Material - Crystal

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Interface-driven Phase Transition of Phase-change Material Minho Choi, Heechae Choi, Jinho Ahn, and Yong Tae Kim Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b01690 • Publication Date (Web): 15 Feb 2019 Downloaded from http://pubs.acs.org on February 17, 2019

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Crystal Growth & Design

Interface-driven Phase Transition of Phase-change Material Minho Choi1, Heechae Choi2, Jinho Ahn3,b*, and Yong Tae Kim1,a* 1Semiconductor

Materials and Device Laboratory, Korea Institute of Science and Technology, Hwarangro 14-gil 5, Seongbuk-gu, Seoul 02792, Korea. 2Institute

of Inorganic Chemistry, University of Cologne, Greinstr. 6, Cologne 50939, Germany.

3Division

of Materials Science and Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Korea. Correspondence authors: a) E-mail: [email protected], and b) E-mail: [email protected]

Keyword: phase-change material, interfacial energy, phase transition, doping, InSbTe

Abstract: In order to be able to control the phase transition of engineered phase-change materials, the specific understanding of phase transition processes is essential. To understand the effect of dopant on phase transition, the phase transition processes of Bi5.5(In3SbTe2)94.5 (Bi-IST) are quantitatively investigated with regard to the interfacial, bulk, entropy, and Gibbs free energies involved in the intermediate InSb and InTe phases and the crystallized Bi-IST. In the first step, InSb is crystallized; InTe and Bi are present in the amorphous phase. In the second step, heterogeneous nucleation of crystalline InTe occurs on the InSb. The energy barrier calculated for this nucleation of crystalline InTe is reduced by 1.5 times owing to the interfacial reaction of 5.5 at.% of Bi atoms compared to the case without Bi. In the third step, crystalline InSb and InTe are crystallized to Bi-IST since Bi atoms substitute Sb sites with a higher interfacial energy. The difference in the Gibbs free energy of the Bi-IST is - 1.4 × 105 eV, which is lower than the - 1.1 × 105 eV of the IST; this is because the differences in entropy with an increase in temperature, and the interfacial energy are increased owing to the added Bi atoms. This lower Gibbs free energy becomes a driving force for the stable phase transition of Bi-IST at a lower transition temperature compared with that of the IST. With these phase transition processes, the contribution shares of enthalpy, entropy with temperature change, and interfacial energy are quantitatively analyzed; moreover, we recommend one of the various methods to design a novel phasechange material.

Introduction Phase-change materials (PCMs) have been used for effective optical data storage and dominantly non-volatile phase-change memories (PCRAM), for several decades1-4. These two applications differ in terms of the variations in the optical reflectivity and the electrical resistivity between the amorphous and crystalline phases2. Although the two phases, which are completely amorphous and crystalline phases, should be used to distinguish the difference in signals, certain intermediate phases are likely. The metastable property of the intermediate phases, such as the rocksalt structure of Ge2Sb2Te5 (GST) and the mixture phases of In3SbTe2 (IST), triggers a few issues in terms of reduced reliability of the PCMs. An in-depth theoretical investigation through the new approach is required to overcome these issues. For the PCRAM, GST, and GeTe–Sb2Te3 pseudo-binary systems5-7 have been popularly used until the present. Other Te-based PCMs such as IST and InSb-InTe pseudo-binary systems8 are recommended to improve the performance of PCRAM. In the case of GST in conjunction with GeTe–Sb2Te3 pseudo-binary systems, the crystalline phases are divided into two: metastable and stable phase. The metastable crystalline phase has been dominantly used as a crystalline phase for recording state ‘1’. However, at present, there is a high demand for maintenance of the stability

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Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

of PCMs during extensive data recording. Moreover, the metastable crystalline phase causes severe problems related to phase stability, such as phase separation and element segregation during repeated switching operations; these finally result in resistance drift and data error9-17. Thus, a doping method has been recommended to solve these problems related with metastable phase change and to improve the characteristics of PCMs, such as endurance, retention, switching speed, and operation voltage. A number of dopants (for example, Sn18, Ti19, Bi20, Zn21-22, W23, In24, Cr25, and Y26) have been studied with GST and IST PCMs; moreover, electrical characteristics are investigated together with the crystal structure, chemical bonding, shift of phase transition temperatures, etc. In our previous works, it was observed that the set and reset switching speeds of PCRAMs fabricated using IST doped with Y and Bi elements (Y12.38(In3SbTe2)87.6226 and Bi5.5(In3SbTe2)94.520) are evidently more effective than those of the devices fabricated with pure IST and GST. Such an improvement is strongly related to the effects of lattice distortion in the doped IST. The rapid switching process from stable crystalline to amorphous phases has been already explained with the lattice distortion model; this process is related to the rapid transition to a stable phase rather than a metastable one, albeit by reducing the transition temperatures. However, as mentioned earlier, to stabilize the phase transition process for reliable operation of PCRAM, the rapid transition from the metastable to the stable crystalline phase is essential. In order to investigate the phase transition process in detail, first, the phase transitions of GST and of IST are compared. The amorphous GST is transformed into the stable hexagonal structured GST at approximately 310 °C through the metastable rock salt structured GST at 140 °C27-30. The phase transition of IST is similar to that of GST; the main differences are in the three steps of phase transition from amorphous to the stable crystalline IST phases. The final transition temperature is 426.2 °C, which is higher than that of GST (310 °C). The amorphous IST is transformed into the first metastable intermediate phase consisting of crystalline InSb together with amorphous InTe phases at approximately 301.5 °C (T1. The amorphous InTe phase is crystallized at approximately 400 °C (T2), forming second metastable crystalline InSb and InTe phases8, 31. Finally, these InSb and InTe phases are transformed into stable crystalline IST at 426.2 °C (T3). The transition temperatures of T1, T2, and T3 are reduced by adding Bi atoms (approximately 208 °C, 300 °C, and 338 °C, respectively. Therefore, it is effective to understand thermodynamically these two metastable intermediate phases with IST and doped IST samples rather than GST because the intermediate processes of IST and doped IST are more complicated than that of GST; moreover, there is still no report of the thermodynamic behavior of the intermediate phase transition. Homogeneous and heterogeneous crystal nucleations have been widely applied to investigate the crystallization from the liquid (or solution) to the solid phase as an important factor32-33. However, in the application to electronic materials for electronic PCRAM devices, we first discuss the dopant-driven phase transition with the interfacial energy. The heterogeneous crystal nucleation model was reported by J. A. Kalb to explain the crystal nucleation from the amorphous to the crystalline phase in PCMs34-36; this implies that the heterogeneous crystal nucleation in the intermediate transition can be explained by Bi doping. In this work, according to the classical theory, the phase transition of IST and Bi-IST will be discussed according to the classical theory, together with the effect of a number of interfaces among the metastable intermediate phases in IST and Bi-IST. In addition, the phase transition of second intermediate phases to stable crystalline IST will be analyzed in conjunction with the interfacial energy, the difference in the bulk free energies between the second intermediate phases and the stable crystalline IST, as well as the interfacial energy of the element. Although the interfacial energy is frequently discussed in conjunction with the heterogeneous crystal nucleation2, 33, 36, the phase transition processes in IST and Bi-IST have not been thoroughly explained in terms of the energy barrier, interfacial energy, and bulk energy26, 34-39. Furthermore, it will be highly effective to implement a noble PCM by regulating the stable phase transition for various applications such as 3D X-point memory and synaptic application37-39.

Results and Discussions Form of doped Bi atoms in the intermediate phase As mentioned in the DFT calculations in the Methods section, the formation energy of IST is changed by the Bidoping. The changed formation energy (ΔEf) provides us the information about whether the Bi atoms substitute host atoms (In, Sb, and Te) or not in the crystalline InSb and InTe phases. When the Bi atoms substitute In sites in InSb, ΔEf = + 1.09 eV; if the Bi atoms substitute Sb sites, ΔEf = + 0.29 eV. When the Bi atoms substitute In and Te sites in InTe, ΔEf = + 1.76 eV and + 3.27 eV, respectively. Note that the Bi composition for calculating the formation energy is fixed at approximately 5% in InSb and InTe; three and six Bi atoms substitute the elements. In addition, the values of ΔS for ΔEf are not considered because the configurational entropic effect (ΔS) in the vicinity of the transition temperature (~610 K) is highly marginal at - 5.12 μeV/K·atom; this is so even when the amount of dopant is assumed to be 10 at.%, Compared to the formation energy prior to Bi-doping, these positive energy values imply that Bi atoms do not occupy substitutional sites in the InSb and the InTe atomic structures; moreover, the magnitudes indicate the

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degree of difficulty of substitution by Bi. Therefore, the Bi atoms are present separately in the amorphous state in the InSb and the InTe phases during the transition from amorphous to crystalline IST phase.

Fig. 1. XRD results of Bi-IST thin film at (a) room temperature and annealed at (b) 250 °C, (c) 330 °C, and (d) 400 °C for 15 min. To verify the sequence of phase transition from amorphous Bi-IST to crystalline Bi-IST, XRD patterns are investigated as shown in Fig. 1. A comparison of this XRD result with the IST result reveals that although the transition temperatures are lowered by Bi-doping, the three-step phase transitions are identical to those of pure IST40; moreover, the peaks of the crystalline Bi atoms are not observed. It is apparent from the XRD and DFT results that Bi atoms exist in the amorphous state throughout the sequence of the transition from amorphous to crystalline IST phase.

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Fig. 2 (a) BFTEM image of Bi-IST annealed at 330 °C. The areas within dashed lines indicate the grains for estimating the average grain size. (b) HRTEM and FFT images of crystalline InSb phase and amorphous InTe and Bi phases annealed at 250 °C. Amorphous parts are InTe and Bi except crystal grains. HRTEM images and SAED patterns of (c) crystalline InSb and amorphous Bi, (d) crystalline InTe with amorphous Bi in the same Bi-IST thin film, and (e) crystalline Bi-IST annealed at 400 °C. All samples were observed with annealed at each temperature and fast cooled. For this reason, Bi phase in Fig. 2 (b), (c), and (d) is showed as the amorphous phase instead of liquid phase although the melting point of Bi is about 270 °C. Figure 2 shows the atomic-level images using HRTEM according to annealing temperature of Bi-IST thin films. When Bi atoms substitute host atom sites, the lattice structures are changed by the Bi atoms; moreover, images of the changed lattice can be conveniently observed by comparing with the pure lattice images of InSb, InTe, and IST. However, the HRTEM images and SAED patterns of Fig. 2 indicate the absence of lattice distortion and of changes in the inter-planar distance and angle in the crystalline InSb and InTe phases. The Bi atoms exist as amorphous clusters in the interfacial area surrounded by InSb and InTe grain boundaries in the Bi-IST thin film; furthermore, the interfacial areas in IST will be further increased together with the Bi clusters during the phase transition process. In the crystalline phase after step 3 in Fig. 3, Bi makes stable Bi-IST phase with lower system energy at Sb site in IST atomic structure20.

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Fig. 3. A sequence of phase transition processes from amorphous to stable Bi-IST crystal. The phase groups I and II are defined as the groups of mixed phases for the intermediate processes of IST and Bi-IST, respectively.

Effect of interfaces induced by dopant on heterogeneous nucleation barrier The above results demonstrate that the sequence of phase transition from amorphous to stable crystalline IST can be described by three steps as shown in Fig. 3. When amorphous Bi-IST is annealed at 250 °C, InSb is crystallized, whereas InTe and Bi exist in the amorphous state. As the annealing temperature increases to 330 °C, the amorphous InTe crystallizes. Subsequently, crystalline InSb and InTe as well as amorphous Bi are transformed into crystalline Bi-IST because the Bi atoms can completely substitute the Sb sites. Thus, the main aim of this work is the theoretical and experimental investigation of these intermediate phase transition processes of steps 2 and 3 and of the effects of the interfacial and Gibbs free energy governing the phase transition of Bi-IST.

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Fig. 4. A kinetic reaction mechanism to govern the heterogeneous nucleation of crystalline InTe on the interface of crystalline InSb involving amorphous Bi in conjunction with the amorphous InTe phase. The prefixes “c-“ and “a-“ indicate crystalline and amorphous phases, respectively. To analyze the processes, we consider the role of the interfacial energy for phase transition in the intermediate phases. The amorphous Bi cluster in IST changes the interfacial energy, resulting in the change in the energy barrier of phase transition. To explain step 2 in Fig. 3, we have used the heterogeneous crystal nucleation model for crystallization of PCM introduced by Johannes A. Kalb36. According to this model, it is assumed that the crystalline InTe phase is nucleated and grown on the interface of the crystalline InSb phase during step 2 because the crystalline InSb is formed during step 1. Figure 4 shows that the heterogeneous nucleation of InTe occurs with or without amorphous Bi at the interface of crystalline InSb. When amorphous Bi is involved in the crystallization of InTe, the crystallization of InTe becomes faster than that of InTe without Bi atoms. An identical result was obtained in our previous work20. To determine quantitatively the effect of the interfacial reactions on the kinetic behaviors among the four phases (i.e., crystalline InSb, amorphous InTe, crystalline InTe, and amorphous Bi), the interfacial energy per unit area is calculated by equation (1) for five combinations of the interface between each pair of phases:

𝛾𝑎𝑠 = 𝛾𝑐𝑠 + 𝛾𝑎𝑐cos 𝜃

(1),

where the subscripts a, s, and c imply the amorphous phase, the substrate for heterogeneous nucleation, and the crystalline phase, respectively. γas, γsc, and γac are the interfacial energies per unit area for the five interfaces between a-InTe (or a-Bi)/c-InSb, c-InTe/c-InSb, and a-InTe (or a-Bi)/c-InTe.

Table 1. Interfacial energy per unit area for five interfaces. Interface

Interfacial energy per unit area, γ (eV/nm2)

c-InTe/c-InSb

1.0 (γcs, γ1)

a-InTe/c-InSb

2.7 (γas)

a-InTe/c-InTe

3.3 (γac)

a-Bi/c-InTe

2.9 (γac’, γ2)

a-Bi/c-InSb

2.8 (γas’, γ2)

Using equation (1), the heterogeneous crystal nucleation can be explained with a classical model of the energy barrier. The energy barrier for heterogeneous nucleation of crystalline InTe (ΔGc ≡ ΔGchet) can be expressed as equation (2)41-42:

∆𝐺ℎ𝑒𝑡 𝑐 = ∆𝐺𝑐 ∙ 𝑓(𝜃), 𝑓(𝜃) =

[

(2 + cos 𝜃)(1 ― cos 𝜃)2

]

4

(2),

where ΔGc is the energy barrier for the homogeneous nucleation of InTe without Bi and θ is the wetting angle between amorphous and crystalline InTe grown on the InSb surface. θ is divided into two wetting angles as shown in Fig. 4. θ1 is the wetting angle between crystalline InSb and InTe with amorphous Bi, and θ2 is the angle between InSb and InTe without Bi. The exposed volume fraction f(θ) for the heterogeneous nucleation of InTe is a function of θ. When amorphous Bi is present on the interface of the InTe phase, f(θ1) is 0.0943. In contrast, the calculated value f(θ2) is increased to 0.148 for the crystallization process of InTe without Bi, which is identical to the nucleation process of pure IST. As a consequence, the energy barrier ΔGchet for heterogeneous nucleation of crystalline InTe in step 2 is reduced by approximately 1.5 times of the former case; this is because f(θ) is reduced from 0.148 to 0.0943 by the interfacial reaction with amorphous Bi. This implies that if f(θ) equals one, homogeneous crystalline InTe is nucleated, and the energy barrier for this homogeneous nucleation is substantial higher than that for the heterogeneous one. Therefore, it is concluded that the heterogeneous nucleation of InTe is more straightforward than the homogeneous one owing to Bi atoms.

Quantitatively analysis of contribution rate of energies for phase transition to stable phase 6


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With regard to step 3 in Fig. 3, the crystalline InSb and InTe phases are transformed into crystalline Bi-IST phase, whereas Bi atoms substitute the Sb sites. This crystallization process can be explained by the difference in the Gibbs free energy (ΔGtot) defined in equation (3) because step 3 is the phase transition process from crystalline rather than amorphous phase. The difference in the Gibbs free energy equals the sum of the difference in bulk energy and the total interfacial energy of phase group II obtained with different combinations of the three phases: c-InSb/c-InTe, aBi/c-InSb, and a-Bi/c-InTe.

∆𝐺𝑡𝑜𝑡 = ∆𝐺𝑏𝑢𝑙𝑘 ― ∑𝐴𝑖𝛾𝑖, ∆𝐺𝑏𝑢𝑙𝑘 = ∆𝐻𝑏𝑢𝑙𝑘 ―T∆𝑆𝑏𝑢𝑙𝑘

(3),

where ∆Gtot and ∆Gbulk are the difference in the Gibbs free energy for phase transition of step 3 in Fig. 3 and the difference in the bulk free energy for phase transition from phase group II to the stable phase, respectively; both are negative. A and γ are the interfacial area and the interfacial energy per unit area between different combinations of phase group II. To calculate the difference in the Gibbs free energy, the difference in the enthalpy of the bulk free energies for BiIST (ΔHbulk,Bi-IST) and IST (ΔHbulk,IST) are calculated by DFT; the values are -24 meV/atom and -21 meV/atom, respectively, for the phase transition process of step 3. This implies that the absolute value (|ΔHbulk,Bi-IST|) of ΔHbulk,BiIST is larger than that of IST, indicating that the energy difference for phase transition of Bi-IST is significantly larger than that of IST. To determine the sum of interfacial energy produced by phase group II, ΣAiγi, each interfacial area (Ai) in equation (3) should be obtained. Ai is defined by the dashed line in the HRTEM image (Fig. 2 (a)) and measured by ImageJ software43 (National Institutes of Health (NIH)). The total area of seven grains appearing in Fig. 2 (a) is 3.77 ⅹ 104 nm2, and the average area of each grain (Agrain) is 5.39 × 103 nm2. However, the interfacial area of nucleated InSb or InTe is not the average area of an InSb or InTe grain. According to the above classical model explained for heterogeneous nucleation43-46, it is assumed that the i) base area of each grain is spherical as we are alluding to the base area, ii) heterogeneous nucleated area grows to form the hemispherical-cap shape in Fig. 5, iii) interfacial area of heterogeneous nucleation and growth (Ai) is the hemispherical surface involved in the base area of the hemispherical cap, iv) Bi cluster is also spherical, and v) Bi atoms are distributed uniformly and are equally in contact with InSb and InTe grains. The growth model is assumed to adopt the hemispherical-cap shape in ii because most of the grain growth from heterogeneous nucleation occurs in interfaces such as the boundary between PCM and other parts (e.g., insulator or heater in the PCRAM cell)47. The grains grow over the whole area while nearly maintaining the shape. Therefore, nucleation and growth are also induced at the center of the PCM area. However, the model with the hemispherical-cap shape can gain more validity according to decrease in the device cell. Therefore, nuclei grow to form the hemispherical-cap shape in the interfaces as the cell area decreases with technological development. Compared with inherent crystallization, which is not formed at the interfaces, the contribution of heterogeneous crystallization toward nucleation and growth also increases according to the temperature increase. The Bi cluster is observed as the small circle-like shape in Figs. 2 (b) and (c); moreover, the area of the Bi cluster is obtained for calculating Aiγi.

Fig. 5. Hemispherical-cap model to calculate interfacial area, Ai.

∑𝐴𝑖𝛾𝑖 = 𝐴1𝛾1 +𝑥(𝐴2𝛾2)

(4)

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A1, A2, γ1, γ2, and x are the interfacial area of a heterogeneous InSb or InTe grain, interfacial areas of a Bi cluster, interfacial energy per unit area between c-InSb/c-InTe, interfacial energy per unit area between a-Bi/InSb or aBi/InTe, and number of Bi clusters in phase group II in Fig. 3. Then, the interfacial area of the InTe crystallized by heterogeneous nucleation on the InSb (A1) is calculated as 𝑅1

𝑟1 = sin 𝜃2

(𝑅1 =

𝐴𝑔𝑟𝑎𝑖𝑛 𝜋

= 41.4 𝑛𝑚)

𝐴1 = π𝑟21(3 ― 2cos 𝜃2 ― cos2𝜃2)

(5) (6)

where R1 and r1 are the radii of the spherical grain and of the base circle of the hemispherical cap, respectively; θ2 is the contact angle between InSb and InTe without Bi. For the IST without Bi, there is only A1γ1; its value is 1.64 × 104 eV, which is calculated by substituting values for r1 (48.3 nm), θ2 (59.0), A1 (1.64 × 104 nm2), and γ1 (1.0 eV/nm2) into equations (5) and (6). That is, for the Bi-IST, the interfacial energies owing to the Bi clusters (A2γ2) depends on the number of individual Bi clusters present in the BiIST; this is owing to the volume of a Bi cluster. V2 equals 4πR23/3, which is significantly smaller than the corresponding value of the hemispherical cap; the number of Bi clusters is conveniently obtained by calculating the volume ratio of the hemispherical cap and the Bi cluster. The volume of a hemispherical cap (V1) is calculated by

𝑉1 =

𝜋𝑟31(2 ― 3cos 𝜃2 + cos3𝜃2)

,

3

(7)

From equation (7), the value of V1 is obtained as 6.99 × 104 nm3. In addition, the composition ratios of Bi and IST in the Bi-IST are 5.5 and 94.5, respectively; this implies that the portion of Bi clusters in the Bi-IST will be 0.058, normalized by the composition of IST. The number of Bi clusters (x) can be calculated as:

0.058 × 𝑉1 = 𝑥 × 𝑉2,

(8)

Equation (8) illustrates that the number of Bi clusters is 16 times that of the InTe or InSb in an identical unit volume. In the second term of equation (4), A2 is 1.95 × 102 nm2 because the area of the sphere is 4πR22, and R2 is 3.94 nm. γ2 is the average value of a-Bi/c-InSb (2.8 eV/nm2) and a-Bi/c-InTe (2.85 eV/nm2) and equals 2.9 eV/nm2. Therefore, the interfacial energies of the Bi clusters (x(A2γ2)) is 8.9 × 103 eV when the Bi concentration is 5.5 at.%. This implies that the total interfacial energy owing to the Bi clusters (A1γ1 + x(A2γ2)) is significantly higher than that of an InTe or InSb grain (A1γ1). From the above assumptions and obtained values, the effect of -TΔS on the bulk free energy can be estimated. The configurational entropy is expressed as

(

S𝑐𝑜𝑛𝑓 = ― 𝑘𝐵 ∙ 𝑙𝑛

𝑁! 𝑁𝑎!𝑁𝑏!⋯

),

(9)

using the Stirling formula,

ln (𝑁!) ≈ 𝑁 ∙ 𝑙𝑛𝑁 ― 𝑁 ,

(10)

it can be straightforwardly expressed as

S𝑐𝑜𝑛𝑓 = ― 𝑘𝐵 ∙ [𝑥𝑎𝑙𝑛𝑥𝑎 + 𝑥𝑏𝑙𝑛𝑥𝑏 +⋯ + (1 ― 𝑥𝑎 ― 𝑥𝑏 ― ⋯)𝑙𝑛(1 ― 𝑥𝑎 ― 𝑥𝑏 ― ⋯)],

(11)

where kB is the Boltzmann constant and x is the fraction of each element (a, b, …) in the material. To calculate ΔSconf, only one sublattice of the two in IST is involved because In forms a face-centered cubic sublattice. According to equation (11) for the entropy calculation, ΔSconf,IST for step 3 from phase group II (-59.8 μeV/atom·K) to IST (-27.3

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μeV/atom·K) is 32.5 μeV/atom·K. ΔSconf,Bi-IST for step 3 from phase group II (-75.8 μeV/atom·K) to Bi-IST (-38.7 μeV/atom·K) is 37.1 μeV/atom·K. Herein, the effect of entropy according to whether Bi atoms are present or not on the bulk free energy and the total Gibbs free energy can be estimated. To determine the difference in the Gibbs free energy in the whole volume, the enthalpy of the bulk free energy (ΔHbulk) and the entropy at the transition temperature (TΔS) can be converted into an identical unit of the total interfacial energy (ΣAiγi); this is based on the assumptions that the unit cell parameters of IST and Bi-IST are fixed at a = b = c = 6.12 Å (unit cell parameter of IST) after omitting the marginal structural changes by Bi atoms and that the number of atoms in a unit cell is 820, 48. In this condition, the volume of the hemispherical cap in Fig. 5 contains 2.44 × 106 atoms. Then, the difference in the enthalpy of the bulk free energies for IST (ΔHbulk,IST= -21 meV/atom) and BiIST (ΔHbulk,Bi-IST = -24 meV/atom) are converted to -5.1 × 104 eV and -5.9 × 104 eV, respectively. -TΔS of Bi-IST at the transition temperature (~610 K) for step 3 is - 5.52 × 104 eV; the absolute value |-TΔS| is larger than the - 4.84 × 104 eV for IST. At an identical temperature, Bi atoms cause larger entropy; thereby, the difference in the bulk free energy of Bi-IST increases further with the temperature term. Equation (3) and the obtained results illustrate that the difference in the Gibbs free energy of Bi-IST is - 1.4 × 105 eV and that of the IST is - 1.1 × 105 eV. This implies that because the Bi-IST crystal exhibits lower Gibbs free energy, the phase transition of the Bi-IST is more stable than the crystallization of the IST. The contribution shares of ΔH, - TΔS, and Aγ toward the total Gibbs free energy are 43%, 41%, and 16%. A comparison of these shares to those of pure IST (46%, 43%, and 11%) reveals increased influence of temperature and interfacial energy. In addition, these results indicate that the increased interfacial energy is one of the important factors that increase the difference in the Gibbs free energy under a similar condition for the other factors. At room temperature, the contribution shares of the Bi-IST material are 55%, 25%, and 20%; moreover, the temperature effect reduces abruptly, whereas the portion of interfacial energy increases. The interfacial energy of Bi atoms causes the difference in the Gibbs free energy of the IST to be increased to a higher degree at a lower temperature. Therefore, the interfacial energy is a driving force toward stable phase transition at a lower temperature, in addition to the bulk free energy; then, Bi atoms stabilize the crystallization of Bi-IST by substituting Sb sites, which also causes InTe and InSb grains to transform into the IST in the intermediate steps20.

Conclusions The purpose of this work is to control the stable phase transition for the engineered phase-change material, which is Bi-IST as a candidate ensuring improved performance of PCM. To achieve the stable phase transition, the effects of the interfacial energy induced by Bi dopant on the total free energy in the intermediate phases is quantitatively investigated in terms of the contribution shares of enthalpy, entropy with temperature change, and interfacial energy. Phase transition processes of Bi-IST and IST are analyzed with the kinetic behavior of the intermediate phases. The intermediate processes are divided into two steps. In the first step, the heterogeneous nucleation of InTe occurs at the interface with crystalline InSb, and the crystalline InTe is grown while Bi exists in the amorphous state. In the second step, crystalline InSb and InTe phases are transformed into crystalline Bi-IST because the Bi atoms substitute the Sb sites. The heterogeneous nucleation step is analyzed with the energy barrier; it is observed that the energy barrier for the heterogeneous nucleation of crystalline InTe is reduced noticeably by the interfacial reaction with amorphous Bi. The Gibbs free energy in the crystallization of Bi-IST is theoretically discussed for understanding the stable crystallization of Bi-IST. The interfacial energy at each of the interfaces of a-Bi/c-InSb and a-Bi/c-InTe becomes higher than that at the interface of c-InTe/c-InSb; this results in a larger difference in the Gibbs free energy with a negative sign and finally produces the stable crystallization of Bi-IST; this is because the difference in the Gibbs free energy functions as a driving force for stable phase transition of Bi-IST at the lower transition temperature compared with the IST. To design the stable materials, this interfacial energy induced by a dopant can be applied to GeSbTebased materials, which have a metastable fcc phase. A certain dopant is likely to cause interfaces in the metastable phase and larger driving force to a stable phase such as Bi atoms in IST. The theoretical understanding of the phase transition process will provide important information for regulating the intermediate phases at a lower temperature; this will prevent phase separation and segregation. In particular, in this work, the role of amorphous Bi as a dopant is investigated in terms of the interfacial energy with intermediate heterogeneous nucleation of InTe and in terms of the crystallization of Bi-IST with the substitution of Bi at Sb sites. The phase transition system of Bi-IST investigated in this paper is more complicated than the other material system. For this reason, the interface-driven phase transition of two steps, which can be applied to other phase-change materials.

Methods 9



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Experiments IST and Bi-IST thin films are prepared with sputtering of an In3SbTe2 target and co-sputtering of In3SbTe2 and bismuth targets. The composition and thickness of the Bi-IST thin film are Bi5.5(In3SbTe2)94.5 and about 250 nm. The samples for diffraction patterns are annealed in an Ar atmosphere by rapid thermal annealing (RTA) at 250 °C, 330 °C, and 400 °C for 15 min. These temperatures have been verified in our previous work as mentioned in Introduction 20. High-resolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED), and bright-field transmission electron microscopy (BFTEM) images are observed using FEI TITAN at 300 kV and analyzed by Gatan Digital Micrograph. The HRTEM samples are annealed at 330 °C under an Ar atmosphere for 30 min and prepared by mechanical polishing.

DFT calculations Density functional theory (DFT)49 calculations are performed using Vienna Ab initio Simulation Package (VASP) code50. For the DFT calculations on IST, InSb, and InTe as well as Bi-doped IST, InSb, and InTe, the plane-wave basis set is expanded to a cutoff energy of 400.00 eV. Moreover, the fully relaxed IST supercell model consisting of 64 atoms is used; the average dimension is 12.540 Å. The 4 × 4 × 4 and 2 × 2 × 2 k-point grids generated by the MonkhorstPack scheme51, the projector-augmented waves (PAW), and the generalized gradient approximation (GGA) are used for calculating the formation energy corresponding to the unit cells and supercells of InSb and InTe that are produced as intermediate phases during the phase transition from amorphous to crystalline IST52-54. The supercells of InSb and InTe consist of 64 and 128 atoms, respectively, with stoichiometry of In:Sb and In:Te. The ionic relaxations of the supercells were achieved using the conjugate-gradient method. The force convergence criterion was set to 0.02 eV/Å along all directions. Because the formation energy is changed by Bi-doping, the formation energy difference (ΔEf) between InSb and Bi-doped InSb or between InTe and Bi-doped InTe is calculated by the following equation: (12) ∆𝐸𝑓 = 𝐸[𝐼𝑛𝑆𝑏:𝐵𝑖 (𝑜𝑟 𝐼𝑛𝑇𝑒:𝐵𝑖)] ― [𝐸{𝐼𝑛𝑆𝑏 (𝑜𝑟 𝐼𝑛𝑇𝑒)} + 𝐸𝐵𝑖 𝑆𝑜𝑙𝑖𝑑],

where E[InSb:Bi (or InTe:Bi)] is the total energy of the Bi-doped InSb or InTe supercell, E{InSb (or InTe)} is the total energy of the defect-free InSb or InTe, and ESolidBi is the chemical potential of a Bi atom. In addition, the calculated values of heats of formation are nearly similar with the experimental results of previous literatures (InSb (0.35 eV/f.u.)55 and InTe (0.74 – 1.00 eV/f.u.)56-58). Because the DFT calculations in this work are mainly used to obtain the energetic parameters for bond formations and breaking, we examined the validity of our computation by comparing the theoretical and experimental heats of formation. To determine the difference in the Gibbs free energy for the transition from the intermediate phases to crystalline IST and Bi-IST phases, the bulk energies of IST and Bi-IST are calculated by the equations of {E(IST) - E(InSb) - E(InTe)}/64 and {E(Bi-IST) - E(InSb) - E(InTe) - E(a-Bi)}/64, respectively. The amorphous–crystal interfacial energies (γac) are calculated using the following equation: 𝑏𝑢𝑙𝑘 (13) 𝛾𝑎c = 𝐸𝑠𝑙𝑎𝑏 ― 𝐸𝑏𝑢𝑙𝑘 ― 𝜎𝑎 ― 𝜎𝑐, 𝑎𝑐 ― 𝐸𝑎 𝑐

where the terms on the right-hand side are the total energies of the amorphous–crystal junctioned slab, bulk amorphous, and bulk crystal and the surface energies of the amorphous and crystalline states, respectively. The surface energies are calculated using the following equation: 1

σ = 2𝐴(𝐸𝑠𝑙𝑎𝑏 ― 𝐸𝑏𝑢𝑙𝑘),

(14)

where A, Eslab, and Ebulk are the area of the supercell and the calculated total energies of the slab and bulk, respectively. The lateral dimensions of a slab for InSb/a-Bi and InTe/a-Bi are 18.79 × 13.288 Å2 and 12.187 × 7.227 Å2, respectively. The models of InSb/a-Bi and InTe/a-Bi consist of In32Sb32Bi64 and In20Te20Bi35, respectively. In our previous work26, the effect of the change in system size on the energy parameters such as doping formation energy was verified; moreover, the reliability of a 2 × 2 × 2 supercell (64 atoms) of IST for doping modeling was tested via a comparison with a 3 × 3 × 3 one (216 atoms)26,59. The energy difference was less than 0.1 eV.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Phone: +82-2-2220-0407. **E-mail: [email protected]. Phone: +82-2-958-5745

Notes The authors declare no competing financial interest.

Author Contributions The manuscript was written with contributions from all the authors. All authors have approved the final version of the manuscript.

Acknowledgements This work has been supported by National Research Foundation (NRF)-2015K1A3A7A03074026, Extremely Low Power Consumption Technology of eDRAM for Internet of Things, and Institutional projects in the Korea Institute of Science and Technology (Grant No. 2E29243). H. C. was supported by “Make Our Planet Great Again – German Research Initiative (MOPGA-GRI)” project fund of DAAD.

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For Table of Contents Use Only

Interface-driven Phase Transition of Phase-change Material Minho Choi1, Heechae Choi2, Jinho Ahn3,b*, and Yong Tae Kim1,a*

ToC synopsis To stably control the phase transition of phase-change materials, the effect of dopant on phase transition is quantitatively investigated in terms of the contribution shares of enthalpy, entropy with temperature change, and interfacial energy. In the intermediate phases of phase-change materials, the interface induced by dopant leads to the stable phase transition.

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Interface-Driven Phase Transition of Phase-Change Material - Crystal

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