The state-of-the-art phase-change memory is usually composed of ovonic threshold switching (OTS) material and ovonic memory switching (OMS) material for selective and data storage, respectively. OMS materials have been intensely studied, while the knowledge of the OTS mechanism is still inadequate. In this article, we have explored the local structure and electronic property of a simple OTS material, the amorphous (a-) SiTe, by first-principles calculations. The results reveal that most of the atoms in a-SiTe obey the “8-N” rule in contrast to a-GeTe, a well-studied OMS material. 76.5% of Si-centered configurations are in the form of randomly distributed tetrahedral clusters, while Te-centered configurations are relatively disordered without notable conformation. Furthermore, a large number of fivefold rings are found in a-SiTe. All of these structural characteristics lead to the high stability of a-SiTe, prohibiting its crystallization. In addition, the p state of Te also contributes much to the mid-gap states, which may be relevant for OTS behavior. Our findings provide an in-depth understanding of the structural signature and electronic properties of a-SiTe, having important implications for the design and applications of OTS materials.

Phase-change memory is a promising candidate for the next-generation non-volatile memory.1–6 The fast and reversible transitions of phase-change materials (PCMs) between crystalline and amorphous phases enable rapid information storage and easy data reading owing to the large contrast in conductivity and reflectivity, representing the ovonic memory switching (OMS) characteristic.7–12 To satisfy the urgent requirement for high-density storage in emerging artificial intelligence (AI) technology, as seen in Fig. 1, a three-dimensional (3D) stacking structure known as 3D XPoint has been proposed by integrating the volatile ovonic threshold switching (OTS) selector on PCMs.13,14

FIG. 1.

The key components of the 3D phase-change memory product (middle) are OMS data storage medium (left) and OTS selectors (right). The disordered configuration in the red rectangle in the left panel represents the amorphous state, while the ordered structure is the crystalline state. In contrast, the ideal OTS materials should remain amorphous without any phase transition, thus requiring high thermal stability.

FIG. 1.

The key components of the 3D phase-change memory product (middle) are OMS data storage medium (left) and OTS selectors (right). The disordered configuration in the red rectangle in the left panel represents the amorphous state, while the ordered structure is the crystalline state. In contrast, the ideal OTS materials should remain amorphous without any phase transition, thus requiring high thermal stability.

Close modal

The typical PCMs are chalcogenides located on the pseudo-binary line of GeTe and Sb2Te3.15–23 Previous studies reveal that amorphous PCMs, such as Ge2Sb2Te5 and GeTe, dominantly consist of a large fraction of defective octahedrons and a small fraction of Ge-centered tetrahedrons.24–27 It is the structural similarity (octahedral structure) of amorphous and crystalline materials that ensures the rapid crystallization behavior, while the structural diversity (tetrahedral structure) could stabilize the amorphous state. Interestingly, OTS selectors are also made from chalcogenides, such as GeS,28 GeSe,29,30 GeTe6,31 and SiTe.32,33 These OTS selectors turn on/off the electric current with typical volatile characteristics, normally in amorphous chalcogenides under an electric field without notable phase transition, which is obviously different from the case in PCMs. To date, many studies have been devoted to explore the switching mechanism of OTS materials.34–36 In addition to the cases focusing on the contributions of Ge-centered configurations to the band structure,35,36 valence alternation pairs (VAPs) induced by lone-pair interactions of chalcogen atoms are also relevant in amorphous chalcogenides.34 The mid-gap states are also believed to play a key role in the OTS mechanism, usually stemming from the over-coordinated Ge.37,38 Recently, it was reported that a-Te could also generate a mid-gap state in the bandgap,39 confirming the importance of the chalcogen Te in the OTS behavior.

By merely replacing the Ge by Si in GeTe, the typical OMS material could be transformed into the OTS one, and experiments demonstrated that a-SiTe possesses the large on/off ratio and good cycling endurance.32 This poses an interesting question: GeTe and SiTe are almost identical in terms of valence electrons, but why their properties differ a lot? To date, the understanding of atomic and electronic structure of a-SiTe, which may be responsible for OTS behavior, remains insufficient. In this article, by comparing a-SiTe with a-GeTe, we explored the local structure of these OTS/OMS materials by ab initio molecular dynamics (AIMD) simulations and calculated the electronic property by the first-principles method, so as to shed light on the origin of structural stability and OTS behavior of a-SiTe. The results reveal that more atoms in a-SiTe obey the “8-N” rule compared with a-GeTe. Many homopolar Si–Si bonds are found in a-SiTe, which are much stronger than Ge–Ge bonds. The Si-centered clusters form a large number of randomly distributed tetrahedrons, which construct the backbone of the a-SiTe structure by connecting with each other. The mid-gap states are also observed from Si atoms, and the p state of Te also contributes much to them. Our findings enrich the understanding of the structure and electronic property of OTS materials, paving the way for the design and applications of selector devices.

The AIMD simulations were performed by the Vienna Ab initio Simulation Package (VASP) code based on the density functional theory (DFT).40,41 The projected augmented-wave (PAW) method and the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA-PBE) were adopted for exchange–correlation functional.42,43 In line with our previous work,27 the a-SiTe composed of 300 atoms was obtained by melt-quenching, with a cooling rate of 30 K/ps. The time step was 3 fs, and only the Γ point was sampled for the Brillouin zone. The canonical (NVT) ensemble with the Nose–Hoover thermostat was applied to control the temperature and the pressure in AIMD simulations. The amorphous configuration at 300 K was fully relaxed to eliminate the internal pressure for structure analysis by adjusting the size of the simulated cell. For the electronic structure calculations, the energy cutoff of PAW basis was 500 eV. The amorphous configuration was relaxed at 0 K with a force convergence of 0.02 eV, and a 2 × 2 × 2 k-point grid was chosen in the Brillouin zone.

Compared with the a-GeTe in a previous study,24 we intend to unveil the different structural characters of a-SiTe. Figures 2(a) and 2(b) show the partial pair distribution functions (PDFs) of a-GeTe and a-SiTe, respectively. Only the Ge–Te configuration presents a notable first peak in a-GeTe, revealing that chemical bonds are mainly in the form of heteropolar bonds (Ge–Te). However, the prominent first peaks are observed in both Si–Te and Si–Si configurations of a-SiTe. In addition, the first peak of Te–Te becomes larger in a-SiTe. This indicates that many homopolar bonds (Si–Si and Te–Te) exist in a-SiTe in addition to Si–Te bonds.44 The bond-angle distribution functions (BADFs) of a-GeTe and a-SiTe are shown in Figs. 2(c) and 2(d), respectively. The main peaks of both Ge- and Te-centered configurations are located at ∼90°, hinting at the octahedral structure in a-GeTe.16,24,45 For a-SiTe, the main peak of Si-centered clusters is located at ∼109°, suggesting that Si-centered clusters tend to form tetrahedral motifs. While the main peak of Te-centered configurations is located at ∼97°, which is between 90° and 109°, deviating much from the cases in both the octahedron and tetrahedron. The partial BADFs of a-SiTe show that the Si-centered configurations have a similar trend [Fig. S1 of the supplementary material], concentrating on an angle of ∼109°, suggesting that all of the Si-centered configurations tend to form the tetrahedral structure. For Te-centered configurations, Si–Te–Si and Si–Te–Te configurations only possess one obvious peak, while the Te–Te–Te configuration also has another prominent peak at ∼170°. The Te-centered configuration with more coordinated Si shifts the first peak to right, indicating that Si–Te bonds result in a large deviation of the Te-centered configuration to the octahedron.46 

FIG. 2.

(a) and (b) PDFs, (c) and (d) BADFs, and (e) and (f) distributions of CNs for a-GeTe and a-SiTe, respectively. The black and blue dashed lines in (c) and (d) mark the angles of 90° and 109°, corresponding to the perfect octahedral and tetrahedral configurations. The radius cutoff of 3.2 Å is used for calculating BADFs and CNs.

FIG. 2.

(a) and (b) PDFs, (c) and (d) BADFs, and (e) and (f) distributions of CNs for a-GeTe and a-SiTe, respectively. The black and blue dashed lines in (c) and (d) mark the angles of 90° and 109°, corresponding to the perfect octahedral and tetrahedral configurations. The radius cutoff of 3.2 Å is used for calculating BADFs and CNs.

Close modal

Figures 2(e) and 2(f) show the distributions of coordination numbers (CNs) for a-GeTe and a-SiTe. The CN of Ge majorly concentrates on 4, while that of Te concentrates on 3 in a-GeTe, deviating from the “8-N” rule in which chalcogen atoms should be twofold. In a-SiTe, 82.6% of Si atoms have a CN of 4, while 80.35% of Te atoms possess a CN of 2. It is probably due to that most of the atoms in a-SiTe obey the “8-N” rule that results in a stiff disordered system, which could endure a lot of OTS cycles. More specifically, the CN of Si–Si is 2.48, and it possesses 60% of average CN of Si atoms, leaving more Te–Te bonds in a-SiTe (Fig. S2). These Si–Si bonds connect with each other to form the chain structures in the amorphous system without phase separation, as shown in Fig. S3(a).

To identify the short-range order visually, an atomistic cluster alignment (ACA) method is utilized.47 2000 clusters are randomly chosen from the atomic trajectories, and each cluster consists of one central atom and its six neighboring atoms. Put these central atoms to one site and then translate and rotate the clusters to minimize the total mean square distance. Finally, the alignment results are obtained at an isovalue of 0.25 Å−3 with the Gaussian smearing, as seen in Fig. 3(a). Both Ge- and Te-centered configurations in a-GeTe present the octahedral pattern.24 For a-SiTe, the Si-centered configuration presents a prominent tetrahedral motif, while the Te-centered configuration shows a rather disordered contour. To quantify the fraction of tetrahedrons in a-SiTe, the local order parameter q is used,48–50 

q=138i>k13+cosθijk2,
(1)

where the sum runs over the couples of atoms bonded to the central atom j. q = 1.0 when the cluster is a tetrahedron without distortion, and the distortion could result in a smaller q. Usually, clusters with the q value ranging from 0.8 to 1.0 are seen as tetrahedral configurations. Figure 3(b) shows the q distributions of a-GeTe and a-SiTe for four-coordinated Ge/Si. Most of the q values lie in the scale from 0.8 to 1.0 for Si-centered clusters. Then, we integrate the q in this range and find that 76.5% of Si-centered configurations favor the tetrahedrons, much larger fraction than Ge-centered tetrahedrons in a-GeTe (31.4%).24 

FIG. 3.

(a) The collective alignment clusters, (b) the local order parameter q, (c) distribution of Si-centered tetrahedrons, and (d) ring distributions of a-GeTe and a-SiTe within 3.2 Å.

FIG. 3.

(a) The collective alignment clusters, (b) the local order parameter q, (c) distribution of Si-centered tetrahedrons, and (d) ring distributions of a-GeTe and a-SiTe within 3.2 Å.

Close modal

The distribution of Si-centered tetrahedrons in a-SiTe is shown in Fig. 3(c). These tetrahedrons are randomly distributed in the simulated cell, which could effectively improve the amorphous stability, in general, by stabilizing the local configurations of the amorphous state. In addition, the ring distribution of a-SiTe is also counted, by using the RINGS code,51 as shown in Fig. 3(d). Similar to the case in a-GeTe,24 the fivefold rings still possess the largest fraction in a-SiTe, with a proportion of 37%. As the fivefold ring is quite stable in amorphous systems,52 it may improve the stability of glass. However, the fraction of the fourfold ring, which is a signature of rapid crystallization in PCMs,53 is reduced in a-SiTe, which may hinder the nucleation and crystal growth. In addition, the fraction of the threefold ring is increased in a-SiTe, resulting in the formation of local triangular configurations.

To explore the bonding nature of a-SiTe and distinguish it from a-GeTe, the crystal orbital Hamilton populations (COHPs) of a-SiTe and a-GeTe are calculated by the LOBSTER code,54–57 as seen in Figs. 4(a) and 4(b). For heteropolar bonds in Fig. 4(a), the COHP of both Si–Te and Ge–Te is negative below the Fermi level, suggesting that these bonds are in the antibonding states. The COHP of SiTe is larger than that of GeTe, indicating that the Si–Te bond is stronger than the Ge–Te bond. For homopolar bonds in Fig. 4(b), COHP of Ge–Ge is negative on left of the Fermi level, while that of Si–Si is positive, revealing that the Ge–Ge bond is in the antibonding state, whereas the Si–Si bond is in the bonding state. This is probably the reason why a-SiTe maintains a high stability despite a large fraction of homopolar bonds.

FIG. 4.

COHP of (a) Si–Te and Ge–Te and (b) Si–Si and Ge–Ge. (c) and (d) The ICOHP in respect of different bonding lengths for a-GeTe and a-SiTe in which the blue stars mark the first peaks of PDFs.

FIG. 4.

COHP of (a) Si–Te and Ge–Te and (b) Si–Si and Ge–Ge. (c) and (d) The ICOHP in respect of different bonding lengths for a-GeTe and a-SiTe in which the blue stars mark the first peaks of PDFs.

Close modal

To further identify the formation energy of these bonds, the integrated COHP (ICOHP) is calculated by summing up the COHP below the Fermi level.58,59Figures 4(c) and 4(d) show the ICOHP of a-GeTe and a-SiTe as a function of bonding length, respectively. As the density of chemical bonds reaches its maximum value at the first peak of PCF [Fig. 2(b)], the bond strength could be estimated by the formation energy under the corresponding bond length. The formation energies of Ge–Ge and Ge–Te in a-GeTe are about 3.2 and 3.1 eV, while those of Si–Si, Si–Te, and Te–Te in a-SiTe are 4.3, 4.2, and 2.5 eV, respectively. The formation energies of Si–Si and Si–Te are much larger than those of Ge–Ge and Ge–Te, while that of Te–Te is the smallest. Since the fraction of Te–Te bonds is small in a-SiTe [seen in Fig. S2(a)], it has a limited impact on the chemical stability of a-SiTe. The Si–Si bonds possess a very large formation energy, even larger than that of the Si–Te bond. Hence, the Si–Si bonds persist in the melt-quenching process without transforming into Si–Te bonds, leading to a large fraction of homopolar bonds in a-SiTe [seen in Fig. S2(a)].

The OTS behavior of amorphous material is believed to be related to the defect states in the bandgap, and thus we calculated the electronic density of states (DOS) of a-GeTe and a-SiTe, as seen in Figs. 5(a) and 5(b), respectively. The calculated bandgaps of a-GeTe and a-SiTe are 0.22 and 0.37 eV, respectively, which are smaller than the experimental values (0.78 and 0.5 eV)60,61 owing to the bandgap underestimation by DFT calculations. Interestingly, the mid-gap or trap states, which are seen as the origin of OTS behavior,28 are found in both a-GeTe and a-SiTe. In addition to the contribution of Si, the p state of Te that contributed to the mid-gap state becomes notable in the a-SiTe. This resembles the case of a-Te in which the mid-gap is generated by Te even without Ge or Si.39 Figure S3(b) shows that the unoccupied regions of Si atomic chains are filled by Te atoms. According to the distribution of the CN of Te in a-SiTe [Fig. 2(f)], in addition to the large fraction of Te atoms with a CN of 2, the Te atoms with the CN of 1 and 3 are also observed, which is in line with the valence alternation pair (VAP) model.34 The p states of Te in a-SiTe also contribute to the valence and conduction bands, which may strengthen the effect of Te on the OTS process due to the lone-pair electrons.

FIG. 5.

DOS of (a) a-GeTe and (b) a-SiTe, both showing mid-gap states but stemming from different electronic orbitals.

FIG. 5.

DOS of (a) a-GeTe and (b) a-SiTe, both showing mid-gap states but stemming from different electronic orbitals.

Close modal

The electron localization function (ELF) is utilized to explore the electronic state and bonding nature in a-SiTe,62,63 as seen in Fig. 6. Figure 6(a) shows the distribution of the normalized ELF for a-GeTe and a-SiTe. Two prominent peaks are found in both glasses, located at the vicinities of 0 and 0.8, respectively. Usually, ELF = 0.5 corresponds to the metallic bond where electrons are totally delocalized, while ELF = 1 corresponds to the covalent bond where the electron is perfectly localized.20 ELF = 0.8 indicates that the electron is partially localized owing to the existence of the lone-pair electron and structural distortion. The a-SiTe shows a larger value at the first peak, revealing that a-SiTe possesses more ionicity, which leads to a larger bandgap (Fig. 5). The value of a-SiTe is smaller than that of a-GeTe at the second peak. This is probably due to that most of the atoms in a-SiTe obey the “8-N” rule, which may reduce the shared electrons in the over-coordinated configuration and then consume more lone-pair electrons. To visualize the bonding type, Fig. 6(b) shows the snapshot of the ELF for a-SiTe with an isovalue of 0.9. In the red rectangle region, highly localized electrons are also observed between two Si atoms, indicating strong Si–Si covalent bonds. Most electrons lie on the opposite side of the bonding region of Te atoms, suggesting that lone-pair electrons stem from Te atoms. There is no electron between Si and Te atoms, hinting that the degree of localization is relatively low in the Si–Te bond. Although the number of lone-pair electrons in a-SiTe is less than that in a-GeTe, the contribution to OTS behavior remains significant due to the existence of a large number of Te atoms.

FIG. 6.

(a) shows the distributions of the ELF for a-GeTe and a-SiTe and (b) displays the ELF of a-SiTe as ELF = 0.9 in which blue and green balls represent Si and Te atoms, respectively. The distribution of electrons can be seen in the red rectangle region.

FIG. 6.

(a) shows the distributions of the ELF for a-GeTe and a-SiTe and (b) displays the ELF of a-SiTe as ELF = 0.9 in which blue and green balls represent Si and Te atoms, respectively. The distribution of electrons can be seen in the red rectangle region.

Close modal

To summarize, we have investigated the local structure and electronic property of a-SiTe in contrast to the cases in a-GeTe by using AIMD simulations. The research results reveal that many homopolar (Si–Si and Te–Te) bonds are formed in a-SiTe. The CNs of Ge and Te in a-GeTe dominantly concentrate on 4 and 3, while those of Si and Te in a-SiTe concentrate on 4 and 2, respectively, making more atoms in a-SiTe obey the “8-N” rule. 76.4% of the Si-centered configurations are tetrahedral structures, and they are randomly distributed in a-SiTe, while no clear pattern is found in Te-centered configurations, prominently different from the cases in a-GeTe where Ge- and Te-centered configurations are dominantly in the form of defective octahedrons. The ring statistic indicates that fivefold rings possess the largest proportion in a-SiTe, even larger than the case in a-GeTe. Furthermore, the formation energies of Si–Si and Si–Te are much larger than the cases of Ge–Ge and Ge–Te. All of these characteristics could improve the stability of a-SiTe, rendering a-SiTe high endurance for multiple OTS operations without crystallization. The mid-gap states, which may play an important role in the OTS process, are found in both a-SiTe and a-GeTe in which the p state of Te contributes little to the mid-gap state of a-GeTe but contributes much to that of a-SiTe. Our investigations enrich the understanding of the structure and electronic property of OTS material, which can promote the rapid development of high-density memory.

See the supplementary material for more structural information on amorphous SiTe.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51772113, 11374055, and 61427815). M.X. acknowledges the Fundamental Research Funds for the Central Universities, HUST (Grant No. 2021GCRC051), and the National Key R&D Plan of China (Grant No. 2017YFB0701701 “Materials Genome Engineering”). C.Q. acknowledges the China Postdoctoral Science Foundation (Grant No. 2020M682387), the Postdoctoral Fund of Hubei Province, and the Key Projects of Basic Research of the Shanghai Municipal Science and Technology Commission (Grant No. 18JC1411500).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

1.
M.
Wuttig
and
N.
Yamada
,
Nat. Mater.
6
,
824
832
(
2007
).
2.
F.
Xiong
,
A. D.
Liao
,
D.
Estrada
, and
E.
Pop
,
Science
332
,
568
570
(
2011
).
3.
F.
Rao
,
K.
Ding
,
Y.
Zhou
,
Y.
Zheng
,
M.
Xia
,
S.
Lv
,
Z.
Song
,
S.
Feng
,
I.
Ronneberger
,
R.
Mazzarello
,
W.
Zhang
, and
E.
Ma
,
Science
358
,
1423
1427
(
2017
).
4.
W.
Zhang
,
R.
Mazzarello
,
M.
Wuttig
, and
E.
Ma
,
Nat. Rev. Mater.
4
,
150
168
(
2019
).
5.
M.
Xu
,
X.
Mai
,
J.
Lin
,
W.
Zhang
,
Y.
Li
,
Y.
He
,
H.
Tong
,
X.
Hou
,
P.
Zhou
, and
X.
Miao
,
Adv. Funct. Mater.
30
,
2003419
(
2020
).
6.
Y. T.
Liu
,
X. B.
Li
,
H.
Zheng
,
N. K.
Chen
,
X. P.
Wang
,
X. L.
Zhang
,
H. B.
Sun
, and
S.
Zhang
,
Adv. Funct. Mater.
31
,
2009803
(
2021
).
7.
L.
Zhang
,
X.
Mai
,
R.
Gu
,
L.
Liu
,
C.
Xiong
,
Z.
Yang
,
H.
Tong
,
X.
Cheng
,
M.
Xu
,
P.
Zhou
, and
X.
Miao
,
Adv. Electron. Mater.
7
,
2100164
(
2021
).
8.
M.
Xu
,
C.
Qiao
,
K.-H.
Xue
,
H.
Tong
,
X.
Cheng
,
S.
Wang
,
C.-Z.
Wang
,
K.-M.
Ho
,
M.
Xu
, and
X.
Miao
,
J. Mater. Chem. C
8
,
6364
6369
(
2020
).
9.
J.
Feng
,
A.
Lotnyk
,
H.
Bryja
,
X.
Wang
,
M.
Xu
,
Q.
Lin
,
X.
Cheng
,
M.
Xu
,
H.
Tong
, and
X.
Miao
,
ACS Appl. Mater. Interfaces
12
,
33397
33407
(
2020
).
10.
X. P.
Wang
,
X. B.
Li
,
N. K.
Chen
,
B.
Chen
,
F.
Rao
, and
S.
Zhang
,
Adv. Sci.
8
,
2004185
(
2021
).
11.
B.
Liu
,
W.
Liu
,
Z.
Li
,
K.
Li
,
L.
Wu
,
J.
Zhou
,
Z.
Song
, and
Z.
Sun
,
ACS Appl. Mater. Interfaces
12
,
20672
20679
(
2020
).
12.
K.
Ding
,
J.
Wang
,
Y.
Zhou
,
H.
Tian
,
L.
Lu
,
R.
Mazzarello
,
C.
Jia
,
W.
Zhang
,
F.
Rao
, and
E.
Ma
,
Science
366
,
210
215
(
2019
).
13.
J.
Hruska
, Intel, Micron reveal Xpoint, a new memory architecture that could outclass DDR4 and NAND https://www.extremetech.com/extreme/211087-intel-micron-reveal-xpoint-a-new-memory-architecture-that-claims-to-outclass-both-ddr4-and-nand,
2015
.
14.
M.
Zhu
,
K.
Ren
, and
Z.
Song
,
MRS Bull.
44
,
715
720
(
2019
).
15.
T.
Matsunaga
and
N.
Yamada
,
Phys. Rev. B
69
,
104111
(
2004
).
16.
J.
Akola
and
R. O.
Jones
,
Phys. Rev. B
76
,
235201
(
2007
).
17.
J.
Hegedüs
and
S. R.
Elliott
,
Nat. Mater.
7
,
399
405
(
2008
).
18.
S.
Caravati
,
M.
Bernasconi
, and
M.
Parrinello
,
Phys. Rev. B
81
,
014201
(
2010
).
19.
C.
Qiao
,
Y. R.
Guo
,
S.
Wang
,
Y.
Jia
,
C.-Z.
Wang
, and
K.-M.
Ho
,
Phys. Chem. Chem. Phys.
22
,
9759
9766
(
2020
).
20.
Z.
Sun
,
J.
Zhou
,
Y.
Pan
,
Z.
Song
,
H.-K.
Mao
, and
R.
Ahuja
,
Proc. Natl. Acad. Sci. U. S. A.
108
,
10410
10414
(
2011
).
21.
Z.
Li
,
C.
Si
,
J.
Zhou
,
H.
Xu
, and
Z.
Sun
,
ACS Appl. Mater. Interfaces
8
,
26126
26134
(
2016
).
22.
Z.
Sun
,
J.
Zhou
,
A.
Blomqvist
,
B.
Johansson
, and
R.
Ahuja
,
Phys. Rev. Lett.
102
,
075504
(
2009
).
23.
M.
Xu
,
R.
Gu
,
C.
Qiao
,
H.
Tong
,
X.
Cheng
,
C.-Z.
Wang
,
K.-M.
Ho
,
S.
Wang
,
X.
Miao
, and
M.
Xu
,
J. Mater. Chem. C
9
,
8057
8065
(
2021
).
24.
C.
Qiao
,
Y. R.
Guo
,
J. J.
Wang
,
H.
Shen
,
S. Y.
Wang
,
Y. X.
Zheng
,
R. J.
Zhang
,
L. Y.
Chen
,
C. Z.
Wang
, and
K. M.
Ho
,
J. Alloys Compd.
774
,
748
757
(
2019
).
25.
M.
Upadhyay
,
S.
Murugavel
,
M.
Anbarasu
, and
T. R.
Ravindran
,
J. Appl. Phys.
110
,
083711
(
2011
).
26.
S.
Gabardi
,
S.
Caravati
,
G. C.
Sosso
,
J.
Behler
, and
M.
Bernasconi
,
Phys. Rev. B
92
,
054201
(
2015
).
27.
C.
Qiao
,
Y. R.
Guo
,
F.
Dong
,
J. J.
Wang
,
H.
Shen
,
S. Y.
Wang
,
M.
Xu
,
X. S.
Miao
,
Y. X.
Zheng
,
R. J.
Zhang
,
L. Y.
Chen
,
C. Z.
Wang
, and
K. M.
Ho
,
J. Mater. Chem. C
6
,
5001
5011
(
2018
).
28.
S.
Jia
,
H.
Li
,
T.
Gotoh
,
C.
Longeaud
,
B.
Zhang
,
J.
Lyu
,
S.
Lv
,
M.
Zhu
,
Z.
Song
,
Q.
Liu
,
J.
Robertson
, and
M.
Liu
,
Nat. Commun.
11
,
4636
(
2020
).
29.
H.-W.
Ahn
,
D. S.
Jeong
,
B.-k.
Cheong
,
H.
Lee
,
H.
Lee
,
S.-d.
Kim
,
S.-Y.
Shin
,
D.
Kim
, and
S.
Lee
,
Appl. Phys. Lett.
103
,
042908
(
2013
).
30.
S.
Clima
,
D.
Garbin
,
K.
Opsomer
,
N. S.
Avasarala
,
W.
Devulder
,
I.
Shlyakhov
,
J.
Keukelier
,
G. L.
Donadio
,
T.
Witters
, and
S.
Kundu
,
Phys. Status Solidi RRL
14
,
1900672
(
2020
).
31.
A.
Manivannan
,
S. K.
Myana
,
K.
Miriyala
,
S.
Sahu
, and
R.
Ramadurai
,
Appl. Phys. Lett.
105
,
243501
(
2014
).
32.
Y.
Koo
,
K.
Baek
, and
H.
Hwang
, in
2016 IEEE Symposium on VLSI Technology
(
IEEE
,
2016
), pp.
1
2
.
33.
A.
Velea
,
K.
Opsomer
,
W.
Devulder
,
J.
Dumortier
,
J.
Fan
,
C.
Detavernier
,
M.
Jurczak
, and
B.
Govoreanu
,
Sci. Rep.
7
,
8103
(
2017
).
34.
M.
Kastner
,
D.
Adler
, and
H.
Fritzsche
,
Phys. Rev. Lett.
37
,
1504
(
1976
).
35.
Y.
Guo
,
H.
Li
,
W.
Zhang
, and
J.
Robertson
,
Appl. Phys. Lett.
115
,
163503
(
2019
).
36.
H.
Li
and
J.
Robertson
,
Sci. Rep.
9
,
1867
(
2019
).
37.
S.
Clima
,
B.
Govoreanu
,
K.
Opsomer
,
A.
Velea
,
N. S.
Avasarala
,
W.
Devulder
,
I.
Shlyakhov
,
G. L.
Donadio
,
T.
Witters
,
S.
Kundu
,
L.
Goux
,
V.
Afanasiev
,
G. S.
Kar
, and
G.
Pourtois
, in
2017 IEEE International Electron Devices Meeting
(
IEEE
,
2017
).
38.
K.
Konstantinou
,
F. C.
Mocanu
,
T.-H.
Lee
, and
S. R.
Elliott
,
Nat. Commun.
10
,
3065
(
2019
).
39.
C.
Qiao
,
M.
Xu
,
S.
Wang
,
C.-Z.
Wang
,
K.-M.
Ho
,
X.
Miao
, and
M.
Xu
,
Scr. Mater.
202
,
114011
(
2021
).
40.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
561
(
1993
).
41.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
11186
(
1996
).
42.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
17979
(
1994
).
43.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
3868
(
1996
).
44.
J. Y.
Raty
,
W.
Zhang
,
J.
Luckas
,
C.
Chen
,
R.
Mazzarello
,
C.
Bichara
, and
M.
Wuttig
,
Nat. Commun.
6
,
7467
(
2015
).
45.
G. C.
Sosso
,
G.
Miceli
,
S.
Caravati
,
J.
Behler
, and
M.
Bernasconi
,
Phys. Rev. B
85
,
174103
(
2012
).
46.
J.
Akola
and
R. O.
Jones
,
Phys. Rev. B
85
,
134103
(
2012
).
47.
X. W.
Fang
,
C. Z.
Wang
,
Y. X.
Yao
,
Z. J.
Ding
, and
K. M.
Ho
,
Phys. Rev. B
82
,
184204
(
2010
).
48.
J. R.
Errington
and
P. G.
Debenedetti
,
Nature
409
,
318
321
(
2001
).
49.
H.
Weber
,
M.
Schumacher
,
P.
Jovari
,
Y.
Tsuchiya
,
W.
Skrotzki
,
R.
Mazzarello
, and
I.
Kaban
,
Phys. Rev. B
96
,
054204
(
2017
).
50.
S.
Caravati
,
M.
Bernasconi
,
T. D.
Kühne
,
M.
Krack
, and
M.
Parrinello
,
Appl. Phys. Lett.
91
,
171906
(
2007
).
51.
S.
Le Roux
and
P.
Jund
,
Comput. Mater. Sci.
49
,
70
83
(
2010
).
52.
J.
Taffs
and
C.
Patrick Royall
,
Nat. Commun.
7
,
13225
(
2016
).
53.
T. H.
Lee
and
S. R.
Elliott
,
Phys. Rev. Lett.
107
,
145702
(
2011
).
54.
R.
Dronskowski
and
P. E.
Bloechl
,
J. Phys. Chem.
97
,
8617
8624
(
1993
).
55.
G. A.
Landrum
and
R.
Dronskowski
,
Angew. Chem., Int. Ed.
39
,
1560
1585
(
2000
).
56.
S.
Maintz
,
V. L.
Deringer
,
A. L.
Tchougréeff
, and
R.
Dronskowski
,
J. Comput. Chem.
37
,
1030
1035
(
2016
).
57.
S.
Maintz
,
M.
Esser
, and
R.
Dronskowski
,
Acta Phys. Pol., B
47
,
1165
(
2016
).
58.
V. L.
Deringer
,
W.
Zhang
,
M.
Lumeij
,
S.
Maintz
,
M.
Wuttig
,
R.
Mazzarello
, and
R.
Dronskowski
,
Angew. Chem., Int. Ed.
53
,
10817
10820
(
2014
).
59.
Y.
Chen
,
L.
Sun
,
Y.
Zhou
,
G. M.
Zewdie
,
V. L.
Deringer
,
R.
Mazzarello
, and
W.
Zhang
,
J. Mater. Chem. C
8
,
71
77
(
2020
).
60.
K.
Shportko
,
S.
Kremers
,
M.
Woda
,
D.
Lencer
,
J.
Robertson
, and
M.
Wuttig
,
Nat. Mater.
7
,
653
658
(
2008
).
61.
T.
Gao
,
J.
Feng
,
H.
Ma
, and
X.
Zhu
,
Appl. Phys. A
124
,
734
(
2018
).
62.
A. D.
Becke
and
K. E.
Edgecombe
,
J. Chem. Phys.
92
,
5397
(
1990
).
63.
A.
Savin
,
O.
Jepsen
,
J.
Flad
,
O. K.
Andersen
,
H.
Preuss
, and
H. G.
von Schnering
,
Angew. Chem., Int. Ed.
31
,
187
188
(
1992
).

Supplementary Material