Yttrium-Doped Sb2Te3: A Promising Material for Phase-Change Memory

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Yttrium Doped SbTe: A Promising Material for Phase-Change Memory Zhen Li, Chen Si, Jian Zhou, Huibin Xu, and Zhimei Sun ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b08700 • Publication Date (Web): 09 Sep 2016 Downloaded from http://pubs.acs.org on September 17, 2016

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ACS Applied Materials & Interfaces

Yttrium Doped Sb2Te3: A Promising Material for Phase-Change Memory Zhen Li,† Chen Si,† Jian Zhou,∗ † Huibin Xu,† ‡ and Zhimei Sun∗ † ‡ ,

,

, ,

†School of Materials Science and Engineering, Beihang University, Beijing 100191, China ‡Center for Integrated Computational Materials Engineering, International Research

Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China

E-mail: [email protected]; [email protected]

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)>IJH=?J Sb2 Te3 exhibits outstanding performance among the candidate materials for phasechange memory, nevertheless, its low electrical resistivity and thermal stability hinder its practical application. Hence, numerous studies have been carried out to search suitable dopants to improve the performance, however, the explored dopants always cause phase separation and thus drastically reduce the reliability of phase-change memory. In this work, on the basis of ab initio calculations, we have identied yttrium (Y) as an optimal dopant for Sb2 Te3 , which overcomes the phase separation problem and signicantly increases the resistivity of crystalline state by at least double that of Sb2 Te3 . The good phase stability of crystalline Y-doped Sb2 Te3 (YST) is attributed to the same crystal structure between Y2 Te3 and Sb2 Te3 as well as their tiny lattice mismatch of only ∼1.1%. The signicant increase in resistivity of c -YST is understood by our ndings that Y can dramatically increase the carrier's eective mass by regulating the band structure and can also reduce the intrinsic carrier density by suppressing the formation of SbTe antisite defects. Y doping can also improve the thermal stability of amorphous YST based on our ab initio molecular dynamics simulations, which is attributed to the stronger interactions between Y and Te than that of Sb and Te.

Keywords phase-change material, Sb 2 Te3 , Y doping, electrical resistivity, thermal stability

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1 Introduction Utilizing dopants is a conventional way to optimize, enhance or even change the properties of semiconductor materials when the performance of the pristine materials is not desirable. 1,2 The identication of suitable dopants for various materials is laborious and is usually carried out in a fashion by intuition and time-consuming trial and error. Even so, the trial and error approach sometimes cannot hit the target that the optimal dopant is not found even after laborious search. This is the case for Sb 2Te3, a promising recording material for phase-change random access memory (PCRAM). 3 PCRAM is investigated as a potential candidate for next-generation non-volatile memory, 4 which utilizes the fast and reversible phase transition between amorphous (high resistance, RESET state) and crystalline (low resistance, SET state) states of certain chalcogenide semiconductors (also referred to as phase-change materials) to achieve the information storage. 58 Among the investigated Sb2Te3-GeTe pesudo-binary chalcogenide phase-change materials, Sb 2Te3 has the advantage of the highest crystallization speed 3 and hence a very high operation rate, which is thus considered as a competitive candidate for PCRAM. However, its relatively low electrical resistivity of crystalline state requires a high power of current or voltage to realize the phase transition from crystalline to amorphous state, and hence is undesirable for reducing the power consumption of PCRAM. Furthermore, the low thermal stability of amorphous state Sb2Te3 reduces the data retention and reliability of phase-change memory cells. Therefore, various dopants such as N, 9 Si, 10 Zn, 11 Al, 12 and Ti 13 have been explored to increase the electrical resistivity of crystalline state and improve the thermal stability of amorphous state Sb2Te3. However, the incorporation of these dopants into Sb 2Te3 causes severe or sluggish phase separation during the write and erase processes in PCRAM. 14 Though these dopants can strengthen the electric scattering, a dominant factor that result in the increase of the resistivity, they can also inevitably introduce extra carriers which would produce an adverse eect on increasing the electrical resistivity. Thus it is of signicant importance to search for suitable dopants that can not only avoid both extra carriers and phase separation, but also 3



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eectively increase the electrical resistivity of crystalline state and improve the thermal stability of amorphous state simultaneously as well. Obviously, it would be extremely dicult and laborious to discover such an optimal dopant by the time-consuming trial and error. Fortunately, recent signicant advances in computational resources accelerate the pace of discovering new materials and materials design. Especially combined with data mining and data analysis from available databases and literature, theoretical computations such as

ab initio total energy calculations can dramatically accelerate the identication of optimal dopants for Sb2 Te3 and other semiconductor materials. In this work, we have identied yttrium (Y) as an optimal candidate dopant for Sb 2 Te3 , which not only eectively increases the electrical resistivity of crystalline state but also improve the thermal stability of amorphous state, and Y-doped Sb 2 Te3 (YST) maintains the same crystal structure in the reversible phase-change process, on the basis of ab initio calculations integrated with data mining and data analysis of ICSD # (Inorganic Crystal Structure Data) as well as results from available literature. Our present results demonstrate that YST is a promising candidate for PCRAM. Furthermore, this work highlights a novel way of designing advanced phase-change materials and fast identifying optimal dopants for semiconductors as well.

2 Computational methods Our calculations were carried out within the framework of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP). $ The projector augmented wave (PAW) potentials % were used with the generalized gradient approximations (GGA) & of Perdew-Burke-Ernzerhof (PBE) ' exchange-correlation functional, where 5 s 2 5p 3 for Sb, 5s 2 5p 4 for Te, and 4p 6 4s 2 4d 1 5s 2 for Y were treated as valence electrons in the pseudopotentials. A cuto energy of 300 eV was chosen for the plane-wave expansion of wave functions and convergence with respect to self-consistent iterations was achieved when the total energy dierence between cycles was less than 1 ×10−5 eV. The k -point of 5×5×1 au-

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tomatically generated with their origin at

Γ

point and the tetrahedron method with Blöchl

corrections 20 were used. The k -point grid has been tested to be sucient to obtain the converged results. In order to take the van der Waals forces into account for better describing the nonbonding interactions, a semi-empirical dispersion potential was added to the conventional Kohn-Sham DFT energy in the scheme of the DFT-D2 21,22 method for the calculations of the Sb2 Te3 structures. Based on the DFT-D2 calcalutions, the optimized lattice constants

a and c for the rhombohedral structure of Sb 2 Te3 are 4.243 Å and 30.928 Å, respectively, in good agreement with experimental values 23,24 and other theoretical calculations. 25 The phonon spectra was calculated by PHONOPY. 26 The electric properties were estimated from the rst-principles data using the semi-classical Boltzmann transport theory within the constant relaxation time and rigid band approximation using the BoltzTraP code. 27 Within the rigid band approximation, the electronic band structure is assumed to not change with carrier doping or temperature. The ab initio molecular dynamics (AIMD) simulations use the canonical NVT (constant number, volume, and temperature) ensembles, in which the temperatures were controlled using the algorithm of Nosé. 28,29 Our model is built on the basis of a 4×4×1 Sb2 Te3 hexagonal supercell. The ensemble of 240 atoms was melted and equilibrated at 3000 K, and then quenched to and equilibrated at 1000 K ( T m of Sb2 Te3 , 900 K), 30 and nally quenched to and equilibrated at 300 K. Every AIMD simulation of the above processes runs for 2000 steps, with each time step for 3 femtoseconds (fs). The AIMD simulations have been checked with a slow quenching rate of -15 K/ps for the quench process form 1000 K to 300 K to generate amorphous congurations.

3 Results and discussion 3.1 Lattice Structure and Electronic Properties of Y2 Te3 . Theoretically, avoiding extra carriers can be realized by introducing dopants with the same number of outmost electrons as the substituted atoms. While the problem of phase separation

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5 Figure 1: (a) Rhombohedral crystal structure of Y 2 Te3 with the space group D3d (R ¯3m ). A quintuple layer with Te-Y-Te-Y-Te is indicated by the orange square. (b) Phonon spectra of rhombohedral Y2 Te3 . (c) The projected band structures of rhombohedral Y 2 Te3 . The red and blue dots represent the contribution from Y 4 d and Te 5p electrons, respectively. The Fermi energy is set to 0 eV.

in the phase-change process could be ruled out if the dopant can form the same crystal structure as the parent phase. Keeping this in mind, a rather extensive literature reviewing and data analysis from ICSD have been performed and nally Y is screened out as a suitable candidate dopant for Sb2 Te3 . Previously, it has been reported that YSbTe 3 31,32 and YBiTe3 33 remain in the same rhombohedral structure (space group R ¯3m ) as Sb2 Te3 . Therefore, we rstly investigated the stability of rhombohedral Y 2 Te3 and its electronic structure. As illustrated in Figure 1a, similar to Sb 2 Te3 , Y2 Te3 consists of three quintuple slabs in one unit cell and each slab is stacked in a sequence of Te-Y-Te-Y-Te along the c direction. The Te-Te bond length in Y2 Te3 is calculated to be 4.025 Å which is larger than the sum of their covalent radii 2.76 Å, 34 suggesting that the adjent Te-Te layers are bonded by weak van der Waals force 35 as that in Sb2 Te3 and other layered Ge-Sb-Te compounds. 36,37 The optimized lattice constants a and c for Y2 Te3 are 4.298 Å and 31.306 Å, respectively. Compared with the values we calculated for Sb 2 Te3 , the lattice mismatch in a between Y2 Te3 and Sb2 Te3 is only ∼1.1%, even smaller than that between GeTe and Sb 2 Te3 (∼2.2% 38 ). Such a small lattice mismatch in a between Y2 Te3 and Sb2 Te3 indicates the possibility of layered single crystal Y2 Te3 -Sb2 Te3 as the case of (GeTe)n (Sb2 Te3 )m and hence the uniformity of Sb 2 Te3 6


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if doped by Y, which is an important factor for cycling stability of phase change memory. It is worth pointing out that for other used dopants Ti

!

), the

:

:

(such as N,

'

Si,

Zn,

Al,

and

-Te alloys have large lattice mismatch with Sb 2 Te3 , wherein the minimum lattice

mismatch between X-Te alloy and Sb 2 Te3 is

∼11%. !'

To verify the stability of rhombohedral Y 2 Te3 , the phonon spectra was calculated by PHONOPY. As shown in Figure 1b, there is no negative frequency modes presented at any wave vector, demonstrating that this phase is dynamically stable. Meanwhile, we have also calculated the elastic constants by the stability criteria of and

? ij

to verify the mechanical stability of rhombohedral Y 2 Te3

c11 − c12 > 0

(c11 + c12 )c33 − 2c213 > 0

constants

? ij

and

(c11 + c12 )c44 − 2c212 > 0

corresponding to the volume eect.

"

for the shear stability Our calculated elastic

satisfy the above criteria, conrming the mechanical stability of rhombohedral

Y2 Te3 . The practical dynamic stability of rhombohedral Y 2 Te3 has been further conrmed by AIMD simulation (see the Supporting Information). At this stage it may be concluded that introducing Y into Sb 2 Te3 will not result in large lattice distortion and YST is expected to be stable both dynamically and mechanically. Furthermore, to verify whether Y is eective to tune the electrical property of Sb 2 Te3 , we calculated the electronic structure of rhombohedral Y 2 Te3 .

Figure 1c shows the pro jected

band structure of Y 2 Te3 , from which it is obvious that Y 2 Te3 is an indirect-band-gap semiconductor with the valence band maximum (VBM) at the

Γ

point and the conduction band

minimum (CBM) near the M point. More notably, the band gap is 0.83 eV for Y 2 Te3 , which is much larger than that of Sb 2 Te3 (

∼0.28

eV

element to increase the band gap of Sb 2 Te3 .

"

), indicating that Y could be an eective

On the other hand, as seen in Figure 1c,

the conduction band edge states are dominated by Y atoms, while the valence band edge states are mainly composed of the states from Te atoms, which is very similar to the case of Sb2 Te3 ,

"

where the states of CBM and VBM are contributed by Sb and Te atoms, respec-

tively. Clearly, the band gaps of both Y 2 Te3 and Sb2 Te3 are charge transfer gaps, which are mainly determined by the bonding strength of Y-Te or Sb-Te. The above similarity in band

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Figure 2: (a) Crystal structure of the 2 ×2×1 supercell of Sb2 Te3 , each slab formed by ve layers stacked along ? in the sequence Te1-Sb-Te2-Sb-Te1, of which the Te atoms where weak van der Waals force exists are dened as Te1. There are three possible substitutional sites at Sb, Te1, and Te2, as well as one interstitial site E between the adjacent Te1 layers for the dopant Y. (b) Formation energies of Y occupying the four dierent positions as Y Sb , YTe1 , YTe2 , and Yi in Sb2 Te3 as a function of the chemical potential of Te. (c)-(e) The most stable congurations for the (c) two, (d) three, and (e) four Y atoms in the supercell. structure features between Y 2 Te3 and Sb2 Te3 further indicates the feasibility of using Y as a dopant to tune the electrical property of Sb 2 Te3 .

3.2 Formation Energies for Y-doping in Sb2 Te3 . To investigate Y doping in Sb 2 Te3 , a 2×2×1 Sb2 Te3 supercell containing 60 atoms was used (Figure 2a). For single Y atom doped system, there are four possible doping types: substituting for a Sb atom (denoted as Y Sb ), substituting for a Te atom at the interface between the neighboring quintuple layers (denoted as Y Te1 ), substituting for a Te atom in the center of quintuple layers (denoted as Y Te2 ), and occupying an interstitial site between the weakly coupled adjacent Te layers (denoted as Y i ). The formation energy of Y doping is calculated as "! E f [X] = Etot [X] − Etot [bulk] −

ni μi ,

i

8


(1)

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where Etot [X] and Etot [bulk] are the total energies of a supercell with and without Y doping, respectively, n i indicates the number of atoms of type i (host atoms or impurity atoms) that have been added to ( n i > 0) or removed from (n i < 0) the supercell when the doping is created, and μi is the corresponding chemical potentials of these species, which can be Te-rich or Te-poor (or anything in between) depending on the experimental growth conditions. The chemical potentials of Sb and Te are limited by the following expression 2μSb + 3μTe = Etot [Sb2 Te3 ]. Considering the case of Y 2 Te3 compound (the other case YTe is seen in the Supporting Information), the chemical potentials of Y and Te are limited by the following expression 2μY + 3μTe = Etot [Y2 Te3 ]. Under extreme Te-rich condition, the chemical potential of Te is subject to an upper bound μmax Te = μTe [bulk]. The upper limit on then results in lower limits on μSb and μY : μmax Te μmin Sb = (Etot [Sb2 Te3 ] − 3μTe [bulk]) /2,

(2)

μmin = (Etot [Y2 Te3 ] − 3μTe [bulk]) /2. Y

(3)

Similarly, under the extreme Te-poor condition, the chemical potential of Te is subject to a lower limit, μmin Te

⎧ ⎪ ⎨ (Etot [Sb2 Te3 ] − 2μSb [bulk]) /3, = max ⎪ ⎩ (Etot [Y2 Te3 ] − 2μY [bulk]) /3

⎫ ⎪ ⎬ ⎪ ⎭

,

(4)

which results in upper limits on μSb and μY :

min /2, μmax Sb = Etot [Sb2 Te3 ] − 3μTe

(5)

μmax /2. = Etot [Y2 Te3 ] − 3μmin Y Te

(6)

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In our calculations, the trigonal phase of Sb and Te, and the hexagonal phase of Y were used as the reference elemental bulk phases for the chemical potentials. The and

Etot [Y2 Te3 ]

Etot [Sb2 Te3 ]

in Eqs. (2)-(6) are the total energies of primitive cell of Sb 2 Te3 and Y2 Te3 ,

respectively. The calculated formation energies are shown in Figure 2b. It is clearly seen that, independent of the chemical environment, Y Sb always has the lowest formation energy among the four possible doping types, demonstrating that Y dopants prefer to substitute for Sb atoms. Moreover, the very low formation energy of around 0.2 eV/f.u. of Y Sb suggests an easy formation process, while the formation energies for Y i , YTe1 , and YTe2 are quite high, in excess of 2 eV/f.u., indicating their formation will be much more dicult than Y Sb . In addition to single Y atom doping, we have also considered the cases of doping two, three, and four Y atoms. The results show that the formation energy is the lowest as the two doped Y atoms substitute for the nearest Sb atoms in the same Sb atomic layer (Figure 2c), and the same is true for the case of three Y doped atoms (Figure 2d). For the case of four Y doped system, the calculated formation energy is the lowest when three Y atoms substitute for three neighboring Sb sites and the fourth Y occupies the nearest Sb site in the adjacent Sb atomic layer (Figure 2e). Hereafter, the 1, 2, 3, and 4 Y atoms doped 60-atom model are denoted by the compositional form Y x Sb2−x Te3 , where correspondingly

N

= 0.083, 0.167,

0.25, and 0.333 (up to 6.67 at% Y).

3.3 Electronic Properties and Origin of the Larger Band Gap of ? -YST. To understand the evolution of eective mass and band structure triggered by Y doping, the band structures of Y x Sb2−x Te3 (N = 0, 0.083, 0.167, 0.25, and 0.333) were calculated along a commonly used path in the Brillouin-zone (see the Supporting Information). Figure 3a displays the band structure for pristine Sb 2 Te3 , which shows a direct band gap of 0.12 eV at the

Γ

point, in agreement with the previous works.

10

25,44,45


It is also noticed that the

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Figure 3: (a) Band structure for Sb 2 Te3 , with energy gap of about 0.12 eV at Γ point. The Fermi energy is set to 0 eV. (b) The projected band structure of Y 0.333 Sb1.667 Te3 . The red, yellow, and blue dots represent the contribution from Y 4 @, Sb 5F and Te 5F electrons, respectively. The Fermi energy is set to 0 eV. (c) The band gap of Y N Sb2−N Te3 as a function of N, where the pentagram indicates the gap of the rhombohedral Y 2 Te3 . (d) Three zones were identied for N based on its distinct band structures. Zones I, II, and III are corresponding to the direct, indirect, and direct gap, respectively. The critical values N for the gap transition are 0.153 and 0.269. gap at A point is 0.52 eV, much larger than that at the

point. After Y doping, in the

Γ

case of the largest Y concentration, Y 0.333 Sb1.667 Te3 , the band gap is increased to 0.30 eV and the positions of both VBM and CBM change from

Γ

to A, i.e., the direct band-gap

character is maintained (see Figure 3b). It is also noticed in Figure 3b that the conduction bands near the Fermi energy are contributed by Sb-5 F and Y-4@ orbitals, while the valence bands near the Fermi energy consist of Te-5 F orbitals, showing a mixed band features from Sb2 Te3 and Y2 Te3 . Obviously, the evolution of energy bands at the A and

Γ

points is due

to the inuence of Y doping on the band gap of the doped system. To further understand A Γ ) and Γ (Egap ) the band-gap change of YST, we plotted in Figure 3c the gap at the A ( Egap

points as well as the whole doped system ( Egap ) with respect to Y concentrations. Clearly, A Egap

Γ decreases while Egap increases with Y concentration and they reach the same value at

N

= 0.167. At N = 0.167 and 0.25 the doped system has an indirect band gap that is slightly lower than the corresponding

Γ Egap

A and Egap . At N = 0.333, the doped system has a direct

band gap again but at A rather than at

Γ

point, as also illustrated in Figure 3b. Overall, 11



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with Y concentration increasing from 0.083 (Y 0.083Sb1.917Te3) to 0.333 (Y0.333Sb1.667Te3) the band gap of the YST is always larger than that of pristine Sb 2Te3, although the gap is not monotonously increasing with Y concentration. It is worth pointing out that Y 0.167Sb1.833Te3 has the largest gap which is 0.21 eV larger than that of Sb 2 Te3 . With considering spin-orbitalcoupling (SOC) eects, the gap of YST still shows an increasing trend with Y doping. The results clearly demonstrate that Y is a suitable dopant to eectively increase the band gap of Sb2Te3 . The change in energy gap of Y xSb2−xTe3 with Y concentration can be understood from the evolution of valance band (VB) and conduction band (CB) at the A and Γ points. As Γ illustrated in Figure 3d, the increase of Egap is due to the upward movement of CB at the Γ point with increasing Y concentration, while the lift of VB towards the Fermi level at the A A . We have also identied point with increasing Y concentration results in the decrease of Egap three zones according to their band-structure features. As illustrated in Figure 3d, zone I is for direct-band-gap YxSb2−xTe3 with x being from 0 to 0.153, for which both the CBM and VBM locate at the Γ point. Zone II corresponds to indirect-band-gap Y xSb2−xTe3 with N ranging from 0.153 to 0.269, where the VBM is at the A point, while the CBM is at the Γ point. Zone III is for a direct band-gap at the A point with N being from 0.153 to 0.333. It is clearly seen that the CB at the A point (the upper triangulars) and the VB at the Γ point (the circulars) are relatively insensitive to Y doping, while there is a growing tendency for the CB at the Γ point (the lower triangulars) and the VB at the A point (the squares) with increasing Y concentration. The direct/indirect nature of band gap is the result of competition among the energies of near-band-edge states at the Γ and A points. To understand the above interesting evolution of electronic band structure for Y xSb2−xTe3 with Y concentration, we have extensively investigated the chemical bonding of the doped system. Figure 4a shows the bonding chemistry of crystalline Y 0.083Sb1.917 Te3 with charge density dierence (CDD). The CDD is the dierence of the charge distribution arising from bonding with neighbors in the structure. Herein we used CDD isosurfaces (transparent 12


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Figure 4: (a) The charge density dierence of Y 0.083 Sb1.917 Te3 , where only two quintuple layers are illustrated. (b) The Sb-centred atomic motif showing three strong bonds and three weak bonds. (c) The Y-centred atomic motif showing six strong bonds. The isosurface value is xed at +0.006 A /a30 (a0 = bohr). magenta area) to determine areas of charge pileup in three dimensions to give a 3D representation. The dierences are calculated with respect to that of a superposition of isolated atoms. Some conclusions can be drawn by analyzing Figure 4. Firstly it is obvious that Sb and Te forms three strong and three rather weak covalent bonds, which is clearly illustrated in Figure 4b. This is in agreement with pristine Sb 2 Te3 , where three strong and three weak bonds are identied by the three shorter Sb-Te1 bonds (2.995 Å) and three longer Sb-Te2 bonds (3.143 Å). Secondly, Y forms six equivalently strong covalent bonds with its neighboring Te atoms as illustrated in Figure 4c. This is in sharp contrast to Sb-Te bonds but is similar to that of Ti doped Sb 2 Te3 . " Moreover, we can clearly see a larger charge accumulation at the Y-Te bonds than that at Sb-Te bonds, showing Y-Te bond is stronger than Sb-Te bond. This enhanced covalent interaction between Y and Te originating from the hybridized Y-4@ and Te-5F orbitals could result in the increased band gap of YST (see the partial DOS analysis in the Supporting Information). Finally, large electron localization is clearly seen at Te1 atoms, which is characterized as lone-pair electrons or non-bonding 13



Sb-Te2 Sb-Te1 Te-Te

3.86

Bond Length (Å)

3.16

Bond Length (Å)

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3.14

3.84

3.00

3.82

2.98 0.000 0.083 0.167 0.250 0.333 x

Figure 5: Bond lengths of Sb-Te1, Sb-Te2, and Te-Te for Y N Sb2−N Te3 within the N ranging from 0 to 0.333, which show almost linearly changes with the increase of Y concentration. electrons similar to that in Ge 2 Sb2 Te5 . "$ Meanwhile, the incorporation of Y in Sb 2 Te3 induces the change of all the bond lengths. Figure 5 shows the bond lengths of the Sb-Te1, Sb-Te2, and Te-Te for Y x Sb2−x Te3 at various Y concentrations, from which it is obvious that the Sb-Te2 and Te-Te bond lengths almost linearly increase with Y concentration, while the bond length of Sb-Te1 decreases linearly with the increase of Y concentration. Taking Y 0.333 Sb1.667 Te3 as an example(corresponding to Y concentration of 6.67 at%), compared with Sb 2 Te3 , the bond length of Sb-Te1 is decreased by 0.45%, while the bond lengths of Sb-Te2 and Te-Te are increased by 0.94% and 1.2%, respectively. The change in the bond lengths could also induce the variation of the band gap of Yx Sb2−x Te3 . To conrm this point, we have performed the following calculations and analysis. Taking Y0.333 Sb1.667 Te3 as an example, we performed

ab initio

calculations using

the same lattice structure and inter atomic coordinates as ideal Sb 2 Te3 , and the results show that the energy gaps at the A and Γ points are 0.36 eV and 0.47 eV, respectively. While for the actual optimized structure of Y 0.333 Sb1.667 Te3 , the calculated energy gaps at the A and Γ

points are 0.30 eV and 0.44 eV, respectively. Correspondingly, the gap at the A point is

decreased by 18.9% while that at the Γ point is decreased by only 5.4%. Obviously, the gap at the A point is more sensitive to bond-length change. To further analyse the role that Sb-Te1, Sb-Te2, and Te-Te bonds play in tailoring the 14


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band gap of Yx Sb2−x Te3 , we manually increase the bond lengths of Sb-Te1, Sb-Te2, and TeTe of pristine Sb2 Te3 slightly, and then calculated the band gaps at the Γ and A points, the results of which are listed in Table 1. Obviously, the change in the Sb-Te1 and Sb-Te2 bond lengths and hence the bonding strength induced by Y doping result in the distinct change of the energy gap at the A point, while the changes in the Te-Te bond length or strength plays a dominate role in changing the gap at the Γ point of Sb2 Te3 . The physical origin for the gap variation introduced by the bond length changes can understood as follows. In Sb2 Te3 , the formation of chemical bonding hybridizes the states on Sb and Te atoms, thus pushing down all of the Te states and lifting up all of the Sb states. Considering the eect of the crystal-eld splitting between dierent F orbitals, the energy levels closest to the Fermi − energy turn out to be the F z levels |21+ z of Sb and |21z of Te, which is similar to the

case of Bi2 Te3 . " Thus the decrease in the bond length of Sb-Te1 or Sb-Te2 will weaken the chemical bonding hybridization rather than the crystal-eld splitting, leading to the A decrease in the Egap . In addition, the increase of Te-Te bond length will decrease the overlap

of wavefunctions between quintuple layers, "% which causes an increase in the band gap. Table 1: The dierences of energy gaps at A and Γ point between pristine Sb 2 Te3 and the Sb2 Te3 with one of the Sb-Te1, Sb-Te2, and Te-Te bond lengths manually changed about 2% and the other bond lengths keeping constant. Model

Δ- gap (eV)

A point

Γ point

Non-deformation

0

0

+2% Sb-Te1

−0.027

+0.038

+2% Sb-Te2

−0.102

+0.008

+2% Te-Te

+0.041

+0.067

15



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Page 16 of 30

3.4 Electrical Conductivity and RESET current.

The enlargement in the band gap ( E gap) of Sb2Te3 induced by Y doping suggests the increase of the carrier eective mass ( m∗ ), as m∗ is correlated to the energy gap E gap, which can be derived from the band edge structure in k·p perturbation theory, "& reduced to the equation as m/m∗ ≈ 2 |c |p| v|2/mEgap, where c and v denote the conduction and valence band v edge, respectively. Based on the band structures calculations, one can get the values of eective masses using m∗ = h¯ 2(∂ 2E (k) /∂k2)−1. "' Table 2 lists the carrier eective masses of YST under dierent Y doping concentration, where it is clearly seen that the eective masses of both the hole and electron carriers increase with Y concentration. Table 2: The calculated eective masses in electron mass units compared with previous works. A

Electrons

Sb2Te3

Γ

A

Holes

−0.038

Y0.083Sb1.917Te3 Y0.167Sb1.833Te3 Y0.25Sb1.75Te3 Y0.333Sb1.667Te3 a Calculated data in Ref. 50.

−0.054a −0.070

−0.138

−0.148

−0.155

+0.104

Γ

+0.051 +0.045a +0.059 +0.075 +0.101

Then we turn to investigate the change of electrical conductivity of Sb 2 Te3 after Y doping. Generally, the electrical conductivity is the sum of the contributions of electron and hole carriers as σ = (n eμe+p eμh), where μe = eτ /m∗e and μh = eτ /m∗h. This shows that the collision time (τ ), the eective mass (m∗e , m∗h) and the carrier density (n, p ) are three important factors that determine the electrical conductivity. As shown above, both m∗e and m∗h increase under the Y doping. Besides, like other dopants such as N, O, and Al considered in previous works, Y dopants will signicantly reduce the collision time τ as 16


Page 17 of 30

2500

0

cm)

0.083

(1/

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


2000

0.167 0.25

1500

0.333 Hinsche

et al.

1000 500 0 -1.5 -1.0 -0.5

0.0

0.5

20

3

n (10

1.0

1.5

/cm )

Figure 6: Calculated electrical conductivity as a function of carrier concentration for YN Sb2−N Te3 with N = 0, 0.083, 0.167, 0.25, and 0.333. Positive and negative carrier concentration represent p and n type doping, respectively. Previous data (triangles) from Ref. 51 is given for comparison. scattering centers. Evidently, both the increase of

m∗e

and

m∗h

and the decrease of

τ

will

trigger the decrease of the carrier mobilities, "& which will directly lead to the reduction of the electrical conductivity σ. To give a better description of the electrical conductivity, the semi-classical Boltzmann transport theory within the constant relaxation time as 12 fs # was adopted using the BoltzTraP code. % The electrical conductivity as a function of carrier concentration at varying x for YN Sb2−N Te3 is presented in Figure 6. Obviously, the calculated electrical conductivity of Sb 2 Te3 is in agreement with the previous data by Hinsche

et al.

With Y concentration increasing, the electrical conductivity at the same carrier concentration (either positive or negative) decreases, which is attributed to the variation of eective masses of the hole and electron carriers, respectively. In addition, we nd that the Y dopants can also decrease the intrinsic carrier density of Sb2 Te3 . Experimentally, the existence of the Sb Te antisite defects was assumed to be the origin of the degenerate p -type charactor with a hole density of about 10 20 cm−3 . # Herein, the formation energy and the charge transfer levels of Sb Te antisite defects are calculated to understand whether Sb Te is indeed the defect type to be taken into consideration (see the Supporting Information). The formation energy of charged defects shows that the Sb Te 17



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Page 18 of 30

defect is stable in a negative charge state (-1). The transition levels, i.e., the Fermi-level positions at which the lowest-energy charge state changes, are thus determined by formation energy dierences:

ε(q/q ) =

E f (X q ; EF = 0) − E f (X q ; EF = 0) (q − q )

(7)

The corresponding thermodynamic transition levels are illustrated in Figure S3. We can clearly see that the transition level from a negative to the neutral charge state ε(1 − /0) is below the VBM, indicating a shallow acceptor. Thus, Sb Te antisite defect is indeed the source that induced the F -type doping. The eects of Y-doping on the formation of Sb Te antisite defects are understood by calculating and comparing the formation energies of Sb Te in Sb2 Te3 with and without Y doping. Without Y-doping, the formation energy of the SbTe antisite defect is calculated to be 0.377 eV. When the Y dopants are introduced, the formation energy of SbTe increases signicantly, as shown in the Table 3. In particular, the closer the SbTe is to the Y dopant, the larger the formation energy of Sb Te is. Considering the concentrations and distributions of the dopants and antisite defects in practical case, Y has a negative eect on the formation of Sb Te antisite defect in Sb2 Te3 . That's to say, Y doping is helpful to reduce the amount of Sb Te antisite defects and accordingly decrease the resultant hole carrier density. Table 3: The formation energies of donor defect Sb Te in Sb2 Te3 with and without Y doping. The distance between Y and Sb Te is recorded as @ (Y-SbTe ). N = 0.083

distribution

Δ- form for SbTe (eV)

Sb2+x Te3−x

SbTe

0.377

Y0.083 Sb1.916+x Te3−x

@ (Y-SbTe ) = 15.384

0.412

@ (Y-SbTe ) = 5.387

0.440

@ (Y-SbTe ) = 3.029

0.812

18


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So far, we can see that except decreasing collision time τ like other dopants, Y dopants will decrease the conductivity of Sb 2 Te3 via two additional routes. First, it increases the eective mass by regulating the band structure of Sb 2 Te3 . Second, it can decrease the carrier densities by suppressing the formation the Sb Te antisite defects. Both the increase of eective mass and the decrease of the carrier density will result in the reduction of the conductivity, which is very helpful to achieve a higher density in data storage applications and hence a lower power consumption required in mobile applications. #! In the process of phase transition from amorphous to crystalline state, the phase-change memory cell could be viewed as the combination of the crystalline state region and amorphous state region, which can be treated as two resistors connected in series. The RESET current can be calculated by the equation of I =

Q/Rc Δt, where Q is the joule heat, Δt is the

pulse length, R c is the average resistance of crystalline state region in phase-change memory cells in RESET process. If only the eects of Y doping-induced change of the eective mass of hole that is the majority carrier in Sb 2 Te3 are considered, from pure Sb 2 Te3 to Y0.25 Sb1.75 Te3 , the hole eective mass is doubled (see Table 2), which, consequently, will make the resistivity raised 3.5 times at

n

= 1 × 1018 cm3 (see Figure 5). In this case, the RESET current will

be reduced by ∼46%, allowing greater driving capability while minimizing the cell area, #! which will lead to an enhancement of the density of data storage.

3.5 Thermal stability of the amorphous YST. One of the constraints on the application of Sb 2 Te3 as phase-change recording materials is the poor thermal stability of its amorphous state at room temperature. Therefore, the eect of Y on the thermal stability of amorphous state is a matter of concern. The inuence of Y on the data retention and reliability of YST-based memory cells can be understood by the comparison of the thermal stability of amorphous Sb 2 Te3 (a -Sb2 Te3 ) and YST (a YST). Compared to the crystalline state, the amorphous state is a higher-energy state, and its crystallization will result in the decrease in energy. Figure 7 shows the evolutions 19



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

Figure 7: The evolutions of total energies of amorphous Sb 2 Te3 (a -Sb2 Te3 ) and amorphous Y0.333 Sb1.667 Te3 (a -YST) from the AIMD at 600 K for 66 ps. of total energies of a -Sb2 Te3 and a -YST at 600 K, where Y0.333 Sb1.667 Te3 is selected as a representative sample for a -YST. Herein, a higher temperature (600 K) instead of room temperature is used to accelerate the structural evolution process of the amorphous phase. It is obvious that the energy of a -Sb2 Te3 decreases monotonically with time while that of a -YST

shows a slight change, which means that the amorphous state of Sb 2 Te3 is more

sensitive to temperature than a -YST. In other words, YST-based memory cells should have better performance in data retention and reliability than Sb 2 Te3 -based memory cells, due to the better thermal stability of a -YST than that of a -Sb2 Te3 . Theoretically, to the best of our knowledge, the present day ab initio calculation methods cannot calculated the resistivity of the amorphous phase. However, the resistivity contrast of YST can be deduced by comparing the structures of crystalline and amorphous states. As seen in Figure 8, which shows snapshot structures of amorphous Sb 2 Te3 and YST after annealed for 66 ps at 600 K, the rocksalt-like characteristic is clearly seen in amorphous Sb2 Te3 but not in amorphous YST. The fast appearance of crystalline domain in pure Sb 2 Te3 indicates that amorphous Sb 2 Te3 is much easier crystalline than amorphous YST. Therefore, using the same quenching route to obtain amorphous state, crystalline nucleus could exist in pure Sb2 Te3 but not in YST. While the existence of these crystalline domain in amor20


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Page 21 of 30

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Figure 8: Model congurations of (a) Sb 2 Te3 and (b) YST materials in simulations of annealing the amorphous state. phous Sb2 Te3 may contribute to the experimentally reported one order of magnitude in the resistivity contrast #" between the set and the reset states. On the other hand, the absence of the rocksalt-like structure in amorphous YST would render the increased crystallization temperature and resistivity contrast in YST-based memory. To study the origins of the improved thermal stability of amorphous YST, the electrons pileup between atoms are investigated by the following analysis. The typical conguration of = -Sb2 Te3 and = -YST as obtained from the melt quenching technique are shown in Figure 9. For = -YST, Y atoms are found distributed randomly in the ensemble (Figure 9d). The main factor contributing to the improved structural stability of = -YST compared to Sb2 Te3 is the stronger interactions between Y and Te than that between Sb and Te. The interaction between cations and anions in the amorphous state can be characterized by the CDD isosurfaces (transparent magenta area), which were adopted to give a 3D representation of the charge pileup. As illustrated in Figure 9b, one Sb atom forms rather weak covalent bonds with three Te atoms, while one Y atom, shown in Figure 9c, forms strong covalent bonds with six Te atoms just like the Y atoms in ? -YST (Figure 4c).

21



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

Figure 9: (a)The charge density dierence of amorphous Sb 2 Te3 . (b) Three weak covalent bonds between one Sb atom and three Te atoms. (c) Six strong covalent bonds between one Y atom and six Te atoms. (d)The charge density dierence of amorphous Y 0.333 Sb1.667 Te3 . The four atoms with three bonds are showed by green polyhedrals, wherein the maximum nearest neighbor distance is set as 3 Å. The isosurface value is xed at +0.008 e /a30 (a0 = bohr).

4 Conclusions By performing

ab initio

calculations on YST at various dopant concentrations, we have

obtained valuable insight into the structural and electronic properties of Y in the parent phase, and the microscopic mechanisms underlining the property enhancements. Our results show that Y prefers to substitute for the adjacent Sb atoms with low formation energy. Y doping can decrease intrinsic carrier density of Sb 2 Te3 by suppressing the formation of the SbTe antisite defect, and can increase the eective mass by regulating the band structure, which will dramatically increase the resistivity of c -Sb2 Te3 and thus decrease the power consumption of phase-change memory devices. The thermal stability of a -YST is improved signicantly compared to a -Sb2 Te3 , facilitating the data retention and reliability, based on our AIMD simulations. Most importantly, c -Y2 Te3 has only a ∼1.1% lattice parameter mismatch with c -Sb2 Te3 , which is better than that between c -GeTe and c -Sb2 Te3 , indicating that the incorporation of Y dopants into Sb 2 Te3 would not cause severe phase separation. Hence, the present ndings that the increased resistivity of crystalline state, the improved 22


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thermal stability of amorphous state, and the good phase stability of YST make yttrium an optimal dopant for Sb 2 Te3 for phase-change memory.

Acknowledgement This work was supported by National Science Foundation for Distinguished Young Scientists of China (51225205) and the National Natural Science Foundation of China (61274005). The authors also acknowledge useful discussions with Prof. Shengbai Zhang from Rensselaer Polytechnic Institute, United States of America.

Supporting Information Available The possibility of phase separation of YST to YTe and Y 7 Te2 , the practical dynamic stability of rhombohedral Y 2 Te3 , YTe considered as the limitation condition of the structures of Y x Sb2−x Te3 (

EF,

the band

x ranging from 0, 0.083, 0.167, 0.25, and 0.333), the partial density

of states of Y2 Te3 , the formation energy and the charge transfer levels for Sb Te antisite defects, total and partial pair-correlation functions and bond angle distribution functions of

a -Sb2 Te3 and a -YST, The crystalline domains in a -Sb2 Te3 .

(PDF)

This material is available free of charge via the Internet at

http://pubs.acs.org/.

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Nanoscale

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(50) Yavorsky, B. Y.; Hinsche, N.; Mertig, I.; Zahn, P. Electronic Structure and Transport Anisotropy of Bi 2 Te3 and Sb2 Te3 .

Phys. Rev. B , 84, 165208.

(51) Hinsche, N. F.; Zastrow, S.; Gooth, J.; Pudewill, L.; Zierold, R.; Rittweger, F.; Rauch, T.; Henk, J.; Nielsch, K.; Mertig, I. Impact of the Topological Surface State on the Thermoelectric Transport in Sb 2 Te3 Thin Films.

ACS Nano #, 9, 44064411.

(52) Shelimova, L.; Karpinskii, O.; Konstantinov, P.; Kretova, M.; Avilov, E.; Zemskov, V. Composition and Properties of Layered Compounds in the GeTe-Sb 2 Te3 System.

Inorg.

Mater. , 37, 342348. (53) Bedeschi, F.; Bez, R.; Bono, C.; Bonizzoni, E.; Buda, E. C.; Casagrande, G.; Costa, L.; Ferraro, M.; Gastaldi, R.; Khouri, O.; Pellizzer, F.; Pirovano, A.; Resta, C.; Torelli, G.; Tosi, M. 4-Mb MOSFET-Selected

μ Trench Phase-Change Memory Experimental Chip.

IEEE J. Solid-State Circuits #, 40, 15571565. (54) Peng, C.; Wu, L.; Song, Z.; Rao, F.; Zhu, M.; Li, X.; Liu, B.; Cheng, L.; Feng, S.; Yang, P. Performance Improvement of Sb 2 Te3 Phase Change Material by Al Doping.

Appl. Surf. Sci. , 257, 1066710670.

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Yttrium-Doped Sb2Te3: A Promising Material for Phase-Change Memory

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