Sn₂Se₃: A conducting crystalline mixed valent phase change memory compound

Phase change memory devices require materials with metastable amorphous and crystalline states having high resistance contrast, low switching energy, fast switching times, and long term stability.^1–5 Ge-Sb-Te (GST) alloys have been widely employed because of their fast crystallization speed and demonstrated high cycle life.^6–14 Sn selenide phases have also been investigated in this context, including SnSe and SnSe₂, which correspond to known bulk compounds, as well as Sn₂Se₃.¹⁵ Recently, studies of Sn₂Se₃ have shown a very rapid low energy reversible switching between a high resistivity amorphous state and a very low resistivity crystalline state, with indications of performance that may exceed GST.^15–18 The high conductivity of the crystalline phase is at odds with the known behavior of the sulfide Sn₂S₃, which is a semiconductor with a gap of ∼1 eV. This suggests a different behavior for the selenide system. However, there are no reported properties of bulk Sn₂Se₃, and the phase is not reported in phase diagrams. There is one report by Palatnik and Levitin who reported the phase but not a structure determination.¹⁹ The corresponding sulfide, Sn₂S₃, is a semiconductor,²⁰ inconsistent with the low resistivities observed for Sn₂Se₃ crystalline films.

Here, we use first principles, genetic algorithm based crystal structure prediction to identify the Sn₂Se₃ phase. We then calculate the properties. We find two low energy structures, both very slightly above the SnSe-SnSe₂ tie line and therefore marginally metastable consistent with the known phase diagram, as well as the fact that the crystalline phase can be formed in thin films,²¹ where phase separation may be kinetically inhibited.

The lowest energy structure has two formula units per cell with the Sn disproportionated into Sn (II) and Sn (IV) similar to Sn₂S₃.^20,22–24 However, in contrast to the semiconducting sulfide, Sn₂Se₃ is semimetallic. We also find a non-disproportionated structure, which is metallic and very slightly higher in energy compared with the disproportionated structure. This competition of structures is consistent with the ready formation of an amorphous phase. As mentioned, semimetallic and metallic nature of the crystalline phases of Sn₂Se₃ is in contrast to semiconducting Sn₂S₃. This explains the low resistance of the crystalline material, which is essential for high resistance contrast.

We used the unbiased swarm structure search method as implemented in the CALYPSO code^25,26 for the crystal structure determination. Our search for the Sn₂Se₃ compounds included cells up to 20 atoms (four formula units) and N_p (N_p = 30) random initial structures followed by full relaxation. The lowest energy structure found has two formula units per cell. We did the evolutionary search for 50 generations. At each step, we retained 60% of the lowest energy structures. The remaining 40% were replaced by new random structures with different symmetries. As seen in Fig. 1, although new metastable structures are introduced, no new ground states were generated in the final generations of the search. In other words, the lowest energy structure was already found in the final generations, and no better structures were produced by continuation of the search. We also tested the approach by applying it to the known compounds such as SnSe, SnS, and SnSe₂. The correct ground state structures in accord with the experiment were predicted.

The structure relaxations were performed with density functional theory (DFT) using the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA).²⁷ We used the projector-augmented wave (PAW) method²⁸ as implemented in the VASP code.²⁹ Good convergence was obtained with an energy cut off of 400 eV for the plane-wave expansion and a Brillouin zone integration grid spacing of 2π × 0.032 Å⁻¹. A higher 600 eV cut-off was used for the final total energy calculations to reliably compare the energies of the phases.

The electronic structure calculations were carried out using the general potential linearized augmented planewave (LAPW) method,³⁰ as implemented in the WIEN2K code,³¹ with well converged LAPW basis sets, including local orbitals for semicore states. The lattice parameters obtained in the VASP calculations as above were used. The electronic structures were then calculated using the modified Becke-Johnson potential of Tran and Blaha (mBJ)³² with spin-orbit coupling. The transport coefficients were obtained from the electronic structure using the BoltzTraP code.³³ The phonon calculation was done using the PHONOPY code with the supercell finite difference method.³⁴ For this purpose, 4 × 2 × 2 supercells were used. The elastic constants were calculated using finite strains with the VASP code.

The LAPW method implemented in WIEN2k is highly precise, and combined with the stable all electron implementation of the mBJ method, including spin-orbit provides more reliable predictions of the electronic properties. On the other hand, for the structure determination and relaxation, it is essential to have an efficient implementation of the stress tensor, which is available with the PAW method implemented in VASP. For this reason, we used two different electronic structure codes in the present study. We cross checked the energy differences between these two codes and found no significant differences, in particular, regarding the ground state. We also performed hybrid functional HSE calculations³⁵ including spin-orbit with the PAW method to verify the band overlap predicted in the mBJ calculations (see below).

Figure 2 shows the lowest-energy structure P2₁/m and second lowest-energy structure $P3¯m1$ as obtained from the structure prediction. The structural parameters are given in Table I. The lowest energy structure has Sn disproportionated into Sn(II) and Sn(IV) sites. It consists of Sn₂Se₃ ribbons running along the c axis in a P2₁/m monoclinic phase. The structure contains two formula units per cell. These Sn₂Se₃ ribbons are similar to those in the mixed valence compound Sn₂S₃, which has an orthorhombic (Pnma) structure with four formula units per cell.²⁰ The relaxation of Sn₂Se₃ in the Pnma structure of Sn₂S₃ yields an energy of 1.7 meV higher per atom than the P2₁/m structure that we find. The other crystal structure, a $P3¯m1$ phase as shown in Fig. 2(b) with one formula unit per cell, is formed by the Sn-Se polyhedra. Its energy is only 0.54 meV/atom higher than the P2₁/m phase. There is only one type of Sn atom, which is coordinated by Se and has valence, Sn(III).

The averaged Sn-Se bond lengths and calculated bond-valence sums of Sn atoms are listed in Table II. The P2₁/m phase has the bond-valence sums of 2.38 and 3.48 for the Sn(II) and Sn(IV) atoms, respectively. This is consistent with Sn²⁺ and Sn⁴⁺. Se is less electronegative than S. Therefore, it is expected that Sn₂Se₃ has more covalency than the sulfide. This would then work against the Sn disproportionation. The sulfide, Sn₂S₃, has bond valence sums of 2.0 and 4.4 for the different Sn atoms.²⁰ The different Sn-Se bond lengths in P2₁/m phase are 2.83 Å for Sn(II) and 2.80 Å for Sn(IV) sites, as compared with the averaged bond length of 2.81 Å in SnSe (Pnma)³⁶ for Sn(II)-Se bonds and 2.75 Å in SnSe₂ (⁠$P3¯m1$⁠)³⁷ compounds for Sn(IV)-Se bonds. It is worth noting that for the Sn(II) sites there is a cross-gap metal-ligand hybridization between the Se p derived valence bands and the nominally unoccupied Sn(II) p states in the conduction band. This cross-gap metal ligand hybridization is reminiscent of the cross-gap hybridization that occurs in GST.³⁸ The $P3¯m1$ phase with one type of Sn with a bond-valence sum of 2.91, corresponding to Sn³⁺ as may be expected. The average bond length is 2.87 Å with 6 as the coordination number.

The thermodynamic stabilities of the Sn-Se phases were evaluated by calculating the formation energies and generating the convex hull. The relative enthalpies of the different Sn-Se phases are shown in Fig. 3. Pnma SnSe and SnSe₂ are the reference ground state structures. The other three reported phases of SnSe, $Fm3¯m$⁠, Cmcm, and P4/nmm, though all synthesized experimentally, are non-ground state structures. The P2₁/m phase Sn₂Se₃ lies slightly above the SnSe-SnSe₂ tie line. This means that it is not thermodynamically stable at 0 K. However, the relative energy is only 9 meV/atom higher than the phase separated ground state consisting of SnSe (Pnma) and SnSe₂ (⁠$P3¯m1$⁠). Therefore, while Sn₂Se₃ is not a ground state, the driving force for phase separation is exceedingly weak. In addition, the energy by which it lies above the tie line is much lower than the energy of the experimentally observable non-ground state structures of SnSe. This low driving energy for phase separation means that while Sn₂Se₃ may not appear in the equilibrium bulk phase diagram, it is likely to exist in thin films where diffusion is kinetically inhibited as discussed in the context of other metastable materials.^39,40 In the context of phase change memory, a phase separation would amount to a changing device geometry and parameters, which would presumably limit device cycle life.

We calculated the phonon dispersion by the finite difference method to check the dynamic stability of P2₁/m Sn₂Se₃. These calculations were done using a 4 × 2 × 2 supercell. There are no imaginary phonon modes except perhaps in the acoustic modes near the zone center. These zone center acoustic modes are not fully converged around Γ due to the limited size of the supercell and the imposition of the acoustic sum rule in the PHONOPY code. In order to establish the stability of these modes, we calculated the elastic constants using finite strains. We find that the material is indeed elastically stable. The elastic constants are c₁₁ = 12 GPa, c₂₂ = 68 GPa, c₃₃= 45 GPa, c₄₄ = 21 GPa, c₅₅ = 10 GPa, c₆₆ = 6 GPa, c₁₂ = 13 GPa, c₁₃ = 13 GPa, c₂₃ = 23 GPa, c₁₅ = 9 GPa, c₂₅ = 3 GPa, c₃₅ = 12 GPa, and c₄₆ = 1 GPa, with the setting of Table I. Thus, the P2₁/m phase Sn₂Se₃ is dynamically stable. It is interesting to note that compared with the Γ to Y direction, the acoustic modes in the Γ to X and Γ to Z directions of the Brillouin zone show a soft character, as also seen in the elastic constants. This is a consequence of weak inter-ribbon bonding (Fig. 4).

The band structures of the two phases are shown in Fig. 5. In addition, band structures, as obtained with the mBJ potential, are shown for Sn₂S₃ (calculations as in Ref. 20) and SnSe₂ in Fig. 6. As seen, both compounds are semiconductors in accord with the previous reports.^20,22,41 The density of states (DOS) and the projections of s and p character on the Sn(II) and Sn(IV) atoms of Sn₂Se₃ is shown in Fig. 7. The band structure of the $P3¯m1$ phase shows that it is metallic. The P2₁/m phase is semimetallic with band extrema that are not on the symmetry lines. It is semimetallic due to a band overlap. This seen in the existence of a Fermi surface, with carrier pockets located in the zone as shown in Fig. 8. We checked the band overlap using different approaches, in all cases, including spin-orbit. We find an overlap of 0.147 eV with the PBE functional, which is known to give too small gaps. With the more reliable mBJ functional, we obtain 0.049 eV, while with the HSE hybrid functional, we obtain a very similar semimetallic overlap of 0.053 eV.

For the P2₁/m phase, the valence and conduction bands show different orbital character. The valence bands within ∼0.5 eV of the valence band maximum (VBM) are derived from the s states of the divalent Sn(II) site, while the conduction bands within ∼0.5 eV of the conduction band minimum (CBM) are derived from the s states of the tetravalent Sn(IV) site. The behavior of two different Sn sites is similar with the Sn in Sn₂S₃. However, the energy range of the valence bands and conduction bands at the band edges in Sn₂S₃ (∼1 eV)²⁰ is almost two times larger than in P2₁/m phase of Sn₂Se₃. As mentioned, the calculated bond valence sums of the different Sn sites in Sn₂S₃ compound are 2.0 and 4.4, while for the selenide, the corresponding values are 2.38 and 3.48, respectively.

The 5s states of the different Sn sites are substantially hybridized with the Se 4p states in both valence bands and conduction bands as shown in Fig. 7. This strong hybridization originates from the region of –1.5 eV in valence band to 1 eV in conduction band. The valence bands within ∼1.5 eV of the band edge are mainly hybridized Sn(II) (divalent, see Table I for the atom labels) antibonding 5s states with the Se2 4p states and Se3 4p states. The conduction bands within ∼1 eV of the band edge are formed by the hybridization of Sn(IV) antibonding 5s states with Se1 4p states. We note that the occurrence of antibonding s states of Sn(II) site in the valence bands is qualitatively similar to SnO compounds.^42–45 Note also the asymmetric structure with all three coordinating seleniums on the same side of the Sn(II) which may be viewed as resulting from the lone pair occupying the position on the opposite side. This antibonding feature would be attributed to a lone pair with the Sn 5s² electrons occupying the sp hybridized orbital, which would be interpreted as being stereochemically active in directing the layered structures. This is also reflected in the cross-gap metal-ligand hybridization mentioned above.

The electrical properties are controlled by the band structures in the vicinity of the Fermi energy. Figure 8 shows the Fermi surfaces of the phases. The Fermi surface of the metallic $P3¯m1$ phase shows significant anisotropy for the carrier pockets at the Γ point. The hole (blue) and electron (red) carrier pockets of the semimetallic P2₁/m phase are along the k_y direction. Both the electron and hole pockets have ellipsoidal shapes with considerable anisotropy. Based on the carrier pocket shapes, the conductivity for the P2₁/m phase may be the highest along the b-axis. Figure 9 shows the calculated thermopower as a function of temperature. There is a large anisotropy of the thermopower, which is different from the normal semiconductors⁴⁶ and reflects the semimetallic nature of the material. Specifically, there is compensation between positive and negative contributions from hole and electron pockets, and these are weighted by the anisotropic conductivities for holes and electrons.

In any case, the electronic structure, specifically the absence of a band gap, will lead to metallic conductivity for crystalline Sn₂Se₃ independent of doping. This is in contrast to SnSe₂, which has a semiconducting gap, as seen in Fig. 6, amounting to 1.1 eV in our calculations. In the experiments of Chung and co-workers, high conductivity is found for the crystalline state of both Sn₂Se₃ and SnSe₂ alloys.¹⁵ While, as mentioned, our results explain metallic conductivity in crystalline Sn₂Se₃, the conductivity of SnSe₂ cannot be explained in the same way. SnSe₂ as a Sn(IV) compound grows naturally n-type presumably due to Se vacancies.¹⁵ The degenerate doping by such vacancies is a likely origin for the conductivity of the reported SnSe₂ films. This explanation is not likely for Sn₂Se₃ where the lower average Sn valence would work against Se vacancies.

We report the structure of Sn₂Se₃ as obtained using first principles structure prediction. We find that the lowest energy structure is a monoclinic P2₁/m semimetallic phase. This lowest energy structure has disproportionated Sn similar to Sn₂S₃. The Sn-Se bonds are more covalent than the corresponding bonds in the sulfide. This reflects the lower electronegativity of Se, relative to S. The relative enthalpy of P2₁/m Sn₂Se₃ is only 9 meV/atom higher than the ground state consisting of phase separated SnSe (Pnma) and SnSe₂ (⁠$P3¯m1$⁠). We also find a competing non-disproportionated Sn₂Se₃ phase, slightly higher in energy. This phase is metallic. We find strong anisotropy in the electronic structure with complex shaped Fermi surfaces for electron and hole pockets in the semimetallic phase. The conducting semimetallic and metallic nature of the crystalline phases no doubt underlies the low resistivity of the crystalline material, which makes possible the high resistivity contrast in Sn₂Se₃ based phase change devices. We note as an aside that conducting phases on the borderline of charge disproportion are potentially of interest as superconductors in analogy with the (K,Ba)BiO₃ system,^47,48 suggesting that low temperature measurements of crystalline films should be made. The results also provide insights into other aspects of Sn₂Se₃ as a phase change material. Specifically, the close competition of disproportionated and non-disproportionated Sn may underlie the ready formation of an amorphous phase with low energy switching, while the very weak driving force for phase separation allows for long term stable devices. Experimental investigation of the structural and spectroscopic properties of thin film crystalline Sn₂Se₃ will be of considerable interest.

This work was supported by the U.S. Department of Energy, Basic Energy Sciences through the Computational Materials Science Program, MAGICS center, Award No. DE-SC0014607. G.X. gratefully acknowledges support from the China Scholarship Council.