Introduction

Cross-point array with non-volatile resistive random-access-memories (RRAM) such as phase change memories (PCM) is a key technology to achieve high memory capacity and cost efficiency. The performance of this architecture depends upon 2-terminal selector devices set in series with the RRAM cells. It filters the parasitic leakage current on half-biased low-resistance-state memory cells, while allowing the correct reading of a high-resistance-state memory cell. To facilitate its integration with IC systems, the selector materials require to be robust under back-end-of-line (BEOL) integration and the electrical cyclic stress. Several amorphous chalcogenide materials show ovonic threshold switching (OTS)1. This is one of the suitable physical mechanisms that can deliver the desired selector properties such that the leakage current through the device is orders of magnitude lower at half of threshold voltage, i.e., leading to high non-linearity2.

The mainstream OTS materials are generally based on As and Se3,4,5,6,7,8,9,10,11, whereas using the materials containing such hazardous chemicals should be avoided as much as possible to minimize their impact on our environment. In this sense, it is crucial to search for As/Se-free OTS materials that meet the performance demands. Extensive device studies have already proposed a set of possible alternative alloys based on Te (B-Te, C-Te, Zn-Te, Ge-Te, Si-Te, Ag-Si-Te, Mg-Te, Ge-C-Te, and Hf-O-Te)12,13,14,15,16,17,18,19,20,21,22 and S-based system Ge-S23,24,25. However, most of these are facing reliability challenges26,27,28,29 hence more robust materials are needed. Initial results of the ab-initio systematic screening for As/Se-free alloys with good OTS electrical behavior and material stability were presented recently30. In this work, we extended and generalized the study to identify OTS material candidates with two target applications in mind, namely “RRAM selector” and “OTS memory”. The latter was recently proposed as a stand-alone self-rectified memory concept31,32. More specifically, we focus on identifying ternary compounds and downselect potentially-promising OTS materials using eight screening filters: undesirable/ toxic element exclusion, OTS-compatible electronic configuration (5 valence-electron rule33,34), phase stability of the amorphous alloys at BEOL temperatures (high glass-transition temperature), high chemical stability (low formation enthalpy), low leakage current (open trap gap), immunity to phase demixing (low spinodal temperature35), application-compatible trap/ mobility gaps, and OTS behavior indicator (OTS gauge). Starting from more than 13,000 candidates, the filtering process yielded 12 material compositions for RRAM selectors and 35 ones for OTS memory applications. In this work, we detail the computational material screening methodology and report the found promising materials. As such, we hope that this will seed works around the design of As/Se-free OTS materials.

Results and discussions

Material preselection

The motivation in this work is to identify As/Se-free OTS materials from a vast number of chemical compositions by using ab-initio simulations. We proceed by generating multiple amorphous models with relatively large size (300 atoms, ~2 × 2 × 2 nm) and computing the electronic structure with density functional theory (DFT). Because DFT simulations are rather time-consuming, it is impractical to simulate all possible combinations of ternary alloys. For that reason, we reduce the number of compositions to be simulated to a smaller subset of materials that complies with certain known OTS criteria, by applying the three-step screening filters illustrated in Fig. 1a.

Fig. 1: Material preselection criteria and ab initio simulated electronic structure parameters.
figure 1

a Preselection flowchart for the materials to be simulated with ab-initio. b Element and composition selection. c Mean number of valence electrons per atom Nve and glass-transition temperature Tg of the compositions on the first, second and third screening steps. d Amorphous atomistic model example, generated with ab-initio simulations. e Ab-initio gap parameters (mobility gap Eμ, electron / hole trap levels Ee/Eh, and trap gap ΔEt) extracted using inverse participation ratio (IPR) denoted by discrete lines. f Statistics of the gap parameters from 10 amorphous models (boxplots show the quartiles and the median, the whiskers show the range of the data, outliers indicated outside whiskers).

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The first filter consists in excluding elements to narrow down the number of combinations to be considered (Fig. 1b). We excluded As, Se and Cd since they are known to be toxic. We hence focused on the following 14 elements: B, C, N, Al, Si, P, S, Zn, Ga, Ge, In, Sn, Sb, and Te. All possible ternary combinations of the 14 elements using a 10% atomic fraction step generate 13,104 compositions.

For a second screening filter, the 5 valence-electron rule was used33,34. Five valence electrons per atom in amorphous chalcogenides result in populating localized antibonding states, which makes bonding in some regions of the material unstable. This local instability is the key to activate the OTS mechanism, which reflects the transition from insulator to conductor of the material. We found that the mean number of valence electrons per atom (Nve) in the conventional OTS materials, Si-Ge-As-Se, Ge-As-Se, and Si-Ge-As-Te with Nve ~ 5.0–5.3 has a good correlation with experimental holding voltage in the metal-OTS-metal devices30,36. Accounting for the condition of Nve = 5.0 ± 0.3 extracts 2370 compositions out of the 13,104 ones.

The third filter ensures that the glass-transition temperature (Tg) is higher than 600 K. This condition is expected to distinguish OTS materials from Phase Chance Materials (PCM), since the glass transition temperature is a lower limit of the crystallization temperature. In our understanding, the OTS material should keep its amorphous character during the BEOL processing steps, where a temperature of ~400 °C (673.15 K) is typically applied. However, for the screening condition we applied a larger margin, since the Tg was estimated with the semi-empirical Lankhorst model37. This model is applicable to covalent amorphous materials with Nve ≥ 4 and is expected to be inaccurate for compositions with lower Nve. In the range of interest, Nve = 5.0 ± 0.3, Tg is expected to be more accurate, though it was found to overestimate the Tg for SiGeTe compositions38. Figure 1c describes the first, second and third screening steps in terms of Nve and Tg. For the condition of Tg > 600 K, 1490 compositions out of the 2370 ones were downselected. As a result, the initial 13,104 compositions were reduced to 1490, which are to be simulated with DFT.

Ab-initio simulations

Our atomistic simulations are divided into two stages as shown in Fig. 1a. The first stage is the generation of 10 different amorphous 300-atom models (Fig. 1d) per composition. In the second stage, we computed accurate electronic structures (Fig. 1e). The process of composition reduction through the ab-initio simulations is summarized in Table 1. For further screening, we applied additional filters to the computed DFT parameters for the 1167 compositions and focused on the median values of 7–10 amorphous models to gain a statistically relevant sampling (Fig. 1f).

Table 1 Composition reduction in ab-initio simulations.
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Figure 2 shows the element occupancy, which indicates the percentage of the screened compositions containing each element, for each pre-selection step, up to the ab-initio simulations. In the first step of the element exclusion filter, all elements are represented with the same probability. The application of the second filter makes 6 valence electrons elements (S and Te) dominant and the dominance of elements with fewer valence electrons is lowered. There are nine elements with less than 5 valence electrons, whereas there are only two elements with more than 5. As a result, S and Te are appearing more frequently than the other elements to satisfy the 5 valence-electrons-rule. The third filter (Tg > 600 K) enhances the contribution of the N element and reduces the Te one. This can be ascribed to stronger, more rigid N, C or Si bonds with higher breaking kinetic barriers4. As a result, the contribution of these elements increases, and S and N become the dominant species. This trend is maintained after the ab-initio simulations, and almost half of the 1167 alloys contain S and N.

Fig. 2: Element occupancy of the screened compositions for each screening step up to the ab-initio simulations.
figure 2

Note that the maximum of each element occupancy is normalized to 100% and the total of all the element occupancies are 300% due to the ternary nature of the alloys.

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Figure 3a describes the flowchart of the material screening procedure based on the ab-initio parameters. Applying the remaining 4 filters reduces the initial 1167 candidates to only 35 or 12 ones, for the “OTS memory” or “RRAM selector” target applications, respectively. The details are explained in the following.

Fig. 3: Material selection criteria on ab-initio simulated data.
figure 3

a Flowchart of the screening process based on the results of the DFT simulations. b Formation enthalpy Eform and trap gap ∆Et of the compositions on the fourth and fifth screening steps. The symbol of each ternary composition is depicted as a pie chart whose occupation reflects the element fractions. The compositions within the shaded region are selected. c Eform and spinodal temperature Tspinodal of the compositions on the sixth screening step. d Mobility gap Eμ and ∆Et of the compositions on the seventh screening step. The upper x-axis maps the threshold voltage from the correlation between the ab-initio Eμ and the experimental data of the existing 20 nm thick OTS materials with As/Se, denoted by cross markers. The closed triangle marker depicts the centroid of the cross markers. e Eμ and OTS gauge gOTS of the compositions on the eighth screening step. #1–12 are the compositions suitable for RRAM selectors.

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Thermodynamic stability and open electronic gap

We introduce two more screening filters to assess the quality of amorphous structures in terms of Eform and ΔEt, which are plotted in Fig. 3b. The fourth filter reflects the negative formation enthalpy (Eform < 0 eV/atom), which assures the thermodynamic stability of the amorphous structure. In contrast, the amorphous structure with positive Eform is thermodynamically unfavorable. Even if such amorphous materials were deposited, they have a high risk of atomic diffusion under thermal or electrical stress39, leading to reliability issues during the device switching40. Therefore, we imposed the condition of Eform < 0 eV/atom for each composition, which narrowed down the list of candidates to 424 stable ones. Figure 4 shows the element occupancy for the screening steps after the ab-initio simulations. The alloys containing Te, N, Sb, and C tend to be screened out: N-rich materials are not thermodynamically stable (decomposing as N2 is energetically very favorable) but also their electronic properties indicate higher leakage potential and high potential for phase demixing. Te and Sb are mainly excluded because of their thermodynamic (fourth filter) and demixing (sixth filter) instability. C compounds also have higher preference for C-C bonds4, which are detrimental to the OFF state of the selector. As a result, S-containing alloys dominate the distribution with a 96.5% occurrence after this filtering step.

Fig. 4: Element occupancy of the screened compositions for the screening steps after the ab-initio simulations.
figure 4

Note that the maximum of each element occupancy is normalized to 100% and the total of all the element occupancies are 300% due to the ternary nature of the alloys.

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The fifth filter relies on the positive trap gap ∆Et > 0 eV as a proxy indicator for low leakage current. In amorphous materials, although trap levels essentially exist in the mobility gap, the opening of a finite ∆Et is required, to suppress the leakage current mediated by gap states and therefore to switch-off the OTS device. Otherwise, the overlapping electron-hole traps will show high probability for the electrons to hop or tunnel and result in high leakage current41. The condition of ∆Et > 0 eV further downselected only 360 compositions out of the 424 ones. The element occupancy is almost unchanged except for a slight decrease of the N case, as illustrated in Fig. 4.

Phase stability

To assess the dynamic phase stability against demixing into more stable constituent components of the remaining 360 compositions, we estimated the spinodal temperature Tspinodal35. This concept implies that if a given-temperature T is higher than the Tspinodal one, the resulting mixing entropy will stabilize the alloy structure. However, if T < Tspinodal, the stability brought by the mixing entropy would not be large enough to stabilize the alloy, which can subsequently demix into more stable sub-compositions. Therefore, Tspinodal is desired to be as low as possible to promote the alloying stability. For example, S0.5Ge0.1Sn0.4, one of the candidate compositions, is surrounded by SnS, SnGeS3, and Ge on the computed (crystalline) phase diagram of the S-Ge-Sn42. This indicates that S0.5Ge0.1Sn0.4 could demix into these three phase-stable compositions at T < Tspinodal.

To estimate Tspinodal of this alloy, we calculated the second derivative (curvature) of the Gibbs free energy Gmix (or Eform) around the composition on the phase diagram, as formalized in Supplementary Note 1. Since the data points (generated compositions) on the phase diagram were insufficient to calculate properly the curvature, we trained a machine learning (ML) prediction model of amorphous Eform for any arbitrary compositions. For that, we mapped each composition to a 14-dimensional vector (e.g. S0.5Ge0.1Sn0.4 to [0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0.1, 0, 0.4, 0, 0]) and used support vector regression with cubic poly-nominal using scikit-learn43,44. The ML Eform dataset contained 12,357 datapoints consisting of 1167 ternary screened compositions (11,657 amorphous models), 28 ternary/binary convex-hull compositions originally not included in the screening set (28 × 10 different amorphous models) and 14 single-element materials (with formation enthalpy set to zero). 90% of the dataset was used for the training step and 10% for testing. As a result, the Eform prediction model reproduced the original data very well: R2 = 0.9784 for testing data and a mean absolute error of 0.034 eV/atom, only slightly higher than the variation (std = 0.022 eV/atom) of the Eform of the amorphous models.

We evaluated Tspinodal of the 366 compositions using the Eform prediction model (Fig. 3c). Many of the compositions including S0.5Ge0.1Sn0.4 were predicted to have Tspinodal = 0 K, i.e., they are expected to be stable against demixing at any temperature. Since typically the deposition temperature of OTS materials is higher than the room temperature, we imposed Tspinodal < 0 °C (273.15 K) as the sixth screening filter, which downselected 153 phase-stable compositions out of the 360 ones. According to Fig. 4, P and Si-occupancies remarkably increase and N-occupancy further decreases. In addition, Ga-containing compositions disappear at this point.

Target gap-trap window

For the seventh screening filter, we tuned the expectation windows of Eμ and ∆Et based on the targeted applications for the OTS materials. In As/Se-based OTS materials, we identified strong correlations between the computed Eμ and experimental electrical parameters such as threshold voltage Vth, first-fire voltage Vff, and leakage current Ileak30,36. Besides, charge excitation from a hole trap level to an electron one induced by an external electric field is a precursor step to switch-on OTS devices45,46. In line with this observation, ∆Et has a correlation with the experimental parameters as well as Eμ15. This means that large Eμ or ∆Et induces high Vth and low Ileak. Therefore, an optimal range of Eμ and ∆Et should be defined based on the targeted application.

In this work, we considered two types of applications, “OTS memory” and “RRAM Selector”, as shown in Fig. 3d. In line with the stand-alone OTS memory that was recently proposed32, we took a relatively large target window for the operation of the “OTS memory”: Eμ ~ 0.8–1.5 eV/∆Et ~ 0.1–0.6 eV, corresponding to Vth ~ 1–5 V as mapped from the correlation in the existing OTS materials with As/Se. This window filter yields 40 S-based compositions out of the 153 ones. Aside from S, they mainly consist of P, Si, Ge, Sn or Te, and can include small amounts of N, Sb, C, B, Al, or In. No Zn-containing compositions are included (Fig. 4).

A second, smaller target window was defined for “RRAM selector” as Eμ ~ 1.05–1.3 eV/∆Et ~ 0.4–0.6 eV, corresponding to Vth ~ 2.5–3.8 V. This window isolated 13 S-based compositions out of the previous 35 and excludes the alloys with C, B, Al, In and Zn.

OTS gauge

The final (eighth) screening filter that we used (the OTS gauge), consists of assessing the probability of the material candidate to exhibit good OTS behavior. We defined the OTS gauge based on the Born effective charges Z*, which are also known as dynamic charges and describe the electrical polarization induced by a small displacement of each atom. It has been shown that in amorphous OTS materials, electronic excitation largely increases the number of Z* at the atoms with a conductive bonding structure45. In this work, we used an electronic charge injection in an atomic model instead of an electronic excitation and defined the OTS gauge gOTS as being the “change induced in the total Born effective charges by unit system charge injection” as formulated in Supplementary Note 2.

In a previous report30, we calculated the OTS gauges for a set of existing OTS materials (Si-Ge-As-Se with 2 different compositions, Ge-As-Se with 3 different compositions, GeSe, Si-Ge-As-Te with 4 different compositions, and SiTe) and non-OTS insulator materials as reference (c-AlN, c-Al2O3, c-HfO2, c-SiO2). The existing OTS materials had relatively large values (17–62) compared to the non-OTS ones (1–2)30. In addition, the OTS gauges had a strong positive correlation with the experimental holding currents30,36, which corresponds to the minimum value of the on-state currents in the OTS devices. This finding indicates that the Z*-based OTS gauge can reasonably reflects the physics of the on-state in the OTS device, even though the Z* are typically a property reflecting the insulative character of the system.

With the validity of the OTS gauge as a quantitative OTS indicator being confirmed on non-OTS materials, we applied it as a funneling parameter to the remaining 40 OTS candidates for the OTS memory (Fig. 3e). The computed OTS gauges spanned in the 5–58 range and only 6 compositions had smaller values than gOTS = 17, the lower limit of known OTS materials36. Therefore, we set the eighth screening filter at gOTS > 17, which yields 35 compositions out of 41 as suitable OTS memory materials. For RRAM selector materials, only 12 compositions out of 13 have suitable OTS gauge (#1–12 in Fig. 3e) and only the Sb-containing composition was excluded.

Analysis of the identified candidates

The screened As/Se-free ternary compositions for OTS memory after the eighth screening filter are summarized in Table 2. The numbers (#1–12) in the RRAM column denote the 12 RRAM selector candidates ordered by the OTS gauge values. Remarkably, all the 35 compositions contain S.

Table 2 As/Se-free OTS candidate compositions.
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Figure 5 shows the spinodal temperature profiles of the 12 S-based ternary systems including the 35 candidates. In general, S > ~40% composition regions tend to be phase-stable (Tspinodal < 0 °C), except (b) C-S-Sb and (c) N-S-Sn systems where C or N > ~20% regions tend to be unstable. On the profiles, we also plotted the compositions either within or outside the target windows of “RRAM selector” and “OTS memory”. It is worth mentioning that for the (a) B-P-S, (b) C-N-Sb, (c) N-S-Sn, (h) Si-S-Sb, and (k) P-S-In systems, there are few stable compositions. However, these fall out of the defined windows for RRAM selector / OTS memory. Within the selected windows, the compositions satisfy Tspinodal < 0 °C and OTS gauge > 17, with an optimal ratio of S that ranges from 30% to 60%.

Fig. 5: Spinodal temperature profiles on the ternary phase diagrams.
figure 5

a B-P-S, b C-S-Sb, c N-S-Sn, d Al-P-S, e Si-P-S, f Si-S-Ge, g Si-S-Sn, h Si-S-Sb, i Si-S-Te, j P-S-Ge, k P-S-In, and l S-Ge-Sn. White line shows Tspinodal = 0 °C (273.15 K). The star/# and triangle markers depict the compositions in the targe windows of RRAM selector and OTS memory. Circle markers depict the compositions outside the target windows but within Eμ ~ 0.6–1.8 eV/∆Et ~ 0.0–1.0 eV. The numbers beside the markers indicate the OTS gauge values.

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From these profiles, we evaluated the robustness of each candidate against phase demixing by calculating the minimum composition change to the line of Tspinodal = 0 °C, which was defined as a “composition change margin” in the Table 2. Some of the OTS memory candidates (B0.2P0.5S0.3, C0.2S0.5Sb0.3, Si0.3P0.4S0.3, Si0.1S0.4Ge0.5, P0.2S0.3Ge0.5, P0.5S0.4In0.1, and S0.6Ge0.3Sn0.1) have a margin lower than 5.0%. For the 12 RRAM selector candidates, the margins of Si0.4S0.3Te0.3 (#5) and N0.1S0.6Sn0.3 (#12) raise slightly to 8.6% and 6.3%, respectively. The other 10 alloys have a 10.0% (or more) and are promising. Out of these, 4 materials (#1, 6, 10, and 11) contain a combination of P and S. Unfortunately, they would turn out to be challenging to use in a mass-production product, since the P-S compounds are known as easily flammable solids47 and H2S is generated by reacting with water. Considering the aforementioned, the remaining 6 compositions (#2, 3, 4, 7, 8, and 9) can be considered as interesting OTS candidates to be developed experimentally.

To summarize, we performed an ab-initio systematic screening for As/Se-free OTS materials, applying eight physics-based OTS screening filters: element exclusions, Nve = 5.0 ± 0.3 valence-electron rule, Tg > 600 K, Eform < 0 eV/atom, ∆Et > 0 eV, Tspinodal < 0 °C, Eμ - ∆Et target windows, and gOTS > 17. Through these filters, we identified 35 S-based ternary compositions suitable for OTS memory, out of which only 12 compositions are expected to deliver good properties for a RRAM selector. Taking the manufacturability aspects into account, our simulations suggest that only the materials Si0.3S0.5Ge0.2 (#3), Si0.3-0.2S0.5Sn0.2-0.3 (#2,7), Si0.5-0.4S0.4Te0.1-0.2 (#8,9), and S0.5Ge0.1Sn0.4 (#4) would be interesting to be experimentally investigated.

Methods

Ab-initio simulations

The initial amorphous models were generated by a decorate-and-relax (D&R) algorithm48. Each model is a 300-atom system with a ~2 × 2 × 2-nm unit cell (Fig. 1d). The D&R was applied to the pre-selected 1490 compositions. However, the amorphous generations of 312 compositions failed. Starting from the 10 × 1178 initial models obtained by the D&R, we performed geometrical optimization based on density functional theory (DFT) using CP2K software49. We used GGA-PBE exchange-correlation functional50, GTH pseudopotentials51 to describe the core electrons, a double-zeta-valence-polarization (DZVP) localized basis sets for the valence electrons and planewaves with a cutoff of 500 Ry and a relative cutoff of 40 Ry were used for the real space integration grid. The Brillouin zone sampling was limited to the Γ-point only. The atomic forces were relaxed with a convergence criterium of 1E-4 Ha/bohr, whereas the pressure was considered converged when below 100 bar. Few compositions faced numerical convergence issues and had less than six atomic models converged, which were excluded from our analysis. As a result, we neglected 11 compositions and used the remaining 1167 ones in the following analysis to consider the statistical behavior of the amorphous models.

The accurate electronic structures were computed using the hybrid exchange-correlation functional (HSE06) in combination with the auxiliary density matrix method (ADMM)52. The hybrid functional and large enough atomic model size will ensure a better detection of the traps in the gap and quantitative accuracy of the mobility gaps53. For the mobility gap estimation, we used the inverse participation ratio (IPR53) to identify the mobility edges of the amorphous models shown in Fig. 1e. The mobility gap (Eμ) was taken as the energy difference between the conduction and valence mobility edges (EC and EV). The electron and hole trap levels (Ee and Eh) were extracted as the deepest levels with respect to conduction and valence bands, respectively. The trap gap ΔEt was taken as the energy difference of Ee and Eh. The formation enthalpy per atom (Eform) of each amorphous model was predicted with the materials graph network (MEGNet) model54, which is based on machine learning trained on the Materials Projects dataset55.