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C: Physical Processes in Nanomaterials and Nanostructures

Exploring the Compositional Ternary Diagram of Ge/ S/Cu Glasses for Resistance Switching Memories Nicolas Onofrio, and Tsz Wai Ko J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12020 • Publication Date (Web): 15 Mar 2019 Downloaded from http://pubs.acs.org on March 21, 2019

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The Journal of Physical Chemistry

Exploring the Compositional Ternary Diagram of Ge/S/Cu Glasses for Resistance Switching Memories Nicolas Onofrio∗ and Tsz Wai Ko Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong SAR E-mail: [email protected] Phone: (+852) 2766 5680. Fax: (+852) 2333 7629

Abstract Amorphous semiconductors with tailored ionic and electronic conductivity are central to the operation of emerging resistive memory. However, because of the large amount of potential candidates and compositions, only limited number of materials have been tested experimentally. To accelerate the search of efficient solid electrolytes for resistive switching device, we developed parameters to describe copper doped germanium sulfides based on ReaxFF; a reactive molecular dynamics framework. The force field was optimized against a training set of first principle calculations including crystals, amorphous structures, some small molecules, and clusters to describe the atomic interactions between Ge, S and Cu elements. Based on this novel atomistic model, we studied the mobility of Cu as a function of the ternary composition of amorphous Gex Sy Cuz and we investigated the corresponding atomic and electronic structure of each solid electrolyte in details. Our analysis led to semiconducting compositions with high Cu mobility and favoring the formation of Cu clusters. Molecular dynamics simulations of switching under an external potential show that devices based on electrolytes

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with high Cu mobility form thick metallic filaments and an amorphous copper sulfide phase was observed at the interface. Such an atomistic model is critical to improve our understanding on the atomic mechanism of filamentary growth and can be used to improve retention and endurance of resistive switching devices which are still limiting their commercial widespread.

Introduction Chalcogenide glasses (CG) are important materials used in a wide range of applications including electrodes for Li-ion battery, 1 wave guide, 2 optical data storage, 3 and more recently solid electrolyte for emerging resistive memory. 4,5 Moreover, low dimensional crystalline phases of mono- and di-chalcogenides present great potential for high performance optoelectronic 6,7 and piezoelectric devices. 8 For example, Gex X100−x (X=S, Se) form two dimensional layered semiconductors for compositions corresponding to x = 50 and 33 with various electronic and optical properties, 9 while non-stochiometric binary glasses present an ensemble of topological elastic and phase transitions for 10 < x < 44. 10,11 The introduction of Ag or Cu to GeX produces a mixed ionic-electronic ternary alloy with composition dependent electronic and ionic conductivities 12–16 exhibiting either threshold 17 or resistive switching 18–20 behavior under an external voltage. Resistance switching devices are foreseen as central components for next generation electronics because of their low power consumption and ultrafast operation, and they have been demonstrated to be building blocks for neuromorphic computing. 21,22 Although there is bourgeoning interest in metal doped CG, the atomic mechanisms that govern the properties of these materials are not fully understood, and there still needs to be an effort to widespread their integration into commercial applications. In the past decade, four main classes of resistance switching devices have emerged: phase change memory, 4 valence change memory, electrochemical metallization cell 5,23 (ECM) and threshold switch 17 (TS). The richness of behaviors observed arise from the complex under2


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lying physics of device operation such as the change in phase, electrochemical dissolution and nucleation, ionic diffusion and charge injection, governed by the variety of materials and compositions. 20 The general structure of resistance switching devices is composed of a solid electrolyte (e.g. CG or an oxide) sandwiched between two metallic electrodes. In ECM cells, the application of a voltage of the appropriate polarity results in the oxidation of the active electrode, its dissolution inside the solid electrolyte and the migration of cations toward the inactive electrode. This electrochemical process leads to the nucleation of metal ions inside the electrolyte or at the inactive electrode, which eventually forms metallic filaments responsible for the resistance switching phenomena. Switching in ECM cells is reversible and highly non-linear due to the filamentary nature of the switching event leading to hysteresis and various I-V curves. 24 By contrast, threshold switching is characterized by a diode-like I-V signal with an abrupt change in the resistance state of the device under an applied voltage. In TS devices, switching has been shown to originate from the motion of metallic ions and vacancies leading to a sharp increase in current, with switching voltage that depends on material’s bandgap. 25 Interestingly, the same materials have been used as electrolytes across the different classes of resistance switching devices. For instance, copper doped germanium sulfides and silicon dioxide have been demonstrated as effective electrolyte for application as both ECM and TS. 17,26,27 However, the relationship between materials composition and the electrochemical response of the cells is still unclear. Therefore, the development of models to describe metal doped CG at the atomic scale is critical to understand the origin of switching. First principle methods have played an important role in the modelization of glass-forming materials and represent the most reliable atomistic model to date. Density functional theory (DFT) has been widely used to generate amorphous glasses following a melt-and-quench procedure, and a variety of transition metal doped CG materials have been successfully investigated. 13,16 However, ab initio simulations are computer intensive and, the generation of a glass from scratch with molecular dynamics can only be achieved for systems of hundreds of atoms and at ultrafast quenching

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rate. Moreover, even with highly parallel machines, only small regions of the compositional space of metal doped CG have been explored. The use of classical interatomic potentials or a combination of classical and ab initio methods can help to overcome the shortcomings aforementioned. 28 The main complexity in the development of a classical interatomic potential to describe oxides or chalcogenides lies in the mixed-ionic covalent nature of the chemical bonds. Moreover, the potential must include many-body components to describe the preferential orientations of bonds due to orbital hybridization, and it must enable various coordinations of the elements at the origin of point defects in the glass. Early attempts to develop interatomic potentials for CG were based on van der Waals (vdW) and Coulomb interactions 29 as well as three-body terms. 30,31 However, the fixed charge on atoms was inconsistent with the evolving polarity of the bonds in different chemical environments. Reactive force fields such as ReaxFF 32 are many-body potentials based on dynamical charges that enable variable coordination via over/under-coordination penalty energy including the effect of highly polarizable lone pair such as those on oxygen and chalcogen atoms. As part of many ReaxFF potentials developed and their applications, 33 ReaxFF_SiO 34 was used to shed the light on the complex mechanism of water in microporous silicates, 35 to quantify defect formation energy in amorphous SiO2 , 28 and to provide the atomistic mechanism of resistive switching in Cu/SiO2 ECM cells. 36 In this study, we propose to explore compositions of the ternary glass Gex Sy Cuz (x+y+z=1) by performing molecular dynamics simulations. To achieve this goal, we developed a reactive force field based on a training set of first principle calculations to describe germanium sulfide glasses and their interaction with copper. We performed high-throughput calculations to generate amorphous structures at various compositions and evaluated the corresponding mobility of Cu. Our procedure led to compositions with a range of Cu diffusivity whose structural and electronic properties were studied. We found that high sulfur and copper contents usually lead to high Cu mobility. Moreover, the glassy mixture is found to be a semiconductor for Cu and S contents lower than 40% and ranging from 30% to 70%, respec-

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tively. The highest Cu mobility is predicted for the composition Ge0.10 S0.85 Cu0.05 with an activation energy as low as 0.17 eV. Finally, we selected three compositions with different Cu diffusivity and studied the formation of a metallic filament using molecular dynamics simulations. The compositions with higher Cu diffusivity switched in shorter timescale and led to thicker metallic filaments. Interestingly, we found that switching occurs via more than one conductive bridge. This work provides a guideline to engineer the morphology of Cu filaments in germanium sulfide glasses.

Computational details Reactive molecular dynamics simulations ReaxFF 32 is a bond-order dependent classical interatomic potential, for which the total energy is expanded as a sum of contributions including bond, angle, dihedral, over/undercoordination and conjugation to describe covalent interactions plus vdW and Coulomb to account for non-bonded interactions. The key concept in ReaxFF is that each covalent contribution depends on the bond order, a functional of the interatomic distance that smoothly decreases to zero with increased separation. This bond order functional is updated at every step of the molecular simulation together with partial atomic charges, leading to environment dependent interactions. Charges are computed following the charge equilibration formalism developed in the early 90s by Goddard and coworkers. 37 A thorough mathematical derivation of the functional form of ReaxFF can be found in the Supporting Information of Ref. 38 All molecular dynamics simulations presented here were performed with the LAMMPS package 39,40 and a timestep of 0.5 fs. Amorphous models were generated following a melt-andquench procedure in the isobaric-isothermal ensemble with a cooling rate of 10 K/ps, similar to that described Ref. 41 Amorphous Ge0.33 S0.66 (i.e. GeS2 ) models contain 90 atoms while two sets of Gex Sy Cuz compositions were generated to span the ternary including a large (540 atoms) and small (60 atoms) batch to enable electronic structure calculations. Diffusion co5



efficients were computed by fitting the mean square displacement versus time over the last 0.5 ns of the 1 ns thermalization simulations at three or four temperatures chosen between 400 and 2,000 K, depending on the composition. We evaluated the activation energy based on the Arrhenius equation to rationalize the thermally activated diffusion process. The procedure to extract diffusion coefficients and activation energies including plots and fits can be found in the Supporting Information, Figures S1-S7. We performed switching simulations with the electrochemical dynamics with implicit degrees of freedom (EChemDID) method. 42 The formalism was previously developed to enable the application of an external voltage between metallic electrodes. Within EChemDID, the local electrochemical potential Φ, corresponding to an additional degree of freedom, is added to every atom and equilibrated by solving a diffusion equation. The voltage is applied by setting a constant potential to some fixed atoms, far from the active region. The charge equilibration is performed at each timestep by including the effect of the local electrochemical potential to the electronegativity of the atoms, which becomes a dynamical variable χ + Φ. Initial structures are composed of a thin layer of the solid electrolyte of approximately 12 Å sandwiched between an active rough Cu electrode and an inactive flat Cu electrode for which we fixed the position of the atoms at all time. 43 The random rough Cu electrode was generated by deleting atoms in a region delimited by a random Gaussian filter with standard deviation of surface heights chosen to be 8 Å. 44 Snapshots of the atomic structures are provided in the Supporting Information, Figure S8. The amorphous structure of the electrolyte was obtained by quenching a melt while fixing the position of the inactive electrode atom’s and allowing the active electrode to translate in the direction perpendicular to the interfaces. To obtain reasonable density of the solid electrolyte, we applied a constant force of 0.1 kcal/mole/Å to each atom of the group constituting the mobile (active) electrode throughout the quenching procedure. For the selected compositions, we found approximated densities (because of the complex geometry defined by the random rough electrode) of 3.9, 3.0 and 1.9 g/cm3 in good agreement with the 4.1, 2.7 and 2.0 g/cm3 of the bulk electrolyte

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generated in the NPT ensemble at 300 K and 1 Atm. Switching simulations were performed by applying a voltage of 4 V and the pseudo current was evaluated by difference between the input electrochemical potential at the fixed regions (where the external potential is applied) and the target potential. 42

DFT calculations and force field optimization DFT calculations were performed with VASP 45–47 to prepare the reference structures to train the reactive force field. Projector-augmented wave pseudopotentials were used to describe the electron-ion-core interactions and the electron exchange-correlation energy was computed within the gradient approximation as proposed by Perdew, Burke, and Ernzerhof (PBE). 48 Crystal structures were relaxed using a threshold of 10−5 and 10−4 eV for electronic and ionic steps, respectively with a k-mesh based on the Monkhorst-pack method 49 using a ratio of ≈ 40 k-mesh/lattice constant. The plane wave basis set was expanded within a 500 eV kinetic energy cutoff. Equations of state (EOS) were performed by varying the volume of the supercells isotropically between -15 % and +15 %. We used grid-based Bader charge calculations 50 to obtain the partial charge distributions for each crystal structure. These partial charges were used to optimized the QEq parameters as described below. Calculations on small molecules were performed with the hybrid B3LYP functional 51 and the def2-TZVP basis set as implemented in ORCA. 52 We choose the B3LYP flavor for the exchange-correlation potential because it is known to accurately describe energy barriers and it has been used previously to optimize various ReaxFF parameter sets. Crystal structures were vizualized with VMD 53 and coordination analysis were performed with R.I.N.G.S. 54 We used cutoffs of 2.68, 2.86, and 2.58 Å to detect Ge-Ge, Ge-S, and S-S bonds, respectively to be consistent with previous study. 55 For validation purpose, we generated amorphous Ge0.33 S0.66 and Ge0.3 S0.61 Cu0.09 based on Born-Oppenheimer molecular dynamics as implemented in VASP. To speed-up simulation time we used gamma point of the supercell to expand the wave functions with a kinetic energy 7



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cutoff of 400 eV and a timestep of 2 fs. Supercells were initialized with 60 (20 Ge and 40 S) and 66 (20 Ge, 40 S and 6 Cu) atoms into simple cubic structures of 11.8 and 12.4 Å side, corresponding to the averaged experimental density of 2.75 g/cm3 . 56,57 The structures were equilibrated at 2,000 K within the canonical ensemble for 15 ps and subsequently quenched to 300 K every 3 ps for a total of 27 and 42 ps corresponding to 10 and 5 independent amorphous structures of Ge0.33 S0.66 and Ge0.3 S0.61 Cu0.09 , respectively. This was achieved with a fast cooling rate of 57 K/ps. The amorphous structures were then equilibrated at 300 K for 5 ps and fully relaxed (ions and lattice parameters) to 0 K. To optimize the reactive force field we used an in-house optimizer written in Python. The optimization algorithm is based on a Monte Carlo procedure coupled with simulated annealing. The error is defined as the sum of mean absolute errors between energies, forces, partial charges and cohesive energies computed with DFT and ReaxFF (Equation 1) and implemented in LAMMPS via its Python wrapper.

PM PN Err = WE

PM PN PNa P3 DF T ReaxF F ReaxF F DF T | | − E |E ij ij i j k l |Fijkl − Fijkl i j + WF N M NE 3M N Na NF PM PN PNa DF T PNc ReaxF F T F | |Ec DF − Ec ReaxF | i j k |Qijk − Qijk i i +WQ + WC i M N Na NQ Nc NC

(1)

Constants M , N , Na and Nc stand for the number of structures in the training set, the number of geometry per structure, the number of atoms per geometry, and the number of cohesive energy defined, respectively. The objectives of the error function are the energy Eij , the force Fijkl (l = x, y and z), partial charge Qijk and cohesive energy Eci . Each element of the multi-objective error function is weighted (via WE , WF , WQ and WC ) in order to enable sequential optimization and constants NE , NF , NQ and NC guaranty unitless summation. The Monte Carlo algorithm proceeds by randomly moving each parameter one by one according to p → p [1 + rand (+δ, −δ)] with rand (+δ, −δ) a random number drawn in the interval [+δ, −δ] and δ the sensitivity of the parameter, provided by the user. After a 8


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parameter move, the error is computed according to Equation 1, compared to the minimum error Err0 and if it is lower, the parameter is accepted. A Metropolis criteria is introduced such that if the current error Err is higher than Err0 , a random number is drawn in the interval [0, 1] and if it is less than exp[−(Err − Err0 )/T ], the parameter move is accepted. The simulated annealing is implemented by decreasing the fictitious temperature T every times (or every tens of times) the parameter loop is completed. The optimization is achieved once the minimum error plateaued and in the present version of the code, it is determined by the user. The algorithm to optimize the force field is reported in the Supporting Information, Figure S9. This procedure has been used previously to optimized ReaxFF parameters for Cu/MoTe2 . 58

Results and discussions Initial parameters and charge equilibration We started from Ge (and H) parameters proposed by Psofogiannakis and van Duin. 59 Parameters for S, Cu and their (many body) interactions Cu/S were taken from Ref. 60 while those corresponding to Ge/S and Ge/Cu were initialized from their homologs Si/O 34 and Si/Cu, 36 respectively. Throughout the optimization we kept the parameters for Ge, Cu and the general parameters for S unchanged (excluding the QEq parameters for Ge and S) and we modified those corresponding to S/S, Ge/S, S/Cu and Ge/Cu. We therefore modified bonding, off-diagonal, angle and torsion parameters corresponding to Ge/S/Cu combinations. The chemistry between Ge/S/Cu (and H) elements is wide and an accurate description of all possible combinations by a classical empirical interatomic potential remains challenging. Our goal is to describe at best condensed phase Gex Sy Cuz structures including crystals and amorphous phases. We first optimized the germanium and sulfur QEq parameters against Bader charges computed for various crystals and amorphous phases of GeS2 and GeS. The mean absolute errors between QEq and Bader charges δQ are reported Tables 1 and S1. We 9



found the best agreement between ReaxFF and Bader charges, with a mean absolute error less than 0.10 e per atom and per atomic structure contained in the training set, with the optimized values of 2.35 eV and 8.00 eV for the electronegativity of Ge and S, respectively. These values are consistent with those for silicon and oxygen reported in ReaxFF_SiO of 2.41 and 8.50 eV, respectively and correspond to slightly less electronegative elements. Additionally, we show the transferability of these QEq parameters to compute charges of other crystals and amorphous Ge/S/Cu structures, not included in the training set. We found that by keeping the original QEq parameters for Cu, we were able to describe with accuracy charges on Ge/Cu crystals as well as on key amorphous Ge0.30 S0.61 Cu0.09 , part of the target ternary diagram (see Table S1). The discrepancies between Bader and QEq charges for CuS2 , Cu2 GeS3 and Cu2 GeS4 crystals originate mainly from the compressive regions of the EOS (see Figure S10) and can therefore be neglected in the present study.

Potential energy surfaces We selected some small molecules to train S/H, S/S and Ge/S (2-, 3- and 4-body) interactions. The potential energy surfaces (PES) corresponding to bond dissociation, angle bending and dihedral torsion are reported Figures 1 and 2. The molecule name displayed as the title of each subplot indicates the location of the bond (angle/dihedral) dissociated (bent/twisted) as dash and equal symbols corresponding to single and double bond, respectively. The environment dependence of S to the sulfur-hydrogen and sulfur-sulfur (single and double bond) dissociations were trained by including the S2 molecule, an S8 cluster, various hydrogen sulfide molecules such as HS-SH, HS-SSH, H-SSH and HS-H and, the germanium sulfide H3 GeS-SGeH3 . Similarly, we included H3 Ge-SH, H2 Ge=S, H3 Ge-SGeH3 and H3 Ge-SSGeH3 to train single and double germanium-sulfur bonds. Three-body H-S-H, S-SS, Ge-S-Ge and Ge-S-S angles and four-body H-S-S-H and S-S-S-S dihedrals were trained by bending and twisting some additional molecules. Overall, the force field describes well the PES around equilibrium and it slightly underestimates bond dissociation energies. Over10


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Table 1: Cohesive energy (kcal/mol/atom) and, mean absolute error based on EOS for energy (kcal/mol/atom) and charges (e/atom) computed with DFT and ReaxFF for various crystals structures. Materials project IDs and first neighbor partial coordinations are also given. Text in bold corresponds to data (cohesive energy, EOS energy, EOS charges) included in the training set during the optimization. Additional data are reported to demonstrate the transferability of the optimized parameters.

Ge-DIA Cu-FCC Cu-BCC Cu-SC Ge16 S32 Ge24 S48 Ge4 S8 Ge4 S4 Cu2 S4 Cu4 S8 Cu2 Ge6 Cu6 Ge2 Cu2 GeS3 Cu2 GeS4

Cohesive energy DFT ReaxFF -102.16 -90.30 -80.70a -81.20 -79.80a -79.51 a -69.90 -67.24 -20.40 -20.97 -20.25 -20.95 -19.92 -21.32 -15.49 -6.51 -15.10 -13.46 -15.01 -14.34 7.00 7.00 -0.12 -0.12 -17.01 -11.75 -15.46 -9.55

Mean absolute error δE δQ 4.15 3.53 1.78 4.01 2.09 0.05 0.79 0.03 0.52 0.05 0.40 0.03 9.36 0.29 10.28 0.30 10.68 0.05 4.21 0.07 2.44 0.40 2.12 0.30 a

From experiment. 60

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ID

mp-572892 mp-542613 mp-7582 mp-2242 mp-849086 mp-1068 mp-1025440 mp-19724 mp-1072589 mvc-13350

Coordination IV XII XII VIII IV/II IV/II IV/II III/III VI/VI VI/VI III/III multiple IV/IV/IV IV/IV/III

Energy (kcal/mol/atom)

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