QuantumATK Case Study: Resistive Switching in Novel Non-volatile RAM-like Systems

Resistive RAM (ReRAM) is a novel non-volatile memory (NVM) for data storage, offering lower programming voltage and faster write/read speed as compared to flash [1]. The resistance switching in ReRAM devices, such as OxRAM/CBRAM, depends on the migration of oxygen/metal ions in amorphous transition metal oxides such as Ta₂O₅, HfO₂, and other materials, to form atomically thin conductive filaments (low resistance state, LRS, or ON) and rupture them (high resistance state, HRS, or OFF), as shown in Figure 1.

A key challenge in the ReRAM cell design is the variability of the resistance switching parameters [1]. QuantumATK simulations provide atomistic-level insight into resistance switching and support the screening of materials for robust ReRAM devices. In this overview we will highlight methods and tools in the QuantumATK platform [2] to study resistive switching in ReRAM-like systems:

• Molecular dynamics (MD) simulations of oxygen/metal ion diffusion in amorphous materials.
• Density functional theory (DFT) combined with non-equilibrium Green’s function (NEGF) method to study electron transport in LRS and HRS states.
• DFT simulations of formation energies and trap levels for oxygen vacancies and metal impurities forming filaments, and external metal dopants.

The overview is based on six QuantumATK papers, published by Western Digital, Micron, RWTH Aachen University (Prof. Rainer Waser), National Cheng Kung University (Po-An Chen), and University of Notre Dame (Prof. Suman Datta).

Molecular dynamics simulations of diffusion in amorphous materials

As the resistance switching in OxRAM/CBRAM devices depends on the migration of oxygen/metal ions in amorphous transition metal oxides (Figure 1), a good understanding of ionic diffusion in these amorphous materials is of paramount importance for optimizing future ReRAM devices. QuantumATK offers tools to generate amorphous materials using e.g. a melt-and-quench classical molecular dynamics (MD) approach [3 - 5], and methods to perform subsequent studies of ion diffusion in these materials [3,5]. According to Western Digital, predicting diffusion barriers in crystalline materials is straightforward and is often done using a nudged elastic band methodology (NEB).  However, in disordered amorphous materials with no well-defined lattice sites, it is no longer possible to identify a specific low-energy path through the material, and thus a different analysis approach is needed to tackle complex energy landscapes. The Western Digital study [3] employed MD simulations to monitor the motion of individual atoms at different temperatures in amorphous Ta₂O₅. From the 10 ns long MD simulations, the evolution of the mean-square displacement of atoms was determined at various temperatures in order to evaluate diffusion coefficients and activation energies for ion self-diffusion, as shown in Figure 2 and Figure 3.  The calculated accurate diffusion coefficients and activation barriers is a key input in analytical and numerical models to describe the formation of conductive filaments and interface electronic structure.

The Notre Dame University study [5] employed MD simulations to investigate CBRAM evolution with an electric field.  For example, Figure 4 illustrates how a Co filament in a Co/HfO₂/Pt device forms a conductive bridge across the HfO₂ dielectric when an electric field is applied across the device, forming the LRS/ON state. The combination of density functional theory (DFT) and non-equilibrium Green’s function (NEGF) method available in QuantumATK can then be used to study electron transport in the LRS and HRS states.

Simulation of electron transport with DFT-NEGF

To complement the MD study on the CBRAM evolution with an electric field, researchers at Notre Dame University performed DFT-NEGF simulations to calculate transmission at various electric field (bias) values [5].For example, the transmission calculation shown in Figure 5 confirms that there is a conductive bridge formed when the electric field is switched on.

Meanwhile, Micron used the DFT-NEGF methodology in QuantumATK to investigate the impact of length, morphology and composition of metal mono-atomic-bridges (present in CBRAM devices) on the electron transport and conductance [6]. This study suggests that there is a small non-monotonic variation in the calculated conductance with increasing length, and that the transmission depends strongly on the morphology (flat or pyramid, asymmetric) of the contacts, and also on the type of the metal, as shown in Figure 6.

Interestingly, MoS₂ 2D material was investigated as an active layer for non-volatile resistive switching applications by researchers at the National Cheng Kung University [7]. The DFT simulations suggest that Au⁺ tends to move to the sulfur vacancy site and possibly form a conductive bridge. Authors suggest that the increasing density of states (DOS) around the Fermi level, showed in Figure 7, as the Au replacement percentage of S gets larger, results in the transition from the HRS to the LRS state in the MoS₂-based atomristor.

The DFT-NEGF approach in QuantumATK was also used to investigate another ReRAM operating mechanism, relying on the collective motion of oxygen ions near the interface with the electrode in the Nb:SrTiO₃/SrTiO₃/Pt model resistive switching system illustrated in Figure 8 [8]. The collective motion of oxygen ions near the interface with the electrode leads to a modulation of the interface Schottky barrier and accompanying change in resistance. By examining the calculated local DOS for different voltages along with the current-voltage (I-V) characteristics obtained at different temperatures and biases, the authors suggest that there are three different ranges of conduction shown in Figure 9.  The study concluded that 1) the direct tunneling process through the Schottky barrier into the conduction band of the resistive switching layer dominates the electronic conductance in SrTiO₃-based resistive switching devices; 2) in ultrathin (~2.8 nm) devices direct tunneling process from electrode to electrode is also important, as it could impact the lower limit for the high resistance state of the resistive switching device.

Defect and dopant simulations

The resistance switching in OxRAM/CBRAM devices is controlled by the migration of oxygen vacancy defects/metal-ion impurities in amorphous transition metal oxides. Micron calculated trap levels for oxygen vacancy in amorphous Hf_0.75Si_0.25O_1.99 and for Cu impurity in amorphous Al₂O₃ within the band gaps for different charge states, and suggested to define the resistive states by microscopically characterizing them based on the distribution of the defect-induced gap states, corresponding wavefunctions and the spatial distribution of the defects [6].  

Meanwhile, Western Digital investigated how to use dopants to tailor and improve the electronic properties of oxides for ReRAM applications [4].  The study investigated how various metal dopants affect oxygen vacancy formation in crystalline and amorphous Ta₂O₅ [4]. As shown in Figure 10, the study suggests that p-type dopants (Al, Hf, Zr, and Ti) can lower the formation energy and thus the forming/set voltage and improve retention properties of ReRAM based on Ta₂O₅.

QuantumATK has an efficient and user-friendly framework for studying the properties of a dopant/defect in a host material, calculate relaxed defect/dopant structures, formation energies and trap levels for neutral and charged defects and various types of defects (vacancies, substitutionals, interstitials, pairs and larger clusters).

Relevant resources

• QuantumATK reference paper giving a general overview of the entire QuantumATK platform
• Molecular Dynamics simulations with QuantumATK
  • Tutorials
  • Paper
  • Webinar
  • Tutorial on generating amorphous structures
• DFT-NEGF simulations with QuantumATK
  • Introduction to NEGF
  • NEGF convergence guide
  • Webinar on simulation of device I-V electrical characteristics
  • Webinar on structural relaxation of devices and interfaces
• Defect and dopant simulation framework
  • Manual on ChargedPointDefect study object
  • Tutorial on calculating formation energies and transition levels of charged defects
  • Tutorial on using Sentaurus Materials Workbench for studying point defects

References

[1] S. Yu and P.-Y. Chen, “Emerging memory technologies: recent trends and prospects”, IEEE Solid-State Circuits Mag. 8, 43 (2016).

[2] S. Smidstrup, T. Markussen, P. Vancraeyveld, J. Wellendorf, J. Schneider, T. Gunst, B. Vershichel, D. Stradi, P. A. Khomyakov, U. G. Vej-Hansen, M.-E. Lee, S. T. Chill, F. Rasmussen, G. Penazzi, F. Corsetti, A. Ojanpera, K. Jensen, M. L. N. Palsgaard, U. Martinez, A. Blom, M. Brandbyge, and K. Stokbro, “QuantumATK: An integrated platform of electronic and atomic-scale modelling tools”, J. Phys.: Condens. Matter 32, 015901 (2020). arXiv: 1905.02794v2.

[3] D. A. Stewart, “Diffusion of oxygen in amorphous tantalum oxide”, Phys. Rev. Mat. 3, 055605 (2019).

[4] H. Jiang and D. A. Stewart, “Using dopants to tune oxygen vacancy formation in transition metal oxide resistive memory”, ACS App. Mater. Interfaces 9, 16296 (2017).

[5] N. Shukla, R. K. Ghosh, B. Grisafe, S. Datta, “Fundamental mechanism behind volatile and non-volatile switching in metallic conducting bridge RAM”, IEDM 2017.

[6] S. C. Pandey, “Atomistic mechanisms of ReRAM cell operation and reliability”, Mater. Red. Express 5, 014005 (2018).

[7] R. Ge, X. Wu, M. Kim, P.-A. Chen, J. Shi, J. Choi, X. Li, Y. Zhang, M.-H. Chiang, J. C. Lee and D. Akinwande, “Atomristors: memory effect in atomically-thin sheets and record RF switches”, IEDM 2018.

[8] C. Funck, P. C. Schmidt, C. Bäumer, R. Dittmann, M. Martin, R. Waser, S. Menzel, “Atomistic investigation of the Schottky contact conductance limits at SrTiO₃ based resistive switching devices”, Non-volatile memory technology symposium, 2018.