Multiscale Modeling of Metal/Oxide/Metal Conductive Bridging Random Access Memory Cells: from Ab Initio to Finite Element Calculations

TL;DR

The paper addresses the challenge of predicting $I$-$V$ characteristics of CBRAM devices without heavy fitting by integrating ab initio-derived parameters into a finite-element framework. The method couples six FEM modules with four atomistic parameter extractions for diffusion, tunneling, interfacial barriers, and filament conductivity, using first-principles to define $D$, $\Delta E$, and related transport quantities. The Ag/$a$-SiO$_2$/Pt example shows quantitative agreement with experiments and reveals that Joule heating becomes significant for filaments of only a few nanometers under currents above about $100\,\mu$A. This framework enables exploration of not-yet-fabricated memories and design optimization across stacks and geometries, with potential extensions to vacancy-based memristors.

Abstract

We present a multiscale simulation framework to compute the current vs. voltage (I-V ) characteristics of metal/oxide/metal structures building the core of conductive bridging random access memory (CBRAM) cells and to shed light on their resistance switching properties. The approach relies on a finite element model whose input material parameters are extracted either from ab initio or from machine-learned empirical calculations. The applied techniques range from molecular dynamics and nudged elastic band to electronic and thermal quantum transport. Such an approach drastically reduces the number of fitting parameters needed and makes the resulting modeling environment more accurate than traditional ones. The developed computational framework is then applied to the investigation of an Ag/a-SiO2/Pt CBRAM, reproducing experimental data very well. Moreover, the relevance of Joule heating is assessed by considering various cell geometries. It is found that self-heating manifests itself in devices with thin conductive filaments with few-nanometer diameters and at current concentrations in the 10s-microampere range. With the proposed methodology it is now possible to explore the potential of not-yet fabricated memory cells and to reliably optimize their design.

Figures (17)

• Figure 1: (a) Scanning electron microscope view of an Ag/a-SiO$_2$/Pt CBRAM cell that was fabricated on a silicon-on-insulator (SOI) wafer Emboras2018. The bottom and top contacts are Pt and Ag, respectively. They surround a 20 nm thick layer of amorphous SiO$_2$ (a-SiO$_2$). The inset shows the bottom Pt electrode, including a buried Si waveguide to confine the active switching region. (b) Illustration of the active region of a typical CBRAM structure with Pt and Ag contacts. A DC voltage is applied to the Ag contact; the Pt one remains grounded. This bias triggers the growth of a nanoscale Ag filament starting from the Pt side, eventually bridging the two contacts through the SiO$_2$ network (not shown in this sub-plot). (c) Typical "current vs. voltage" (I-V) characteristics of a non-volatile CBRAM as in (a) and (b). Starting from the high-resistance state (HRS), the cell switches into its low-resistance state (LRS) at $V_\text{set}$. A compliance current $I_{cc}$ is applied to avoid current-driven damages. The RESET back to the HRS occurs at $V_\text{reset}$, which must be negative for non-volatile storage.
• Figure 2: (a) Schematic view of the axially symmetric CBRAM geometry considered in the FEM model. In case of an Ag/a-SiO$_2$/Pt cell, the active top electrode is made of an Ag slab, the ion-conducting solid electrolyte layer consists of an a-SiO$_2$ switching layer, and a Pt slab acts as inert counter electrode. A moving cone-shaped Ag filament seed is initially placed within the switching layer. (b) Corresponding 2-D simulation domain under the assumption of rotational symmetry indicating the interfaces between the a-SiO$_2$ switching layer and (1) the Ag electrode, (2) the moving Ag filament, and (3) the Pt electrode. The dimensions of the structure are indicated by double arrows and are inspired by the experimental CBRAM cell from Ref. Emboras2018.
• Figure 3: Summary of the six modules implemented in the FEM model. Each box represents one module (anti-clockwise starting top left: (i) deformation, (ii) electrochemistry, (iii) transport, (iv) electrostatics, (v) currents, and (vi) Joule heating). It includes the underlying physical equation(s) in Sec. \ref{['sec:fem']}, as well as the input and output parameters. All time-dependent variables that are calculated by the model are listed in the boxes, while the material parameters are given on the side in colored arrows. The material parameters can either be derived from ab initio and semi-empirical methods (green boxes with a reference to the corresponding section in the manuscript), used as fitting parameters (blue), or derived from experiments (yellow). The applied voltage ($V$) and the compliance current ($I_{cc}$) are taken from the experimental measurement of Sec. \ref{['sec:result_iv']} (white). The dependence between the different modules is marked as black arrows that indicate the flow direction of the exchanged data. The insets in the boxes show a schematic of the modeled geometry following Fig. \ref{['fig:fig_model']}(b). The regions to which the respective module is applied are colored red.
• Figure 4: (a) Diffusion trajectory of an Ag$^+$ ion through a cube of a-SiO$_2$ with a side length of 1.5 nm at 1200 K. The position of the Ag$^+$ ion, displayed as gray spheres, is shown every 0.1 ps for a duration of 39 ps. The yellow and red spheres represent Si and O atoms, respectively. (b) $z$ component of a 12 ps long inset of the diffusion trajectory in (a) before (thin line) and after (thick line) the application of the smoothing algorithm of Ref. Sahli2007.
• Figure 5: Arrhenius plot of the diffusion coefficient $D$ of Ag$^+$ cations dissolved in a-SiO$_2$ vs. the reciprocal temperature based on 25 ps long trajectories. The light blue dots represent individual measurements of the diffusion coefficient coming from eleven different samples, the dashed blue line is their average at each temperature, the error bars denote the standard deviation, and the red line is a linear fit of the mean values.