Kinetics study of ions in conductive filament growth process of electrochemical metallization resistive memory

Abstract

<sec>In this work, a system of modified Mott-Gurney differential equations is based on Arrhenius’ law and the overpotential theory of ionic motion in bipolar electrochemical metallization (ECM) resistive devices. The average displacement of ions is solved by the modified Mott-Gurney equation. Then, the relation between the average displacement and the growth length of the conductive filament is obtained by a geometric model based on cells. The equation of applied voltage versus Forming/Set time and the equation of length of conductive filament growth versus time are deduced by using this relation.</sec><sec>In this work, an algorithm for extracting kinetic parameters of ions in a bipolar ECM device is also proposed. By using this algorithm, the characteristics of the applied voltage versus Forming/Set time for Ag/<i>γ</i>-AgI/Pt, Ag/TiO<sub>2</sub>/Pt, Ag/GeS<sub>2</sub>/W, and Cu/SiO<sub>2</sub>/Au devices are calculated and the calculation results are consistent with experimental data. It is found that in the Forming/Set process, the jump step of silver ion is the lattice constant along the <i>c</i> direction of a unit cell of the crystal for TiO<sub>2</sub> and the lattice constant of the cubic, <i>a</i>, for <i>γ</i>-AgI. These results are explained in the following. In a unit cell of the two crystals there are some tetrahedral and octahedral interstitial sites. The cationic motion path consists of alternating octahedral and tetrahedral sites or some octahedral sites. The cation jumps from tetrahedron to octahedron to tetrahedron, etc. in the <i>γ</i>-AgI with coplanar polyhedron and from octahedron to octahedron in the TiO<sub>2</sub> with edge shared octahedron. In GeS<sub>2</sub> crystal, it is found that the jump step of silver ions is the lattice constant in the <i>c</i> direction of a unit cell. Owing to the periodicity of the lattice, the pathways of the ion motion in the three materials can be expressed by a periodic potential barrier each. For the jump situation of the copper ion in amorphous SiO<sub>2</sub>, the jump step of copper ions is calculated to be 1.57 times the length of the O—O bond, and the jump pathway can also be explained by a periodic potential barrier.</sec><sec>By introducing the cosine potential barrier, the ionic activation frequency, potential barrier height, ionic mobility and diffusion coefficient, and characteristics of the conductive filament growth versus time in several devices are calculated. The criteria of selecting dielectric materials for bipolar ECM devices are discussed by using these data. It is found that the standards for selecting dielectric materials of bipolar ECM devices are the ion activation energy ≤0.5 eV, preferably between 0.1–0.2eV, and the DC conductivity as close to 10<sup> –4</sup> Ω<sup>–1</sup>·cm<sup>–1</sup> as possible.</sec>