Study on the kinetics of ions in the process of the conductive filament growth for the electrochemical metallization resistive memory

In this paper, a modified Mott-Gurney differential equation set was built by Arrhenius' law and the overpotential theory of ionic motion in bipolar ECM resistive devices. The average displacement of ions was solved by the modified Mott-Gurney equation. Then, the relation between the average displacement and the growth length of the conductive filament was obtained by a geometric model based on cells. The applied voltage versus Forming/Set time equation and the length of the conductive filament growth versus time equation have been deduced by using this relation. This article proposed also an algorithm for extracting kinetic parameters of ions in bipolar ECM devices. By using this algorithm, the characteristics of the applied voltage versus Forming/Set time for Ag/γ-AgI/Pt, Ag/TiO₂/Pt, Ag/GeS₂/W, and Cu/SiO₂/Au devices were calculated and the calculative results were consistent with experimental data. We found that in the Forming/Set process, the jump step of silver ions is the lattice constant along c direction of a unit cell of the crystal for TiO₂ and the jump step is equal to the lattice constant of the cubic, a, for γ-AgI. These results are explained as followings. In a unit cell of the two crystals there are some tetrahedral and octahedral interstitial sites. The cationic motion paths consist of alternating octahedral and tetrahedral sites or some octahedral sites. The cations jump from tetrahedron to octahedron to tetrahedron etc. in the γ-AgI with coplanar polyhedron and octahedron to octahedron in the TiO₂ with edge shared octahedron. In GeS₂ crystal, we have found that the jump step of silver ions was the lattice constant in the c direction of a unit cell. Due to the periodicity of the lattice, the pathway of the ion motion in the three materials can be expressed by a periodic potential barrier. There had been calculated for the jump situation of the copper ion in amorphous SiO₂, the jump step of copper ions was 1.57 times of the length of the O-O bond, and the jump pathway could be also explained by a periodic potential barrier. By introducing the cosine potential barrier, the ionic activation frequency, potential barrier height, ionic mobility & diffusion coefficient, and characteristics of the conductive filament growth versus time in several devices were calculated. The criteria of selecting dielectric materials for bipolar ECM devices was discussed by using these data. It was found that the standard for selecting dielectric materials of bipolar ECM devices is the ion activation energy ≤ 0.5eV, preferably between 0.1-0.2eV, and the DC conductivity as close as possible to 10^‒4 (Ω cm)^‒1.