Non-Uniform Spline Quasi-Interpolation to Extract the Series Resistance in Resistive Switching Memristors for Compact Modeling Purposes

Abstract

An advanced new methodology is presented to improve parameter extraction in resistive memories. The series resistance and some other parameters in resistive memories are obtained, making use of a two-stage algorithm, where the second one is based on quasi-interpolation on non-uniform partitions. The use of this latter advanced mathematical technique provides a numerically robust procedure, and in this manuscript, we focus on it. The series resistance, an essential parameter to characterize the circuit operation of resistive memories, is extracted from experimental curves measured in devices based on hafnium oxide as their dielectric layer. The experimental curves are highly non-linear, due to the underlying physics controlling the device operation, so that a stable numerical procedure is needed. The results also allow promising expectations in the massive extraction of new parameters that can help in the characterization of the electrical device behavior.

Modeling the Variability of Au/Ti/h-BN/Au Memristive Devices

“…2(b)]. Calculating the derivate of I LRS is challenging because this current changes during reset processes and also due to the electrical noise; therefore, different numerical techniques can be employed [25], [27], [28], [29].…”

“…More specifically, even in the domain of widely investigated metal-oxide memristors, very few works discuss reliable parameter extraction methods [25], [26]. On this subject, the lack of literature is aggravated by the numerical difficulties to deal with memristive device experimental data [25], [27], [28], [29].…”

On spline quasi-interpolation through dimensions

“…In particular, [62,79] deal with the construction and study of new quasi-interpolating operators, in [12,48,59] generalized spline quasi-interpolants are proposed, in [1,20,[49][50][51]53] new integration formulas based on spline quasi-interpolants are constructed, in [15,54,61,63,64,80,81,84] and [4,11] quasi-interpolants are used for the numerical approximation of the solution of differential and integral equations, respectively. Furthermore, in [7,16,17,23,52,65,66] quasi-interpolants are used in different areas of science and engineering: imaging, Computer Aided Geometric Design, industry, etc. Finally, in [19], we find some other interesting references to papers on the above topics.…”

Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images

“…A rather simple generalization, known as Variation Diminishing Spline Approximation (VDSA), generalizes this construction to B-splines (see, for example [5,6]). Since its inception, quasi-interpolation has been studied to obtain methods that apply to different domains and with the aim of increasing the order of convergence: recent developments include univariate and tensorproduct spaces [7][8][9], triangular meshes [10][11][12][13], quadrangulations [14] and tetrahedra partitions [15], among others.…”