Estimation of the reset voltage in resistive RAMs using the charge–flux domain and a numerical method based on quasi-interpolation and discrete orthogonal polynomials

Resistive RAMs (RRAMs) are the most promising devices for the near future in terms of non-volatile memory applications. This new technology requires advances in all the fronts that need to be addressed prior to industrialization. One of them is connected with compact modeling, i.e, the development of analytical expressions to account for the most important physical effects that are needed to calculate the current, capacitance, transient response, etc. The device models should be accurate and this issue is achieved by implementing the correct physics in a flexible and robust mathematical architecture. We will focus on this latter problem here since we will deal with a good numerical approximation of experimental data based on spline quasi-interpolation to perform the integrals of the current and voltage as function of time. We do so to transform the usual modeling domain, consisting of a current–voltage representation, to a charge–flux domain; i.e., the time integral of the current and voltage measured variables. In this domain we introduced a new method to obtain the reset voltage of RRAMs and avoid the effects of the usual measurement noise. The main features of the mathematical technique we propose along with practical examples built upon real experimental data will be explained. The numerical stability of this new technique is of great interest for the implementation in automatic measurement environments for industrial applications.