A Modified Tantalum Oxide Memristor Model for Neural Networks with Memristor-Based Synapses Valeri Mladenov Dept. Theoretical Electrical Engineering Technical University of Sofia Sofia, Bulgaria E-mail: valerim@tu-sofia.bg Abstract — This paper presents an improved modification of tantalum oxide memristor model and its application in neural networks. The proposed model is based on the standard Hewlett Packard tantalum oxide model with three improvements – application of a modified Biolek window function, optimization of its performance using simplified current-voltage relationship and by replacements of step model’s components by continuous differentiable functions. The optimal values of the tuning model’s coefficients are derived by comparison with experimental data and parameter estimation algorithm. A PSpice library memristor model is created in accordance to its mathematical model. The considered memristor model is applied in a simple neural network for function fitting with memristor-based synapses. A comparison with several existing tantalum oxide memristor models is made and the main advantages of the proposed model are established – higher performance, improved tuning capability and operation for hard-switching mode. Keywords— tantalum oxide memristor, improved window function, PSpice library model, neural network. I. INTRODUCTION The memristors based on transition metal oxides have stable properties and many applications, as in nonvolatile computer memories, neuromorphic circuits, logical schemes, analog and digital configurable devices [1], [2], [3]. Among the resistance switching materials so far analyzed, as non- stochiometric titanium dioxide, hafnium oxide and silicon oxide [1], [4], the tantalum oxide partially doped by oxygen vacancies represents good resistance switching properties, mainly endurance, low voltage and current, high switching speed, low power consumption, long retention time and a sound compatibility with the CMOS integrated circuits technology [5], [6], [7]. The tantalum oxide based memristors contain a conducting channel and a partially depleted by oxygen vacancies region [8], [9]. The conductance and the respective memristor state could be changed by externally applied voltage [7]. To accurately express the tantalum oxide memristors behavior in electronic circuits a precise model is needed [8]. Several attempts for application of titanium dioxide memristor models for approximate modeling of tantalum oxide resistance switching elements exist in the literature [7], [8]. However the structure and principal of operation of TaO and TiO 2 memristors are different [7]. Due to this reason several special TaO memristor models are generated so far [8], [9], [10]. The Hewlett Packard standard model [8] uses step functions in the state differential equation and a modulus function in the current-voltage relationship, which unfortunately are continuous but not differentiable [9], [10]. This is a disadvantage of the model if it is used for PSpice library model creation due to occurrence of convergence problems [8], [9]. An improvement of this model is proposed in [9] by Ascoli, Tetzlaff and Chua. This modified model uses continuous and differentiable functions in the model equations instead of the described above non-differentiable expressions in [8]. Although the modified model [9], [10] is appropriate for PSpice incorporation it is a complex and time consuming one and requires many elementary calculations due to the large number of exponents and hyperbolic sine function in the state equation [9]. No window function has been used and sometimes the state variable is not limited in the interval [0, 1] which is another disadvantage of the above mentioned models. Another model proposed in [11], [12] is applicable for tantalum oxide memristor modeling. Unfortunately it uses non-differentiable step functions and due to this it has convergence problems [11]. The motivation for the present research is the partial absence of a simple and accurate TaO memristor model. The purpose of this investigation is to propose a precise, tunable and simplified model with window function [13], [14] for TaO memristors, applicable for PSpice library model generation. For adjustment of the offered memristor model experimental data [6] and algorithms for parameters estimation [15], [16] are applied. The criterion used for optimization the model is the minimum of the mean square error between the experimental and the simulated current-voltage characteristics [16]. A PSpice [17] library memristor model is created using the proposed modified mathematical model. The model is applied and successfully tested in a simple memristor neural network for function fitting [18], [19], [20]. The rest of the paper is organized as follows. In Section 2 a brief description of the structure, principle of operation and of the basic models of TaO memristors is made. The adjustment of the proposed memristor model made by the use of experimental current-voltage relationships, a methodology for optimal coefficients determination and an algorithm for parameters estimation in MATLAB - Simulink is described in Section 3. The corresponding PSpice memristor model is presented in Section 4. The operation of the TaO memristor model in a simple neural network with memristor-based synapses is described in Section 5. The concluding remarks are given in Section 6. II. A DESCRIPTION OF THE BASIC TANTALUM OXIDE MEMRISTOR MODELS AND THE PRESENT MODIFICATION A schematic of the tantalum oxide memristor structure is presented in Fig. 1. It contains two metallic electrodes – anode and cathode, respectively [7], [8]. The element has a square intersection. Several parallel channels are existing in the memristor structure [7]. The external channel is formed by pure isolating Ta2O5. The internal channel is made by a solid solution of oxygen atoms in tantalum material – Ta(O) with high conductance. Between these two channels an intermediate partial channel of non-stochiometric tantalum oxide doped by oxygen vacancies exists [7], [8].