PSpice switch-based versatile memristor model Alon Ascoli and Ronald Tetzlaff Faculty of Electrical and Computer Engineering, Technische Universit¨ at Dresden, Mommsenstraße 12, 01062 Dresden, Germany Fernando Corinto and Marco Gilli Department of Electronics and Telecommunications Politecnico di Torino Corso Duca Degli Abruzzi, 24 10129 Torino, Italia Abstract—This paper proposes a simple PSpice implemen- tation of the boundary condition model for memristor nano- structures. The boundary condition model is equivalent to the linear drift model except for the introduction of adaptable boundary conditions, which impose an activation threshold of the state dynamics at the boundaries, i.e. once the state gets clipped at one of the boundaries, it may not be released from it unless the input reverses its sign and gets larger than a certain activation threshold in magnitude. Thanks to the adaptability of the boundary behavior, the boundary condition model is able to describe a variety of physical nano-scale systems, where mem- ristor dynamics arise from distinct physical mechanisms. The proposed PSpice emulator may be used for the investigation of potential applications of memristive systems in integrated circuit design, especially for the development of non-volatile memories and neuromorphic platforms. The accuracy of the PSpice circuit model is validated through comparison with experimental results relative to the Hewlett-Packard memristor. I. I NTRODUCTION The memristor is a passive bipole linking charge q and flux ϕ through a nonlinear relation, i.e. ϕ = ϕ(q) under current- control. From Faraday’s Law it follows that voltage v depends upon current i through v = dϕ dt = M (q) i, where M (q)= dϕ dq is the memristance of the bipole. Since q =  t -∞ i(t ′ )dt ′ , then M (q)= M (  t -∞ i(t ′ )dt ′ ). In other words the resistance of the memristor depends upon the time history of the current flowed through it. This explains the memory capability of the memristor, theoretically envisioned by Chua in 1971 [1] and later classified by Chua and Kang in 1976 as the simplest element from the class of memristive systems. Since 2008, when its existence at the nano-scale was certified at Hewlett- Packard (HP) Labs [2], the memristor has attracted a strong interest for its central role in the set up of novel integrated circuit (IC) architectures, especially in the design of non- volatile memories and neuromorphic systems. The development of innovative strategies for the design of memristor-based ICs requires the availability of accurate mathematical models ( [2], [3], [4]) for the memristive nano- structures. A good model should be as general as possible, i.e. it should be able to capture the memristive dynamics of a large number of nano-films. In this respect the boundary condition model (BCM), recently-introduced in [5], was de- veloped so as to meet this generality requirement. In fact its distinctive feature is the adaptability of the nano-device behavior at boundaries, which enables it to stand out over other models available in literature for the larger number of detected behaviors. Another necessary requirement for the investigation of po- tential applications of these nano-devices is the implementa- tion of their mathematical models into some software package for computer aided IC design. This requirement drove us towards the development of a PSpice realization of the BCM, which we intend to present in this manuscript. II. THE BCM Let us briefly review the BCM [5]. Each memristor from the class under modeling is a nano-scale film composed of two layers, whose different doping levels may be modulated through the flux across the memristor under a certain input voltage. The time derivative of the state variable x = w D ∈ [0, 1], i.e. the spatial extension w of the conductive layer normalized to the entire film length D, and the voltage v- current i relationship are respectively given by dx(t) dt = η i 0 W (x(t)) v(t) f (x(t),ηv(t),v th0 ,v th1 ) (1) i(t) = W (x(t)) v(t) (2) where η ∈ {-1, +1} is the polarity coefficient, i 0 is a system-dependent normalization factor (in the case of the HP memristor [2] i 0 = q 0 t -1 0 is the magnitude of charge q 0 = D 2 G on μ -1 required to flow through the nano-device for the layer boundary to move across the whole film length over characteristic time interval t 0 = D 2 μv0 , where v 0 denotes the amplitude of the input voltage and μ stands for the average dopant mobility within the conductive layer), W (x(t)) describes the state-dependent memductance, expressed by W (x(t)) = G on G off (G on - ΔGx(t)) -1 , where G on and G off respectively indicate the memductance of the nano- structure in the fully-conductive and fully-insulating state, ΔG = G on - G off , while f (x(t),ηv(t),v th0 ,v th1 ) ∈ {0, 1}, the proposed switching window function with adapt- able thresholds v th0 ∈ R + and -v th1 ∈ R - , is defined as f (x, η v, v th0 ,v th1 )=  1 if C 1 holds 0 if C 2 or C 3 holds. (3) where tunable boundary conditions C n (n = 1, 2, 3) are modeled by 978-1-4673-5762-3/13/$31.00 ©2013 IEEE 205