Switching dynamics in titanium dioxide memristive devices

Abstract

Memristive devices are promising components for nanoelectronics with applications in nonvolatile memory and storage, defect-tolerant circuitry, and neuromorphic computing. Bipolar resistive switches based on metal oxides such as TiO 2 have been identified as memristive devices primarily based on the "pinched hysteresis loop" that is observed in their current-voltage ͑i-v͒ characteristics. Here we show that the mathematical definition of a memristive device provides the framework for understanding the physical processes involved in bipolar switching and also yields formulas that can be used to compute and predict important electrical and dynamical properties of the device. We applied an electrical characterization and state-evolution procedure in order to capture the switching dynamics of a device and correlate the response with models for the drift diffusion of ionized dopants ͑vacancies͒ in the oxide film. The analysis revealed a notable property of nonlinear memristors: the energy required to switch a metal-oxide device decreases exponentially with increasing applied current.

Phenomenological modeling of memristive devices

“…In these regions, the changes in R 0.5 are insignificant and typically too noisy to be used for reliable fitting. To address this issue, the modeling approach can be extended by applying variable duration pulse stress [2,36]. Measured changes in the device state upon application of long-duration voltage pulses can be normalized with respect to Dt duration and used reliably for the proposed fitting approach.…”

“…Taking into account the described assumptions, the first step of dynamic equation modeling is the collection of large amounts of data by switching the device with fixed short-duration voltage pulses with different amplitudes and measuring the I-V at a non-disturbing bias after each pulse, e.g., similar to the pulse algorithms described in Refs. [2,36]. To simplify the model, it is convenient to use as few state variables as possible, so that only a small number of measurements along non-disturbing I-V is required to characterize uniquely the internal state of the device.…”

“…Because resistive switching devices have memory, the current i(t 0 ) should also depend on the history of applied voltage bias before time t 0 , or, equivalently, on the memory state variable vector w at time t 0 . Such memory state variables represent certain physical parameters, which are changing upon switching the device, e.g., radius and/or length of switching filament [13,29,36,50]. A very convenient method for capturing the complete I-V behavior is to use a set of two equations describing memristive system [11].…”

“…Alternatively, some models are too computationally intensive, e.g., due to necessity of solving coupled differential equations [8, 16, 23-25, 27, 31, 32, 40] or running molecular dynamic simulations [9,35,38]. Several compact (SPICE) models, which are the most suitable for largescale simulations, have been also very recently proposed for valence change [1,17,36,39,45] and electrochemical resistive switching devices [29,50]. Unfortunately, models for at least the former type of devices are still not sufficiently accurate and require further improvement.…”

“…For example, in Ref. [36], both dynamic and static equations are fitted assuming modulation of the tunneling barrier width, which is certainly a simplification of the actual physical mechanism and as a result, the model does not predict accurately set transition. Because multiple mechanisms are possibly involved in resistive switching [49], such simplification may not always be adequate for accurate models.…”