Implementation of Multinary Łukasiewicz Logic Using Memristive Devices

Abstract

In the group of emerging non-volatile storage technologies, redox-based memristive devices stand out due to their possibility for extreme dense integration, low power consumption and multilevel capabilities. The opportunity to directly perform Boolean logic operations using memristive devices opens a promising path towards Computation-in-Memory. Recently 7state memristive devices based on TaOx were used to realize a ternary adder circuit as well as a ternary Łukasiewicz logic and fuzzy logic. Logic that uses more than two truth values promises to reduce the number of devices that are needed for a certain operation and thereby further increases the integration density. In this work, we propose a multinary logic for three, five and seven truth values based on the Łukasiewicz logic and show the performance for the implication and negation operation. We, therefore, used the physics-based compact model JART VCM v1b to describe the relation between RESET voltage and high resistive state and then performed the logic operations.

Tailor-made synaptic dynamics based on memristive devices

“…They are 4•10 26 1 m 3 for the delay regime, 3•10 26 1 m 3 for the linear regime and 12•10 26 1 m 3 for the saturation regime. The reasoning behind this is similar to the one used in (Bengel et al (2021b;), that the high conductance range can be very easily controlled through the variation of this parameter.…”

“…This leads to the wanted gradual synaptic dynamics, as the switching process is stochastic, in the way that there exists a voltage range in which the devices have a certain probability to switch upon receiving a programming pulse. This probability can be included in a stochastic gradient descent algorithm, in which the switching probability is coupled to the error of the neural network classification (Bengel et al (2021b)). By applying multiple constant voltage pulses, the NR synapse can be made to change rather gradually, as individual devices are switching one after another.…”

“…By applying multiple constant voltage pulses, the NR synapse can be made to change rather gradually, as individual devices are switching one after another. We have shown in the past, that the origin of the stochastic voltage range, in which all devices are switched, mainly originates from the d2d variability of the VCM cells, while c2c variability is less significant (Bengel et al (2021b)). The stochastic voltage ranges are depicted in SET and RESET probability curves (Dalgaty et al (2019); Singha et al (2014); Bengel et al (2021a)).…”

“…To account for the device variability, 100 cells were simulated at each combination of voltage and pulse length for one voltage pulse. In this way, the simulation only displays the d2d variability which has been shown to be the main contributor to the stochastic switching (Bengel et al (2021b)). As expected, higher absolute voltages, as well as longer pulse durations increase the respective probabilities.…”

Endurance of 2 Mbit Based BEOL Integrated ReRAM

“…Furthermore, the unknown values of the filament geometry l disc , l plug and the radius r are chosen in a reasonable way. The number of oxygen vacancies in the plug region N plug is chosen with regard to typical oxygen vacancy densities used in simulations for VCM cells [30], [33]. The key parameter is the number of oxygen vacancies in the disc region N disc and is chosen quite high in view of the LRS being investigated in the beginning.…”