# Logic and memory based on memristive circuits

Prior to the foundation of the PGI-10, JARA-FIT activities in the field of Green-IT explored the potential of memristive devices and memristive crossbar arrays for memory-intensive computing paradigms. The non-volatility of the devices enables logic-in-memory operations [1]. The logic operations are directly processed in the memory and arithmetic tasks, e.g., additions are carried out within the array [2]. Thus, by blurring the boundaries between memory and arithmetic logic units the von-Neumann-bottleneck can be eliminated.

The realization of minimum and maximum gate function through resistive RAM devices can enable the implementation of memristive fuzzy logic gates in future. With highly reliable (106 cycles) and multi-level Pt/W/Ta2O5/Pt Resistive RAM devices, 3-bit modular arithmetic operation is performed. This will reduce the computational complexity by decreasing the number of needed digits for high radix number system. Thus the number of calculation operations in an addition and the number of logic devices can directly be reduced. Furthermore, these devices in crossbar arrays enable implementation of multi-parallel search algorithms for pattern recognition tasks, which are widely required for neuromorphic applications in a very efficient manner.

A further application of resistive switching cells is their use in associative capacitive networks (ACN). An ACN, as a content-addressable memory, is able to detect the Hamming distance between search and stored patterns. Such an ACN can be implemented by an architecture consisting of nanocrossbar array of complementary resistive switching (CRS) devices and using the nondestructive capacitive readout of the CRS device [4]. As compared with conventional CAMs the fully passive network gets along without MOSFETs leading to a significant area and energy efficiency. A technical realization of such an ACN has been demonstrated using preprogrammed test arrays [5].

References:

[1] A. Siemon, T. Breuer, N. Aslam, S. Ferch, W. Kim, J. van den Hurk, **V.** **Rana, S. Hoffmann-Eifert, R. Waser**, S. Menzel, E. Linn, *Realization of Boolean Logic Functionality using Redox-based Memristive Devices,* Advanced Functional Materials, vol. **25**, pp. 6414–6423 (2015) doi: 10.1002/adfm.201500865

[2] T. Breuer, A. Siemon, E. Linn, S. Menzel, **R. Waser**, **V.** **Rana,** *A HfO2-Based Complementary Switching Crossbar Adder,* Advanced Electronic Materials, vol. **1**, pp. 1500138 (2015) doi: 10.1002/aelm.201500138

[3] T. Breuer, A. Siemon, E. Linn, S. Menzel, **R. Waser**, **V.** **Rana,** (2015) *Low-current operations in 4F ^{2}-compatible Ta_{2}O_{5}-based complementary resistive switches*, Nanotechnology, vol. 26, pp. 415202 (2015) doi: 10.1088/0957-4484/26/41/415202

[4] O. Kavehei, E. Linn, L. Nielen, S. Tappertzhofen, S. Skafidas, I. Valov, **R. Waser**, *Associative Capacitive Network based on Nanoscale Complementary Resistive Switches for Memory-Intensive Computing,* Nanoscale, vol. **5**, pp. 5119-5128 (2013) doi: 10.1039/c3nr00535f

[5] L. Nielen, A. Siemon, S. Tappertzhofen, **R. Waser**, S. Menzel, E. Linn, *Study of Memristive Associative Capacitive Networks for CAM Applications,* IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. **5**, pp. 153-161 (2015) doi: 10.1109/JETCAS.2015.2426491