TY - GEN A1 - Bischoff, Carl A1 - Leise, Jakob A1 - Perez-Bosch Quesada, Emilio A1 - Pérez, Eduardo A1 - Wenger, Christian A1 - Kloes, Alexander T1 - Implementation of device-to-device and cycle-to-cycle variability of memristive devices in circuit simulations T2 - Solid-State Electronics N2 - We present a statistical procedure for the extraction of parameters of a compact model for memristive devices. Thereby, in a circuit simulation the typical fluctuations of the current–voltage (I-V) characteristics from device-to-device (D2D) and from cycle-to-cycle (C2C) can be emulated. The approach is based on the Stanford model whose parameters play a key role to integrating D2D and C2C dispersion. The influence of such variabilities over the model’s parameters is investigated by using a fitting algorithm fed with experimental data. After this, the statistical distributions of the parameters are used in a Monte Carlo simulation to reproduce the I-V D2D and C2C dispersions which show a good agreement to the measured curves. The results allow the simulation of the on/off current variation for the design of RRAM cells or memristor-based artificial neural networks. KW - RRAM KW - circuit simulation KW - HfO2 Y1 - 2022 U6 - https://doi.org/10.1016/j.sse.2022.108321 SN - 0038-1101 VL - 194 ER - TY - GEN A1 - Bogun, Nicolas A1 - Perez-Bosch Quesada, Emilio A1 - Pérez, Eduardo A1 - Wenger, Christian A1 - Kloes, Alexander A1 - Schwarz, Mike T1 - Analytical Calculation of Inference in Memristor-based Stochastic Artificial Neural Networks T2 - 29th International Conference on Mixed Design of Integrated Circuits and System (MIXDES), 23-24 June 2022 , Wrocław, Poland N2 - The impact of artificial intelligence on human life has increased significantly in recent years. However, as the complexity of problems rose aswell, increasing system features for such amount of data computation became troublesome due to the von Neumann’s computer architecture. Neuromorphic computing aims to solve this problem by mimicking the parallel computation of a human brain. For this approach, memristive devices are used to emulate the synapses of a human brain. Yet, common simulations of hardware based networks require time consuming Monte-Carlo simulations to take into account the stochastic switching of memristive devices. This work presents an alternative concept making use of the convolution of the probability distribution functions (PDF) of memristor currents by its equivalent multiplication in Fourier domain. An artificial neural network is accordingly implemented to perform the inference stage with handwritten digits. KW - RRAM KW - neural network Y1 - 2022 SN - 978-83-63578-22-0 SN - 978-83-63578-21-3 SN - 978-1-6654-6176-4 U6 - https://doi.org/10.23919/MIXDES55591.2022.9838321 SP - 83 EP - 88 ER - TY - GEN A1 - Dersch, Nadine A1 - Roemer, Christian A1 - Perez, Eduardo A1 - Wenger, Christian A1 - Schwarz, Mike A1 - Iñíguez, Benjamín A1 - Kloes, Alexander T1 - Fast circuit simulation of memristive crossbar arrays with bimodal stochastic synaptic weights T2 - 2024 IEEE Latin American Electron Devices Conference (LAEDC) N2 - This paper presents an approach for highly efficient circuit simulation of hardware-based artificial neural networks by using memristive crossbar array architectures. There are already possibilities to test neural networks with stochastic weights via simulations like the macro model NeuroSim. However, the noise-based variability approach offers more realistic setting options including elements of a classical circuit simulation for more precise analysis of neural networks. With this approach, statistical parameter fluctuations can be simulated based on different distribution functions of devices. In Cadence Virtuoso, a simulation of a crossbar array with 10 synaptic weights following a bimodal distribution, the new approach shows a 1,000x speedup compared to a Monte Carlo simulation. Initial tests of a memristive crossbar array with over 15,000 stochastic weights to classify the MNIST dataset show that the new approach can be used to test the functionality of hardware-based neural networks. KW - RRAM Y1 - 2024 SN - 979-8-3503-6130-8 U6 - https://doi.org/10.1109/LAEDC61552.2024.10555829 SN - 979-8-3503-6129-2 SN - 2835-3471 SP - 1 EP - 4 PB - IEEE ER - TY - GEN A1 - Kloes, Alexander A1 - Bischoff, Carl A1 - Leise, Jakob A1 - Perez-Bosch Quesada, Emilio A1 - Wenger, Christian A1 - Pérez, Eduardo T1 - Stochastic switching of memristors and consideration in circuit simulation T2 - Solid State Electronics N2 - We explore the stochastic switching of oxide-based memristive devices by using the Stanford model for circuit simulation. From measurements, the device-to-device (D2D) and cycle-to-cycle (C2C) statistical variation is extracted. In the low-resistive state (LRS) dispersion by D2D variability is dominant. In the high-resistive state (HRS) C2C dispersion becomes the main source of fluctuation. A statistical procedure for the extraction of parameters of the compact model is presented. Thereby, in a circuit simulation the typical D2D and C2C fluctuations of the current–voltage (I-V) characteristics can be emulated by extracting statistical parameters of key model parameters. The statistical distributions of the parameters are used in a Monte Carlo simulation to reproduce the I-V D2D and C2C dispersions which show a good agreement to the measured curves. The results allow the simulation of the on/off current variation for the design of memory cells or can be used to emulate the synaptic behavior of these devices in artificial neural networks realized by a crossbar array of memristors. KW - RRAM KW - memristive device KW - variability Y1 - 2023 U6 - https://doi.org/10.1016/j.sse.2023.108606 SN - 0038-1101 VL - 201 ER - TY - GEN A1 - Dersch, Nadine A1 - Perez-Bosch Quesada, Emilio A1 - Pérez, Eduardo A1 - Wenger, Christian A1 - Roemer, Christian A1 - Schwarz, Mike A1 - Kloes, Alexander T1 - Efficient circuit simulation of a memristive crossbar array with synaptic weight variability T2 - Solid State Electronics N2 - In this paper, we present a method for highly-efficient circuit simulation of a hardware-based artificial neural network realized in a memristive crossbar array. The statistical variability of the devices is considered by a noise-based simulation technique. For the simulation of a crossbar array with 8 synaptic weights in Cadence Virtuoso the new approach shows a more than 200x speed improvement compared to a Monte Carlo approach, yielding the same results. In addition, first results of an ANN with more than 15,000 memristive devices classifying test data of the MNIST dataset are shown, for which the speed improvement is expected to be several orders of magnitude. Furthermore, the influence on the classification of parasitic resistances of the connection lines in the crossbar is shown. KW - RRAM KW - Neural network Y1 - 2023 U6 - https://doi.org/10.1016/j.sse.2023.108760 SN - 0038-1101 VL - 209 ER - TY - GEN A1 - Blumenstein, Alan A1 - Pérez, Eduardo A1 - Wenger, Christian A1 - Dersch, Nadine A1 - Kloes, Alexander A1 - Iñíguez, Benjamín A1 - Schwarz, Mike T1 - Evaluating device variability in RRAM-based single- and multi-layer perceptrons T2 - 2025 32nd International Conference on Mixed Design of Integrated Circuits and System (MIXDES) N2 - This work investigates the impact of stochastic weight variations in hardware implementations of artificial neural networks, focusing on a Single-Layer Perceptron and Multi-Layer Perceptrons. A variable neural network model is introduced, applying Gaussian variability to synaptic weights based on an adjustment rate, which controls the proportion of affected weights. By studying how stochastic variations affect accuracy, simulations under device-to-device and cycle-to-cycle variation conditions demonstrate that Single-Layer Perceptrons are more sensitive to weight variations, while Multi-Layer perceptrons show greater robustness. Additionally, stochastic quantization improves the performance of Multi-Layer Perceptrons but has minimal effect on Single-Layer Perceptrons. KW - RRAM Y1 - 2025 SN - 978-83-63578-27-5 U6 - https://doi.org/10.23919/MIXDES66264.2025.11092102 SP - 74 EP - 77 PB - IEEE CY - New York ER - TY - GEN A1 - Dersch, Nadine A1 - Perez, Eduardo A1 - Wenger, Christian A1 - Lanza, Mario A1 - Zhu, Kaichen A1 - Schwarz, Mike A1 - Iñíguez, Benjamín A1 - Kloes, Alexander T1 - Statistical model for the calculation of conductance variations of memristive devices T2 - 2025 IEEE European Solid-State Electronics Research Conference (ESSERC) N2 - This paper presents a statistical model which calculates the expected conductance variations from device to device or from cycle to cycle of memristive devices. The mean readout current and its standard deviation can be calculated for binary and multi-level devices. These values are important for simulating hardware-based artificial neural networks at circuit level and testing their functionality. Research into hardwarebased artificial neural networks is important because they are energy-efficient. Furthermore to calculating the variations, the statistical model can be used to determine what influence the cumulative distribution function of switching has on the variations and which behavior provides the best results for the hardwarebased artificial neural network. Some memristive devices exhibit multi-level behavior due to defects in the switching layer. The number of these defects and the optimal amount can be estimated. KW - RRAM KW - Memristive devices KW - Statistical variations KW - Binary KW - Multi-level KW - Artificial neural networks KW - Cumulative distribution Y1 - 2025 U6 - https://doi.org/10.1109/ESSERC66193.2025.11213973 SP - 373 EP - 376 PB - IEEE CY - Piscataway, NJ ER - TY - GEN A1 - Dersch, Nadine A1 - Perez, Eduardo A1 - Wenger, Christian A1 - Schwarz, Mike A1 - Iniguez, Benjamin A1 - Kloes, Alexander T1 - A closed-form model for programming of oxide-based resistive random access memory cells derived from the Stanford model T2 - Solid-state electronics N2 - This paper presents a closed-form model for pulse-based programming of oxide-based resistive random access memory devices. The Stanford model is used as a basis and solved in a closed-form for the programming cycle. A constant temperature is set for this solution. With the closed-form model, the state of the device after programming or the required programming settings for achieving a specific device conductance can be calculated directly and quickly. The Stanford model requires time-consuming iterative calculations for high accuracy in transient analysis, which is not necessary for the closed-form model. The closed-form model is scalable across different programming pulse widths and voltages. KW - RRAM KW - Closed-form KW - Modeling KW - Oxide-based KW - Pulse-programming KW - Resistive random access memory KW - Stanford model KW - Variability Y1 - 2025 U6 - https://doi.org/10.1016/j.sse.2025.109238 SN - 0038-1101 VL - 230 SP - 1 EP - 5 PB - Elsevier BV CY - Amsterdam ER - TY - GEN A1 - Blumenstein, Alan A1 - Pérez, Eduardo A1 - Wenger, Christian A1 - Dersch, Nadine A1 - Kloes, Alexander A1 - Iñíguez, Benjamín A1 - Schwarz, Mike T1 - Exploring variability and quantization effects in artificial neural networks using the MNIST dataset T2 - Solid-state electronics N2 - This paper investigates the impact of introducing variability to trained neural networks and examines the effects of variability and quantization on network accuracy. The study utilizes the MNIST dataset to evaluate various Multi-Layer Perceptron configurations: a baseline model with a Single-Layer Perceptron and an extended model with multiple hidden nodes. The effects of Cycle-to-Cycle variability on network accuracy are explored by varying parameters such as the standard deviation to simulate dynamic changes in network weights. In particular, the performance differences between the Single-Layer Perceptron and the Multi-Layer Perceptron with hidden layers are analyzed, highlighting the network’s robustness to stochastic perturbations. These results provide insights into the effects of quantization and network architecture on accuracy under varying levels of variability. KW - Single-Layer Perceptron KW - Multi-Layer Perceptron KW - Cycle-to-Cycle variability KW - Quantization KW - Stochastic variability KW - Simulation Y1 - 2026 U6 - https://doi.org/10.1016/j.sse.2025.109296 SN - 0038-1101 VL - 232 SP - 1 EP - 4 PB - Elsevier BV CY - Amsterdam ER -