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An artificial neural network based on resistive switching memristors is implemented and simulated in LTspice. The influence of memristor variability and the reduction of the continuous range of synaptic weights into a discrete set of conductance levels is analyzed. To do so, a behavioral model is proposed for multilevel resistive switching memristors based on Al-doped HfO2 dielectrics, and it is implemented in a spice based circuit simulator. The model provides an accurate description of the conductance in the different conductive states in addition to describe the device-to-device variability
Accomplishing multi-level programming in resistive random access memory (RRAM) arrays with truly discrete and linearly spaced conductive levels is crucial in order to implement synaptic weights in hardware-based neuromorphic systems. In this paper, we implemented this feature on 4-kbit 1T1R RRAM arrays by tuning the programming parameters of the multi-level incremental step pulse with verify algorithm (M-ISPVA). The optimized set of parameters was assessed by comparing its results with a non-optimized one. The optimized set of parameters proved to be an effective way to define non-overlapped conductive levels due to the strong reduction of the device-to-device variability as well as of the cycle-to-cycle variability, assessed by inter-levels switching tests and during 1k reset-set cycles. In order to evaluate this improvement in real scenarios, the experimental characteristics of the RRAM devices were captured by means of a behavioral model, which was used to simulate two different neuromorphic systems: an 8×8 vector-matrixmultiplication (VMM) accelerator and a 4-layer feedforward neural network for MNIST database recognition. The results clearly showed that the optimization of the programming parameters improved both the precision of VMM results as well as the recognition accuracy of the neural network in about 6% compared with the use of non-optimized parameters.
Achieving a reliable multi-level programming operation in resistive random access memory (RRAM) arrays is still a challenging task. In this work, we assessed the impact of the voltage step value used by the programming algorithm on the device-to-device (DTD) variability of the current distributions of four conductive levels and on the energy consumption featured by programming 4-kbit HfO2-based RRAM arrays. Two different write-verify algorithms were considered and compared, namely, the incremental gate voltage with verify algorithm (IGVVA) and the incremental step pulse with verify algorithm (ISPVA). By using the IGVVA, a main trade-off has to be taken into account since reducing the voltage step leads to a smaller DTD variability at the cost of a strong increase in the energy consumption. Although the ISPVA can not reduce the DTD variability as much as the IGVVA, its voltage step can be decreased in order to reduce the energy consumption with almost no impact on the DTD variability. Therefore, the final decision on which algorithm
to employ should be based on the specific application targeted for the RRAM array.
With the rapid emergence of in-memory computing systems based on memristive technology, the integration of such memory devices in large-scale architectures is one of the main aspects to tackle.
In this work we present a study of HfO2-based memristive devices for their integration in large-scale CMOS systems, namely 200 mm wafers. The DC characteristics of single metal–insulator–metal
devices are analyzed taking under consideration device-to-device variabilities and switching properties. Furthermore, the distribution of the leakage current levels in the pristine state of the
samples are analyzed and correlated to the amount of formingless memristors found among the measured devices. Finally, the obtained results are fitted into a physic-based compact model that
enables their integration into larger-scale simulation environments.
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.
The resistive switching properties of HfO2 based 1T-1R memristive devices are electrically modified by adding ultra-thin layers of Al2O3
into the memristive device. Three different types of memristive stacks are fabricated in the 130 nm CMOS technology of IHP. The switching properties of the memristive devices are discussed with respect to forming voltages, low resistance state and high resistance state characteristics and their variabilities. The experimental I–V characteristics of set and reset operations are evaluated by using the quantum point contact model. The properties of the conduction filament in the on and off states of the memristive devices are discussed with respect to the model parameters obtained from the QPC fit.
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.
Memristive devices integrated in 200 mm wafers
manufactured in 130 nm CMOS technology with two different
dielectrics, namely, a HfO2 monolayer and an Al2O3/HfO2 bilayer,
have been measured. The cycle-to-cycle (C2C) and device-todevice (D2D) variability have been analyzed at the wafer scale using different numerical methods to extract the set (Vset) and reset (Vreset) voltages. Some interesting differences between both technologies were found in terms of switching characteristics
We characterize TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing. We analyze different features that allow the devices to mimic biological synapses and present the models to reproduce analytically some of the data measured. In particular, we have measured the spike timing dependent plasticity behavior in our devices and later on we have modeled it. The spike timing dependent plasticity model was implemented as the learning rule of a spiking neural network that was trained to recognize the MNIST dataset. Variability is implemented and its influence on the network recognition accuracy is considered accounting for the number of neurons in the network and the number of training epochs. Finally, stochastic resonance is studied as another synaptic feature.It is shown that this effect is important and greatly depends on the noise statistical characteristics.
Accomplishing truly analog conductance modulation in memristive arrays is crucial in order to implement the synaptic plasticity in hardware-based neuromorphic systems. In this paper, such a feature was addressed by exploiting the inherent stochasticity of switching dynamics in amorphous HfO2 technology. A thorough statistical analysis of experimental characteristics measured in 4 kbit arrays by using trains of identical depression/potentiation pulses with different voltage amplitudes and pulse widths provided the key to develop two different updating rules and to define their optimal programming parameters. The first rule is based on applying a specific number of identical pulses until the conductance value achieves the
desired level. The second one utilized only one single pulse with a particular amplitude to achieve the targeted conductance level. In addition, all the results provided by the statistical analysis performed may play an important role in understanding better the switching behavior of this particular technology.
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.
In this work, three different RRAM compact models implemented in Verilog-A are analyzed and evaluated in order to reproduce the multilevel approach based on the switching capability of
experimental devices. These models are integrated in 1T-1R cells to control their analog behavior by means of the compliance current imposed by the NMOS select transistor. Four different resistance
levels are simulated and assessed with experimental verification to account for their multilevel capability. Further, an Artificial Neural Network study is carried out to evaluate in a real scenario the viability of the multilevel approach under study.
Resistive random access memory (RRAM)-based hardware accelerators are playing an important role in the implementation of in-memory computing (IMC) systems for artificial intelligence applications. The latter heavily rely on vector-matrix multiplication (VMM) operations that can be efficiently boosted by RRAM devices. However, the stochastic nature of the RRAM technology is still challenging real hardware implementations. To study the accuracy degradation of consecutive VMM operations, in this work we programed two RRAM subarrays composed of 8x8 one-transistor-one-resistor (1T1R) cells following two different distributions of conductive levels. We analyze their robustness against 1000 identical consecutive VMM operations and monitor the inherent devices’ nonidealities along the test. We finally quantize the accuracy loss of the operations in the digital domain and consider the trade-offs between linearly distributing the resistive states of the RRAM cells and their robustness against nonidealities for future implementation of IMC hardware systems.
The stochastic nature of the resistive switching (RS) process in memristive devices makes device-to-device (DTD) and cycle-to-cycle (CTC) variabilities relevant magnitudes to be quantified and modeled. To accomplish this aim, robust and reliable parameter extraction methods must be employed. In this work, four different extraction methods were used at the production level (over all the 108 devices integrated on 200-mm wafers manufactured in the IHP 130-nm CMOS technology) in order to obtain the corresponding collection of forming, reset, and set switching voltages. The statistical analysis of the experimental data (mean and standard deviation (SD) values) was plotted by using heat maps, which provide a good summary of the whole data at a glance and, in addition, an easy manner to detect inhomogeneities in the fabrication process.
This work presents a quasi-static electrical characterization of 1-transistor-1-resistor memristive structures designed following hardness-by-design techniques integrated in the CMOS fabrication process to assure multi-level capabilities in harsh radiation environments. Modulating the gate voltage of the enclosed layout transistor connected in series with the memristive device, it was possible to achieve excellent switching capabilities from a single high resistance state to a total of eight different low resistance states (more than 3 bits). Thus, the fabricated devices are suitable for their integration in larger in-memory computing systems and in multi-level memory applications.
Index Terms—radiation-hard, hardness-by-design, memristive
devices, Enclosed Layout Transistor, in-memory computing
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.
In this work, we present an integrated read and programming circuit for Resistive Random Access Memory (RRAM) cells. Since there are a lot of different RRAM technologies in research and the process variations of this new memory technology often spread over a wide range of electrical properties, the proposed circuit focuses on versatility in order to be adaptable to different cell properties. The circuit is suitable for both read and programming operations based on voltage
pulses of flexible length and height. The implemented read method is based on evaluating the voltage drop over a measurement resistor and can distinguish up to eight different states, which are coded in binary, thereby realizing a digitization of the analog memory value. The circuit was fabricated in the 130 nm CMOS process line of IHP. The simulations were done using a physics-based, multi-level RRAM model. The measurement results prove the functionality of the read circuit and the programming system and demonstrate that the read system can distinguish up to eight different states with an overall resistance ratio of 7.9.
The use of resistive random-access memory (RRAM) for in-memory computing (IMC) architectures has significantly improved the energy-efficiency of artificial neural networks (ANN) over the past years. Current RRAM-technologies are physically limited to a defined unambiguously distinguishable number of stable states and a maximum resistive value and are compatible with present complementary metal-oxide semiconductor (CMOS)-technologies. In this work, we improved the accuracy of current ANN models by using increased weight resolutions of memristive devices, combining two or more in-series RRAM cells, integrated in the back end of line (BEOL) of the CMOS process. Based on system level simulations, 1T2R devices were fabricated in IHP's 130nm SiGe:BiCMOS technology node, demonstrating an increased number of states. We achieved an increase in weight resolution from 3 bit in ITIR cells to 6.5 bit in our 1T2R cell. The experimental data of 1T2R devices gives indications for the performance and energy-efficiency improvement in ITNR arrays for ANN applications.
Influence of variability on the performance of HfO2 memristor-based convolutional neural networks
(2021)
A study of convolutional neural networks (CNNs) was performed to analyze the influence of quantization and variability in the network synaptic weights. Different CNNs were considered accounting for the number of convolutional layers, size of the filters in the convolutional layer, number of neurons in the final network layers and different sets of quantization levels. The conductance levels of fabricated 1T1R structures based on HfO2 memristors were considered as reference for four or eight level quantization processes at the inference stage of the CNNs, which were previous trained with the MNIST dataset. We also included the variability of the experimental conductance levels that was found to be Gaussian distributed and was correspondingly modeled for the synaptic weight implementation.
We have performed different simulation experiments in relation to hardware neural networks (NN) to analyze the role of the number of synapses for different NN architectures in the network accuracy, considering different datasets. A technology that stands upon 4-kbit 1T1R ReRAM arrays, where resistive switching devices based on HfO2 dielectrics are employed, is taken as a reference. In our study, fully dense (FdNN) and convolutional neural networks (CNN) were considered, where the NN size in terms of the number of synapses and of hidden layer neurons were varied. CNNs work better when the number of synapses to be used is limited. If quantized synaptic weights are included, we observed thatNNaccuracy decreases significantly as the number of synapses is reduced; in this respect, a trade-off between the number of synapses and the NN accuracy has to be achieved. Consequently, the CNN architecture must be carefully designed; in particular, it was noticed that different datasets need specific architectures according to their complexity to achieve good results. It was shown that due to the number of variables that can be changed in the optimization of a NN hardware implementation, a specific solution has to be worked in each case in terms of synaptic weight levels, NN architecture, etc.