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Low-Energy Truly Random Number Generation with Superparamagnetic Tunnel Junctions for Unconventional Computing
Damir Vodenicarevic, Nicolas Locatelli, Alice Mizrahi, Joseph S. Friedman, Adrien F. Vincent, Miguel Romera, Akio Fukushima, Kay Yakushiji, Hitoshi Kubota, Shinji Yuasa, Sandip Tiwari, Julie Grollier, Damien Querlioz
TL;DR
Emerging computing schemes need large quantities of random numbers, but conventional generators impose costly energy and area overheads. This paper uses thermally switching superparamagnetic tunnel junctions as intrinsic noise amplifiers and experimentally evaluates their random-bit quality, scaling, and computing use. The devices achieve high-quality generation at 20fJ/bit using less than 2µm2, while XOR whitening and application-specific trade-offs support unconventional computing.
Problem
Stochastic and neuromorphic computing schemes require many random numbers, but existing pseudo-random and true-random generators can impose substantial energy and area costs.
Method
The paper generates bits from thermally induced switching in superparamagnetic tunnel junctions, applies XOR whitening, evaluates quality with NIST tests, and uses experimental streams in a Bayesian email-classification circuit.
Results
20fJ/bit using less than 2µm2 enables high-quality random-number generation, while XOR8 achieves cryptographic-quality NIST results and device scaling supports generation rates up to tens of MHz.
Takeaways & Limitations
Superparamagnetic tunnel junctions provide highly efficient true randomness, with quality, speed, and energy trade-offs selectable for unconventional and low-energy computing applications.
Abstract
from arXiv · showhide
Low-energy random number generation is critical for many emerging computing schemes proposed to complement or replace von Neumann architectures. However, current random number generators are always associated with an energy cost that is prohibitive for these computing schemes. In this paper, we introduce random number bit generation based on specific nanodevices: superparamagnetic tunnel junctions. We experimentally demonstrate high quality random bit generation that represents orders-of-magnitude improvements in energy efficiency compared to current solutions. We show that the random generation speed improves with nanodevice scaling, and investigate the impact of temperature, magnetic field and crosstalk. Finally, we show how alternative computing schemes can be implemented using superparamagentic tunnel junctions as random number generators. These results open the way for fabricating efficient hardware computing devices leveraging stochasticity, and highlight a novel use for emerging nanodevices.
I. INTRODUCTION
Emerging stochastic and neuromorphic computing schemes need many random numbers, but existing generators impose substantial energy and area costs. The paper proposes superparamagnetic tunnel junctions, which use thermal fluctuations to generate high-quality random bits with very low overhead.
- Motivation: Stochastic and neuromorphic computing schemes require large quantities of random numbers, making generator area and energy major limitations.The TrueNorth example dedicates one third of neuron area to random-number generation and requires one million random bits per integration step.
- Motivation: Pseudo-random generators can provide low-quality outputs or consume substantial energy and area, while physical true-random generators typically require energy-intensive event triggering.Existing alternatives include metastable CMOS, stochastic memory devices, and thermal-noise amplification, but their reported energy costs remain high.
- Proposed approach: Superparamagnetic tunnel junctions intrinsically amplify thermal noise without an external energy supply.Their low energy barrier allows thermal fluctuations to switch the magnetization repeatedly between two states at room temperature.
- Proposed approach: The devices generate high-quality random numbers at 20fJ/bit using less than 2µm2, representing orders-of-magnitude improvements in energy and area over current solutions.No write operation is required; low-energy readout of the fluctuating device state produces random bits.
- Study scope: The study experimentally evaluates random-bit generation, models scaling and environmental effects, estimates circuit energy efficiency, and demonstrates email classification with experimental random bits.The computing demonstration targets schemes that trade speed for ultra-low energy consumption.
II. EXPLOITING THE STOCHASTIC BEHAVIOR OF SUPERPARAMAGNETIC TUNNEL JUNCTIONS
Superparamagnetic tunnel junctions use a low-stability free nanomagnet whose thermal switching between parallel and antiparallel states produces a random telegraph signal. Electrical resistance readout and thresholding convert this signal into random bits whose statistics agree with a Poisson switching model.
- Device structure: Superparamagnetic tunnel junctions contain pinned and free nanomagnets separated by a tunnel oxide layer, in a structure similar to MRAM cells.The free magnet is intentionally low stability, unlike the highly stable free magnet in conventional MRAM.
- Stochastic switching: The free magnet spontaneously switches between parallel and antiparallel states because its energy barrier is low relative to thermal fluctuations.No bias or perturbation is needed to provoke these random fluctuations; temperature is sufficient.
- Readout: A small 10µA constant current enables resistance measurements while having negligible influence on magnetic behavior and extending device lifetime.The resulting resistance trace has two levels corresponding to the magnetic states and is binarized by thresholding.
- Readout: The measured resistance follows two-state fluctuations analogous to a random telegraph signal, with a mean switching frequency determined by junction shape and material properties.The resistance is higher in the antiparallel state than in the parallel state because of tunnel magnetoresistance.
- Signal statistics: Exponential dwell-time histograms and agreement between measured and expected power spectra support a Poisson-process model for the junction signal.The statistics were obtained from a 10-second measurement of a single junction.
III. OPTIMIZING THE QUALITY OF RANDOM BITS
Raw junction signals exhibit bias and sampling-dependent correlation, so the paper uses XOR whitening and evaluates quality with the NIST Statistical Test Suite. Increasing the number of combined streams and lowering sampling frequency improves randomness, with XOR8 at Fsampling/FMTJ = 3.0 identified as an optimal tested choice.
- Sampling: The measured junction switches at FMTJ = 1.66kHz, and sampling frequency must be selected relative to this mean switching frequency.The mean switching period is approximately 604µs.
- Raw-bit bias: The raw bitstream has a 60.5% mean state because the device spends more time in the parallel state than in the antiparallel state.The bias is linked to the pinned magnet’s stray field and varies between devices.
- Whitening: XOR whitening reduces both autocorrelation and mean-state bias exponentially as more independent junction bitstreams are combined.The post-whitening autocorrelation equals the product of the individual autocorrelations, while the mean state moves toward 50%.
- Whitening: XOR4 reduces consecutive-bit correlation below 1% and reaches a 49.9% mean state, whereas XOR8 reduces autocorrelation below 0.06% and reaches 50% with 0.5% standard deviation.These results show that XOR whitening corrects both correlation and mean-value bias.
- Quality assessment: The NIST STS evaluates 188 tests by measuring the pass rate of independently tested 1Mbit sequences.Cryptographic-quality consistency requires all test pass rates to lie in the expected green region.
- Quality assessment: XOR8 passes the cryptographic-quality requirement, while XOR4 passes it for only a fraction of the tests.The comparison uses experimental data sampled at 5kHz.
- Optimization trade-off: XOR8 at Fsampling/FMTJ = 3.0 gives 100% of NIST tests in the cryptographic-quality region and the highest tested sampling frequency.More XOR-combined streams improve quality but increase circuit area and energy consumption.
IV. SCALING CAPABILITIES OF THE RANDOM NUMBER GENERATORS IN TERMS OF SPEED AND ENERGY CONSUMPTION
Scaling superparamagnetic tunnel junctions can substantially increase random-bit generation speed, while whitening and readout circuitry preserve quality at low energy and area costs.
- Speed scaling: Smaller device volumes and areas increase random-bit generation speed exponentially by lowering the free magnet’s stability.This scaling behavior contrasts with MRAMs, where maintaining stability during aggressive scaling is challenging.
- Randomness quality: 25% correlation between consecutive bits can be whitened by XOR8, allowing generated random numbers to pass all NIST STS tests.The resulting sampling constraint is used to evaluate scaled random-bit generators.
- Speed scaling: Tens of MHz generation is predicted for energy barriers below 5kBT, corresponding to an 8nm device diameter.The estimate is based on the device model and energy-barrier scaling.
- Readout circuitry: A PCSA circuit is used to read junction states, and its simulated read energy is relatively independent of the junction resistance.The circuit is evaluated using 28nm transistor models and an Arrhenius-Néel device model.
- Energy and area: XOR8 whitening requires 20fJ/bit and less than 2µm2 in 28nm technology, while XOR4 requires 9.8fJ/bit and 1µm2.The XOR8 energy includes the XOR gate operation and multiple junction read operations.
V. SENSITIVITY OF THE RANDOM NUMBER GENERATORS TO PERTURBATIONS
Superparamagnetic tunnel junctions are sensitive to temperature, magnetic fields, and dipolar crosstalk, requiring operating conditions and layouts that preserve random-bit quality.
- Temperature: Higher temperatures increase switching rates and allow faster sampling, so devices should be sized for their lowest operating temperature.The maximum sampling frequency depends on both temperature and effective barrier.
- Magnetic field: Fields of a few Oe shift the junction mean state beyond correction by XOR8 whitening, making magnetic shielding necessary.The required shielding technology, based on mu metals, has already been developed for MRAM.
- Crosstalk: Closely packed junctions can interact through dipolar coupling, producing correlations in the generated random numbers.For perpendicular magnetization, negligible crosstalk is defined as less than ρc = 0.1% cross-correlation.
- Crosstalk: The critical center-to-center distance for negligible crosstalk falls below 100nm when junction diameter is scaled to 10nm at room temperature.This distance provides a layout design rule for integration.
VI. USING SUPERPARAMAGNETIC TUNNEL JUNCTIONS FOR UNCONVENTIONAL COMPUTING
The paper applies whitened superparamagnetic-junction bitstreams to a stochastic Bayesian email classifier, showing that generator count, averaging time, and whitening quality govern accuracy and energy use.
- Classifier architecture: The stochastic circuit classifies email as spam or not spam by combining probabilistic word generators with C-Elements for approximate Bayesian inference.Each word generator encodes occurrence rates in spam and non-spam messages, while output averaging estimates spam probability.
- Accuracy and energy: More random bit generators per word and longer output averaging improve spam-probability accuracy, with 8 generators per word and 2000 samples offering an energy–accuracy trade-off.The experiment uses XOR4-whitened experimental data sampled at 5kHz.
- Whitening: Unwhitened 5kHz experimental bitstreams do not perform satisfactorily because the classifier depends on multiple stages of bitstream combination and probability tuning.The circuit was tested with raw, XOR4-whitened, and XOR8-whitened streams.
- Energy: Using 8 random bit generators per word and 2,000 clock cycles, circuit simulation classifies a message using only nJ energy.The exact energy depends on the number of words in the dictionary.
VII. CONCLUSION
Superparamagnetic tunnel junctions generate high-quality random bitstreams with minimal energy and circuit overhead, supporting low-power unconventional computing while imposing speed, whitening, and environmental trade-offs.
- Conclusion: Natural switching dynamics produce random telegraph signals that become high-quality random bitstreams with minimal energy and circuit overhead.The devices remain compatible with standard CMOS fabrication processes.
- Trade-offs: XOR8 whitening typically requires 20fJ/bit and 2µm2, whereas scaled junctions could generate bits at speeds of dozens of MHz.Lower energy and area come with lower speed than higher-energy generators and additional whitening overhead.
- Application design: Lower-quality whitening can achieve extreme energy efficiency without degrading performance in many alternative computing schemes.The suitable balance among random-number quality, generation speed, and energy depends on the target application.
- Conclusion: Emerging nanodevices could provide highly efficient sources of true randomness for a wide range of applications.The study demonstrates this potential through superparamagnetic tunnel junctions acting as natural noise amplifiers.
SUPPLEMENTARY MATERIALS
The supplementary materials cover random-bit quality, switching and sampling behavior, crosstalk, classifier architecture and performance, energy consumption, and XOR whitening.
- Random-bit generation: The supplementary materials include analyses of whitening, NIST tests, switching, sampling frequency, and correlations between consecutive samples.
- Computing application: They also document dipolar crosstalk, the spam-detector architecture, whitening effects, bit-count effects, energy consumption, and XOR-whitening effects.