Magnetic memories from a broad IT, materials, and physics perspectives T. Jungwirth Institute of Physics, Czech Academy of Sciences University of Nottingham, United Kingdom [email protected]1. Recording & computers 2. Conventional & neuromorphic computing 3. Non-CMOS materials and devices 4. Physical principles of operation of magnetic devices Lecture I Lecture II
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Magnetic memories from a broad IT, materials, and physics perspectives
T. JungwirthInstitute of Physics, Czech Academy of Sciences
2.2.2 CMOS mixed digital/analog Neurogrid (Stanford) – 60k neuronsDynap-SEL (Zurich Univ.) – 1000 neuronsHICANN (Heidelberg Univ.) – 500 neuronsBenjamin et al. Proceedings of the IEEE 102, 699 (2014)
Digital communication Analog neuronAnalog synapse with weights stored in digital RAM
Loihi (Intel) – 100k neuronsIncludes learning
Merolla et al. et Science 345, 668 (2014)
Reviews:Thakur et al. Frontiers in Neuroscience 12, 891(2018)Yu (ed.), Neuro-inspired Computing Using Resistive Synaptic Devices, Springer (2017)Burr et al. Adv. Phys. X 2, 89 (2017)
2. Asynchronous: Individual components have local clocksSpiking Neural Networks: Input/output/internal variables coded in spikes and their timing
3.1 Analog memristive synapseCBRAM (Michigan Univ.)Jo et al. Nano Lett., 10, 1297 (2010)
RRAM (Pohang Univ.)Moon et al. Nanotechnology 25, 495204 (2014)
PCRAM (IBM)Eryilmaz et al. Frontiers in Neuroscience 8, 205(2014)
FRAM (Panasonic)Ueda et al. PLOS ONE 9, e112659 (2014)
Analog AFMEM (Prague/Nottingham/Mainz/…)Discrete synapse or neuronKaspar et al. preprint (2019)
Ferromagnetic domains
Ferroelectric domains
Antiferromagnetic domains
Reviews:Thakur et al. Frontiers in Neuroscience 12, 891(2018)Yu (ed.), Neuro-inspired Computing Using Resistive Synaptic Devices, Springer (2017)Burr et al. Adv. Phys. X 2, 89 (2017)
Crystalline AmorphousDefects in insulator
MRAM
CBRAM/RRAM PCRAM FRAM
AFMEM
modificationsto increasethemetal electrodethickness,so that thelineresistanceswerereduced to about 800V for thetop layer of thecross-bar and 600V for itsbottom layer.Thecrossbarsretained theexcellentuniformity of virgin (pre-formed) crossbar-integrated devices (seeSupplementary Figs 3, 4 and 5), allowing individual electric formingand tuning of each memristor. Theelectroforming wasperformed bygrounding the corresponding bottom electrode and applying a cur-rent-controlled ramp-up to the top electrode, while leaving all otherline potentials floating (Supplementary Fig. 4). To minimize currentleakageduring thesubsequent forming of other devices, each formedmemristor wasimmediately switched into itslow-current (OFF) state.The measured individual characteristics of the formed memristorsweremostly similar to thoseof stand-alonedevices,except for asome-what smaller ( 100) ON/OFF current ratio. This difference may bepartly explained by current leakage through other crosspoints at themeasurements,and partly by thesomewhat smaller switchingvoltagesused for thecrossbar to lower therisk of devicedamage. In addition,some deviations from the optimal device performance could becaused by theelectron-beam evaporation of thicker electrodes, whichrequired breaking of thevacuum, asopposed to thefully in situ sput-tering of single device layers, and their subsequent annealing (seeSupplementary Information).
Thefabricated memristivecrossbar wasused to implement asimpleartificial neural network with thetop-level (functional) schemeshownin Fig. 2. This isasingle-layer perceptron22 with ten inputsand threeoutputs, fully connected with 10 3 3 5 30 synaptic weights(Fig. 2b).
HereVj with j 5 1,…,9 are theinput signals, V10 isaconstant bias, bis a parameter controlling the function’s nonlinearity, and Wij areadjustable (trainable) synaptic weights. Such a network is sufficientfor performing, for example, the classification of 3 3 3-pixel black-and-white images into three classes, with nine network inputs(V1,…,V9) corresponding to the pixel values. We tested the networkon a set of N 5 30 patterns, including three stylized letters (‘z’, ‘v’and ‘n’) and three sets of nine noisy versions of each letter, formedby flipping one of the pixels of the original image (see Fig. 2c).Becauseof thevery limited sizeof theset, it wasused for both trainingand testing.
Physically,each input signal wasrepresentedbyavoltageVj equal toeither 1 0.1 V or 2 0.1 V, corresponding, respectively, to theblack orwhitepixel, whilethebiasinput V10 wasequal to 2 0.1V.Such codingmakes the benchmark input set balanced, in particular ensuring thatthe sum of all input signals across all patterns of a particular classis close to zero, which speeds up the convergence process28. Tosustain this balance at the network’s output as well, each synapse
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a bTop electrodes
Bo
tto
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s[Δ
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Pt (60 nm)
Pt (60 nm)
Ta (5 nm)
Ti (15 nm)
TiO2 – x
(30 nm)
Al2O
3 (4 nm)
SiO2/Si
Conductance, G (μS)
Figure 1 | Memristor crossbar. a, Integrated 123 12crossbar with an Al2O3/TiO2 2 x memristor at each crosspoint. b, A typical current–voltagecurveof aformedmemristor.c,Absolutevaluesof conductancechangeunder theeffect of
500-msvoltagepulsesof two polarities, asafunction of theinitial conductance,for variouspulseamplitudes. The inset in b showsthedevicecross-sectionschematically.
d
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Inputneurons
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Setn = 1Δij = 0
Desired class fi(g)(n)
Lastpattern?
No
Yes
n = n +1
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Eq. (1)
CalculateIi(n)
Eq. (2)
Next epoch
End ofepoch
UpdateweightsEq. (5)
3 × 3 binaryimage
Training set:
initialize Wij
{Vj(n), fi(g)(n)}n = 1
N
Figure 2 | Pattern classification experiment (top-level description). a, Inputimage. b, Thesingle-layer perceptron for classification of 33 3 binary images.c, Theused input pattern set. d, Theflow chart of oneepoch of theused in situ
training algorithm. In d, thegrey-shaded boxesshow thesteps implementedinsidethecrossbar, while thosewith solid black bordersdenotetheonly stepsrequired to perform theclassification operation.
RESEARCH LETTER
G 2015 Macmillan Publishers Limited. All rights reserved
6 2 | N A T U R E | V O L 5 2 1 | 7 M A Y 2 0 1 5
W1,1
W3,10
I1 I2 I3
3.3 Analog memristive weighted-sum (dot product) array RRAM passive array (UCSB)Prezioso et al. Nature 521, 61 (2015)