Memristive Tunneling Devices: From Device Principles to Neuromorphic Applications

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1 Memristive Tunneling Devices: From Device Principles to Neuromorphic Applications Martin Ziegler, A. Petraru, R. Soni, and H. Kohlstedt AG Nanoelektronik Technische Fakultät Christian-Albrechts-Universität zu Kiel FOR Jülich,

Learning: Capability to process new information:

2 2 Neuromorphic Systems non-biogical systems functioning similarly to brains Carver Mead, 1986 Learning: Capability to process new information: Creation of knowledge Memory: Capability to capture knowledge

Neuromorphic Systems CNS program at the California Institute

networks and their computations, whether natural or synthetic

3 Neuromorphic Systems CNS program at the California Institute of Technology, 1986 Analog VLSI and Neural Systems, Carver Mead, Addison-Wesley 1989, p. 44 Exploring the relationship between structure of neuronal networks and their computations, whether natural or synthetic 3 Richard Feynman Neuroinformatics John Hopfield Carver Mead VLSI Technology Integrated Circuits

4 Richard Feynman s last bord 4 Richard Feynman (* 11. Mai 1918 in Queens, New York; 15. February 1988 in Los Angeles)

5 5 Computer vs. Brain = Computing Gap Computer: Arithmetic operation Brain: Pattern Recognition (Associative Memory)

6 6 Computer vs. Brain = Computing Gap Try to close the gap Computer: Arithmetic operation Brain: Pattern Recognition (Associative Memory)

7 7 Computer vs. Brain Energy Efficiency 216kW 25W IBM Watson IBM J. RES. & DEV. VOL

8 Building neuromorphic circuits 8 non-volatile device neuromorphic systems biological model neural network

9 Current Transport through Energy Barriers Formation of Barriers Electron Tunneling Thermonic Emission Theory

10 Formation of Energie Barriers 10 *taken from C. J. Chen, Introduction to Scanning Tunneling Microscopy, Oxford University Press, 1993

11 Formation of Energie Barriers 11 *taken from C. J. Chen, Introduction to Scanning Tunneling Microscopy, Oxford University Press, 1993

12 Formation of Energie Barriers 12 E F qφ m φ m : Work function: is the minimum energy to remove an electron Metal Vacuum

13 Formation of Energie Barriers 13 E F qφ m φ m : Work function: is the minimum energy to remove an electron Metal Vacuum qχ φ m = χ + φ n E C E F qφ n χ : electron affinity: minimum energy to remove an electron from the bottom of the conductance band E V Semiconductor Vacuum φ n = E C - E F

14 Formation of Energie Barriers 14 Tunnel barrier qφ m-1 E F-1 δ qv qφ m-2 E F-2 Metal 1 Metal 2 Insulator

15 Formation of Energie Barriers 15 Tunnel barrier qφ m-1 E F-1 δ qv qφ m-2 E F-2 Metal 1 Metal 2 Insulator qχ Schottky barrier qφ m qφ B E C E F Metal δ E V

16 Elastic Electron Tunneling 16 qφ 0 qφ(x) E ψ 1 ψ 2 δ Region 1 Region 2 x 1 x 2 Energy conservation: elastic Transmission probability:

17 Elastic Electron Tunneling 17 qφ 0 qφ(x) E ψ 1 ψ 2 δ Region 1 Region 2 x 1 x 2 Energy conservation: elastic Transmission probability: planar wave: ψ =ψ 0 exp(±ikx) with and WKB approximation (using classical momentum)

18 Elastic Electron Tunneling 18 qφ 0 qφ(x) E ψ 1 ψ 2 δ Region 1 Region 2 x 1 x 2 Energy conservation: elastic Transmission probability: planar wave: ψ =ψ 0 exp(±ikx) with and WKB approximation (using classical momentum)

19 Elastic Electron Tunneling 19 Tunneling current: occupied states N1 unoccupied states N2 E δ Region 1 Region 2 f1, f2: Fermi-Dirac distribution

20 Elastic Electron Tunneling 20 Fowler- Nordheim tunneling current: electron tunneling at higher voltages Region 1 Region 2 applied electrical field tunneling area

21 Thermionic Emission Theory 21 current conduction mechanism in metal-semiconductor contacts. E C qφ B Major assumptions: (1) the barrier height qφ B is assumed to be much larger than kt (2) drift diffusion effects within the barrier layer are neglected (3) the energy barrier is not affect by the image force. E F Semiconductor Metal

22 Thermionic Emission Theory 22 current conduction mechanism in metal-semiconductor contacts. number of electrons above Φ B qφ B effective density of states in conductance band E C E F Semiconductor Metal

23 Thermionic Emission Theory 23 current conduction mechanism in metal-semiconductor contacts. random motion of carriers within a Maxwellian distribution number of electrons above Φ B effective thermal velocity

24 Thermionic Emission Theory 24 current conduction mechanism in metal-semiconductor contacts. number of electrons above Φ B effective thermal velocity A*- Richardson constant

25 Thermionic Emission Theory 25 current conduction mechanism in metal-semiconductor contacts. number of electrons above Φ B effective thermal velocity +

26 Memristive Tunneling Devices How to change the transmission probability? MemFlash Cell Ionic Tunnel Junction Ferroelectric Tunneling Junctions

27 Change of Transmission Probability 27

Mead, IEEE Trans. on Elec. Dev. 43, 1972 (1996).

28 Floating Gate Transistor as Memristive Device? 28 H. C. Card and W.R. Moore, Electronic Letters 25, 805 (1989). C. Diorio, P. Hasler, B.A. Mimich, and C. A. Mead, IEEE Trans. on Elec. Dev. 43, 1972 (1996). Control Gate Floating Gate Tunnel Window Source Drain Bulk Memristive operation mode of a single EEPROM cell? Reduction to a two-terminal device: simultaneous read/write I = M(x,V) V dx/dt = f(x,v)

29 MemFlash - Cell Ziegler et al., Appl Phys. Lett. 101, (2012) 29 Control Gate Floating Gate Tunnel Window Source Drain ±V D Bulk x = Q FG I D = M(Q FG,V D ) V D 1. = I FG (Q FG,V D ) dq FG /dt = I FG (Q FG,V D )

30 Capacitive Device Model Ziegler et al., Appl Phys. Lett. 101, (2012) 30 CG C C C S FG C OX C D S B D

31 Capacitive Device Model Ziegler et al., Appl Phys. Lett. 101, (2012) 31 CG C C C S FG C OX C D S V C = V S = 0 B D k B 0

32 Capacitive Device Model Ziegler et al., Appl Phys. Lett. 101, (2012) 32 CG C C C S FG C OX I FN C D S B D

33 Capacitive Device Model C. Riggert, M. Ziegler et al., Semicond. Sci. Technol. 29, (2014). 33 CG C C C S FG C OX I FN I PF I INJ C D S B D Fowler-Nordheim Pool-Frenkel Hot electrons

34 Capacitive Device Model C. Riggert, M. Ziegler et al., Semicond. Sci. Technol. 29, (2014). 34

35 Capacitive Device Model C. Riggert, M. Ziegler et al., Semicond. Sci. Technol. 29, (2014). 35 MOSFET

36 Scaling Perspective C. Riggert, M. Ziegler et al., Semicond. Sci. Technol. 29, (2014). 36 Tunneling oxide scaling

37 Scaling Perspective C. Riggert, M. Ziegler et al., Semicond. Sci. Technol. 29, (2014). 37 Tunneling oxide scaling

38 Scaling Perspective C. Riggert, M. Ziegler et al., Semicond. Sci. Technol. 29, (2014). 38 Retention times

39 C-MemFlash N-MemFlash 39 Ziegler et al., IEEE EDL 37, 186 (2016) P-MemFlash

40 C-MemFlash 1. increased number of end- resistant states 40 Ziegler et al., IEEE EDL 37, 186 (2016) 2. realizing a rich variety of memory and logic functionalities

41 Change of Transmission Probability 41 Metal Metal

42 Interface-based Memristive Devices 42 Memristive layer Tunnel barrier D. S. Jeong, H. Kohlstedt, Solid-State Electronics 63 (2011) Baik et al., Appl. Phys. Lett. 97, (2010) Modulation of the tunnel barrier by the reactive Ti layer

43 Interface-based Memristive Devices 43 Sawa, Mat. Today 11, 28 (2008) Modulation of oxygen vacancies at Metal-Semiconductor interfaces Mikheev et al., Nat Commun. 5: 3990 (2014).

44 Interface-based Memristive Devices 44 Interface trap states Metal Mobile Ions Memristive Layer E C E C Metal E C Memristive Layer E C Simmons & Verderber (1967) contribution from memristive layer Voltage-time dilemma: Schroeder et al., J. Appl. Phys. 107: (2010). long set pulses at low voltages low retention

45 Interface-based Memristive Devices 45 Aims: homogeneous interfacial effect (high resistance, contineus switching) no contribution from memristive layer retention in the order of days weeks

46 A Double Barrier Memristive Device 46 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Tunnel barrier Limit resistive switching to interface effects by using thin insulating layers Schottky barrier Φ HRS TB LRS Φ S TB S Change of electron tunneling due to the modulation of Schottky barrier

47 A Double Barrier Memristive Device 47 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Au 2.5 nm Nb x O y Solid state electrolyte 1.3 nm Al 2 O 3 Al Tunnel barrier

48 A Double Barrier Memristive Device 48 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Au Nb x O y Al 2 O 3 Al

49 A Double Barrier Memristive Device 49 Hansen, Ziegler et al., Sci. Rep. 5: (2015) 10 8 Homogeneity on wafer level 4 '' 1 mm Resistance map

50 A Double Barrier Memristive Device 50 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Interface effect 10 8 Homogeneity on wafer level 4 '' 1 mm Resistance map

51 A Double Barrier Memristive Device Interface Contribution Tunnel barrier Nb Nb x O y Al 2 O 3 Al Au 51 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Schottky barrier Nb x O y Nb Schottky barrier + Tunnel barrier Au Nb x O y Al 2 O 3 Al

52 A Double Barrier Memristive Device Retention Retention for single barrier device characteristic for traps Significantly longer retention for double barrier devices 52 Hansen, Ziegler et al., Sci. Rep. 5: (2015)

53 A Double Barrier Memristive Device Retention Retention for single barrier device characteristic for traps Significantly longer retention for double barrier devices 53 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Two mechanisms involved (short- and long-term)

54 A Double Barrier Memristive Device 54 Hansen, Ziegler et al., Sci. Rep. 5: (2015) During set process, mobile oxygen ions increase interface potential V I and decrease effective barrier width d eff

55 A Double Barrier Memristive Device 55 Hansen, Ziegler et al., Sci. Rep. 5: (2015) During set process, mobile oxygen ions increase interface potential V I and decrease effective barrier width d eff

56 A Double Barrier Memristive Device 56 Hansen, Ziegler et al., Sci. Rep. 5: (2015) Tunnel distance Simulation Experiment variable constant

57 Change of Transmission Probability 57 Metal Metal

58 Dielectric Barrier Ferroelectric Tunnel Junction Kohlstedt, Pertsev, Waser, Ferroelectric Thin Films X, Vol. 688 (Material Research Society) 2002, p Magnet Magnet Density of states effects 2p e A I( V ) = T ( E) n ( E -ev ) n ( E )[ f ( E ev ) - f ( E) ]de h - Cooperative phenomenon located in the barrier! Metal Metal Ferroelectric Barrier

59 Ferroelectric Tunnel Junction 59 Ferroelectric Materials

2161 (1971) Kohlstedt, Pertsev, Waser, Ferroelectric Thin

60 Ferroelectric Tunnel Junction Ferroelectric Materials Esaki et al., IBM Tech. Discl. Bull (1971) Kohlstedt, Pertsev, Waser, Ferroelectric Thin Films X, Vol. 688 (Material Research Society) 2002, p thickness < 3 nm

61 Ferroelectric Tunnel Junction 61 Garcia et. al., Nature (2009) PFM + C-AFM P E P P E P Correlation between tunneling resistance and ferroelectric switching

62 Ferroelectric Tunnel Junction 62 A ferroelectric memristor Chanthbouala et al., Nature Materials 11, (2012)

63 3 mechanisms affecting the tunneling resistance H. Kohlstedt et al., Phys. Rev. B 72, (2005). 63

64 Ferroelectric Tunnel Junctions on Silicon 64 Guo et al., Scientific Reports 5:12576 (2015)

65 Application in Neuromorphic Systems cellular mechanisms Associative learning Pattern recognition

66 Basic Building Block: The Neuron Spikes the information units Stimulus 66 Pulse duration 3.5 ms (in electronics: 60 ns) Signal speed-along the axon 100 m/s (in electroncis 2.4 x 10 8 m/s) Memristive device as chemical synapse Sung Hyun Jo et al., Nano Lett. 10, (2010)

67 Hebbian Plasticity 67 neurons that fire together wire together local synaptic Plasticity D.O. Hebb (1949) ν i ν j ν i associative cooperative local cellular mechanism ν j competition global multidimensional network level

Hebb (1949) cooperative ν i F(ν i,ν j )= β ν i ν j ν j ν i associative β

68 Hebbian Plasticity 68 neurons that fire together wire together dω(t)/dt = F(ω, ν i, ν j ) local ν = f(u) synaptic Plasticity D.O. Hebb (1949) cooperative ν i F(ν i,ν j )= β ν i ν j ν j ν i associative β = β(ω,<ν j >) local cellular mechanism ν j competition global multidimensional network level

69 Associative Learning: Pavlov s Dog 69 Classical conditioning I. Pavlov (1903)

70 Associative Learning: Pavlov s Dog 70 Principles of associative learning can be understood on cellular level S Sensory neuron unconditional stimulus (UCS) S Sensory neuron conditional stimulus (CS) + I M Strengthen interneuron Motor neuron E. R. Kandel 1971

Associative Learning: Pavlov s Dog 71 Principles of associative learning can be understood on cellular level i j S Sensory neuron unconditional

71 Associative Learning: Pavlov s Dog 71 Principles of associative learning can be understood on cellular level i j S Sensory neuron unconditional stimulus (UCS) S Sensory neuron conditional stimulus (CS) + I M Strengthen interneuron Motor neuron E. R. Kandel 1971 dω(t)/dt = β ν bell ν food

72 Associative Learning: Pavlov s Dog 72 Principles of associative learning can be understood on cellular level ω bell E. R. Kandel 1971 ν food ʃω > ϴ ω food Heterosynaptic plasticity dω bell (t)/dt = β ν bell ν food

73 Associative Learning: Pavlov s Dog 73 Ziegler et al., Adv. Func. Mat. 22, 2744 (2012) An Electronic Version of Pavlov s Dog V bell V food LRS -> HRS SET dr M /dt = β f[t, (V bell + V food )]

74 Pavlov s Dog Ziegler et al., Adv. Func. Mat. 22, 2744 (2012) circuit with thresholds V bell < V cth & V food > V cth V bell + V food > V p mth (before) & V bell > V cth (after) 74

75 Pavlov s Dog Ziegler et al., Adv. Func. Mat. 22, 2744 (2012) How to scale it to a network level? 75? How realistic is a heterosynaptic rule?! different time-scales for (Pavlov s) behavioral experiments and synaptic plasticity processes: Pavlov: up to 4 seconds At neurons: ms

76 Spike Pairing: Asymmetric Hebbian rule Bi &Poo J. Neurosci (1998) 76 Spike-Time- Dependent-Plasticity (STDP) pre +ΔT time pre -ΔT time post t time post t time Potentiation dω(t)/dt = +β ν pre (t-δt) ν post (t) Depression dω(t)/dt = -β ν pre (t)ν post (t+δt)

77 Spike Pairing: Asymmetric Hebbian rule Bi &Poo J. Neurosci (1998) Spike-Time- Dependent-Plasticity (STDP) dω(t)/dt = +β f[v pre (t-δt) - V post (t)] dω(t)/dt = -β f[v pre (t) - V post (t-δt) ] 77 pre V pre post t pre V post post t Δ V Δt t Jo et al., Nano Lett. 10, (2010). LTD C. Zamarreño-Ramos et al., Front. Neurosci. 5, 26 (2011)

78 Realization of artificial synapses You have the choice a few Examples D.S. Jeong, I. Kim, M. Ziegler, H. Kohlstedt, RSC ADVANCES, 3, 3169 (2013) 78 Ferroelectric Tunnel Junctions Andrè Chanthbouala, et al. Nature Nanotechnology 2012 Nanoionics R. Waser et al. Adv. Mater Ionics and Interface Barriers D. S. Jeong et al. Solid-State Electronics 63, 1 (2011) Baik et al., Appl. Phys. Lett. 97, (2010) D. B. Strukov et al. Nature 2008, 453, 80 Spin Transfer Torque Devices P. Krzysteczko et al. Adv. Mater Floating-Gate Transistors: MemFlash Ziegler et al. Appl. Phys. Lett. 2012

79 Plasticity model Ziegler, Bartsch et al., IEEE TBioCAS 79 o local + cooperative o voltage dependence: dω/dt= α(δv) o pulse width dependence: dω/dt= λ(δt) o weight saturation: ω min < ω(t) < ω max

80 Plasticity model Ziegler, Bartsch et al., IEEE TBioCAS o local + cooperative o voltage dependence: dω/dt= α(δv) o pulse width dependence: dω/dt= λ(δt) o weight saturation: ω min < ω(t) < ω max weight dependent learning rate: β(ω,t) dω(t)/dt = β ω(t) ( 1 - ω(t)/ω max ) Logistic function ω p,d (t) = ω p,d (t 0 )+ ω max [ 1+ exp{-β(t-t 0 )} ] -1 β(ω,t) = K p,d ω(δv,t) ω(δv,t) = G(ΔV,n,Δt) 80 V pre pre pre V pre V post post post V post

81 Plasticity model Ziegler, Bartsch et al., IEEE TBioCAS 81 dω(t)/dt = β ω(t) ( 1 - ω(t)/ω max ) ω (t) = α(δv) λ(δt) G(t-1)

82 Plasticity model Ziegler, Bartsch et al., IEEE TBioCAS Potentiation (Set) 82 +ΔV Depression (Reset) -ΔV Pulse time Δt

83 Pattern recognition 83 LeCun et al., Proceedings of the IEEE, 86 (1998) (website: MNIST: hand writen digits of 250 hand writer

84 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 84 Querlioz et al., IEEE Transactions on Nanotechnology 12, 288 (2013). Memristive device digits Receptive field

85 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 85 Stochastic Input white t U t black Condition for positive pulse random number ε (0,1) Querlioz et al., IEEE Transactions on Nanotechnology 12, 288 (2013).

86 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 86 Leaky-Integrate-and Fire Neurons i(t)~ ω ij (t) N i V t v Mem > V th homeostasis Winner-take-it-all (WTA) N 1 N 2 N 3

87 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 87 STDP-based learning locality through proper thresholds positive pre-pulse U t Above threshold U th post-pulse t

88 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 88 STDP-based learning locality through proper thresholds negative pre-pulse U t Below threshold post-pulse t U th

89 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 89

90 Unsupervised learning network 90 Zahari, Ziegler et al., AIMS 2, 203 (2015). 93.3% Double barrier memristive devices Querlioz et al., IEEE Transactions on Nanotechnology 12, 288 (2013). TiOx-based devices

91 Unsupervised learning network 75% 91 Zahari, Ziegler et al., AIMS 2, 203 (2015). Au Nb x O y Al 2 O 3 Al Nb 60% Al TiOx Al Nb Al 2 O 3

92 Unsupervised learning network Zahari, Ziegler et al., AIMS 2, 203 (2015). 92 Device Performance Requirements: device variability (reliability, retention, fatigue, ) I-V nonlinearity defined threshold voltages device model - statistics of device parameters compatibility with Si-fabrication technology

93 Thanks to 93 Hermann Kohlstedt Rohit Soni Adrian Petraru Members AG Nanoelectronic Members FOR2093 Financial support by the DFG through FOR2093 is gratefully acknowledged.

94 94 FOR

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