Analog Control of Retainable Resistance Multistates in HfO2 Resistive

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Analog control of retainable resistance multi-states in HfO2 ReRAM Cecilia Giovinazzo, Jury Sandrini, Elmira Shahrabi, Oguz Tolga Celik, Yusuf Leblebici, and Carlo Ricciardi ACS Appl. Electron. Mater., Just Accepted Manuscript • DOI: 10.1021/acsaelm.9b00094 • Publication Date (Web): 09 May 2019 Downloaded from http://pubs.acs.org on May 9, 2019

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ACS Applied Electronic Materials

Analog control of retainable resistance multi-states in HfO2 ReRAM Cecilia Giovinazzo,∗,† Jury Sandrini,‡ Elmira Shahrabi,‡ Oguz Tolga Celik,‡ Yusuf Leblebici,‡ and Carlo Ricciardi∗,† †Department of applied science and technology (DISAT), Politecnico di Torino, Turin, Italy ‡Microelectronic Systems Laboratory (LSM), Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland E-mail: [email protected]; [email protected]

Abstract ReRAM technologies are nowadays a good candidate to overcome the bottleneck of Von Neumann architectures, taking advantage from their logic-in-memory capability and the ability to mimic the biological synapse behavior. Although it has been proved that ReRAMs can memorize multi-bit information by the storage of multiple internal resistance states, the precise control of the multi-states, their non-volatility and the cycle-to-cycle reliability are still open challenges. In this study, the analog resistance modulation of (Pt/HfO2 /Ti/TiN) devices is obtained and studied in response to different programming stimuli, linking the electrical response to the internal dynamics of the ReRAM cells. The resistance modulation during RESET operation is explained by the progressive dissolution of the conducting filament, whose switching kinetics is inspected in detail, describing the filament evolution during voltage sweep measurements and under the effect of 1 µs pulses. Exploiting the gradual nature of RESET process, which is an intrinsic property of our devices, a linear resistance modulation over the

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wide operating window of 103 is obtained by negative pulse ramping. The intermediate resistance states are characterized by small spatial and temporal variability and stable retention over time. To explore the synaptic long term plasticity properties, the resistance variation over 102 consecutive depression-potentiation cycles is presented and up to 15 discrete distinguishable states are defined through the evaluation of the maximum step-to-step variability. The linear resistance modulation over a wide resistance window coupled with the stable retention of intermediate states represent a fundamental step forward to enhance the HfO2 ReRAM performances in neuromorphic applications.

Keywords: ReRAM, Multi-state, Synapses, HfO2 , Switching

Introduction Large amount of data and complex computational operations have forced conventional Von Neumann architectures to a bottleneck, due to the limits in device scalability and data transfer rate between the memory and the processing unit. New generation technologies based on statefull logic and co-localization of storage and computing resources 1,2 can overcame these limits. In particular, neuro-inspired architectures are one of the most promising candidates, where synapse-like devices modulate the connection between neuron components by weight updating under spiking voltage. In this scenario resistive-switching random access memories (ReRAM), belonging to the wide family of memristor devices, have recently attracted big interest for their logic-in-memory capability 3,4 and their ability to emulate the synapse behavior. 5–8 A ReRAM cell is a two terminal electronic device whose memory properties are related to the retention of an internal resistance state, tunable by resistive switching between a high and a low resistance state (HRS, LRS) through the applied voltage stimuli. Among different ReRAM classes, oxide-based valence change memories (VCMs), consisting in simple structures, in which a metal oxide layer (e.g. HfO2 , TiO2 , Ta2 O5 ) 3,9–13 is sandwiched between 2


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two asymmetric electrodes, show excellent properties in terms of high density integration, 14,15 sub-nanosecond operational speed, 16? good memory retention 17 and low power consumption (≤0.1 pJ). 18,19 In VCM, the working principle behind resistance switching between HRS and LRS has been extensively studied by several works. 20–25 The phenomenon is related to the formation/rupture of an oxygen deficient conductive nano-filament (CNF) 26 in the oxide layer by oxygen exchange at the insulator/electrode interface and O2− ion migration under applied voltage. The SET process determines the transition from HRS to LRS due to CNF formation in correspondence of Vset , while the RESET process is responsible of the opposite transition and the CNF is ruptured at Vreset . In bipolar switching, SET and RESET occur in opposite voltage polarities. Beside the fabrication of bi-stable memories, which can switch between HRS and LRS states, it has been proved that the ReRAM resistance can be modulated in an analog way, achieving a multitude of separated resistance states. Since the moment in which Jo et al. 27 demonstrated the gradual ReRAM resistance tuning and the synaptic behavior of these devices in 2010, a growing interest in ReRAM-based neural networks, has been reported. 28 By analogy with the weights of biological synapses, the ReRAM resistance can be gradually modified by spiking pulse control in order to enforce or weaken the connection between two artificial neurons. 27 The long-lasting change in the connection strength is called long-term potentiation (LTP) for the resistance decrease and depression (LTD) for the antagonist process. 29 Various programming voltage schemes have been proposed in order to modulate the resistance transition in an analog way, defining a number of distinct intermediate resistance states. 30–35 However, one of the main current issues is to find a compromise between high resolution in the number of discrete resistance states and wide programming window, 36 i.e. interval of resistance states bounded by the LRS and HRS extreme values. In fact, the cycle-to-cycle resistance fluctuations, due to the intrinsic randomicity of the process and the non-ideality of physical devices, become dominant when the measured resistance are high (∼1 MΩ). Moreover, although artificial synapses usually show nonlinear response to pulse inputs, 37 this has high impact on the learning accuracy of

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the neural networks. 38,39 Therefore, a linear modulation during depression and potentiation operations is a fundamental request for the improvement of ReRAM-based neural network performances In this work, we inspect the analog resistance modulation of Pt/HfO2 /Ti/TiN ReRAMs by various input voltage schemes. Taking advantage of the extremely gradual nature of RESET in our devices, distinct retainable and uniform resistance multi-states are obtained on a wide programming window by control of negative voltage amplitude(Vstop ) and voltage pulse ramping. The conduction mechanism during RESET is investigated for DC and pulsed measurements, linking the internal device dynamics to the electrical response of the device. The correlation between gradual switching kinetics and CNF evolution offers a higher awareness on the control of resistance modulation, giving the opportunity to reduce the stochasticity of the process. Finally, the multi-level control is used to test the synaptic ability of our devices by analog pulse train depression and binary level potentiation cycles. Temporal variability, including resistance variation between consecutive steps and consecutive programming cycles, are studied.

Methods Stand-alone ReRAM cross-point devices are fabricated on a Si/SiO2 substrate, as presented in Figure 1a. The Pt bottom electrode (BE) is deposited by radio frequency (RF) magnetron sputtering, inserting a Ti adhesion layer. The BE patterning is performed through standard lithography and reactive ion etching (RIE), using Cl2 /Ar chemistry. Then, a Si-based passivation layer of 100 nm is grown by low pressure chemical vapor deposition (LPCVD) at 425◦ C and vertical interconnected accesses (VIAs) with the dimensions of 1 µm to 10 µm are patterned using photolithography and wet etching in buffered hydrofluoric acid (BHF), to define the memory active area (Figure 1b). A HfO2 and a Ti layers are used as active switching layer and oxygen reservoir, 40 respectively. Highly uniform 5 nm HfO2 film is

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(a)

(b)

TiN Ti (3nm) HfO2 (5nm) Pt Si-based

TE

Si/SiO2

tion

100μm

siva Pas

BE

Figure 1: (a) Schematic representation of the fabricated single-cell Pt/HfO2 /Ti/TiN ReRAM; (b) Optical image of the cross-point structures fabricated on a 1x1 cm die and micrograph enlargement by scanning electron microscope (SEM) on the 10 µm VIA of a single device. deposited by atomic layer deposition (ALD) at 200◦ C, and 3 nm Ti is deposited by DC sputtering at room temperature. Finally, a sputtered TiN layer is grown at room temperature as the top electrode (TE) without breaking the vacuum. TE patterning is done by means of photolithography and RIE process.

Results and discussion DC characteristics In order to define the main electrical properties of the (Pt/HfO2/Ti/TiN) ReRAM, the devices are tested through voltage sweep (DC characterizations) with biased TE and grounded BE. Figure 2a reports the I-V characteristic for 50 consecutive DC cycles. The cells are initially at high resistance state and a forming operation is conducted to trigger the switching. The presence of the Ti oxygen scavenging layer results in a considerable low forming voltage (∼2 V), which is an essential requirement for the realization of selector-free structures, 8 making this stack a suitable candidate for future crossbar-geometry realization. The

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(b) Vreset

1E-3 1E-4

Forming 50 Cycles

Vstop

1E-5

(c)

Vset

Count

1E-6 1E-7 1E-8

1E+7 1E+6 1E+5 1E+4 1E+3

Resistance (Ω)

(a)

Current (A)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-2

-1

0

1 2 Voltage (V)

3

4

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5

LRS HRS

0

50 40 30 20 10 0 -1.0

10

20 30 Cycle (n)

40

50

Vset Vreset

-0.5

0.0 0.5 Voltage (V)

1.0

1.5

Figure 2: ReRAM performances by voltage sweep stimulation: (a) initial forming (red) and I-V characteristic for 50 consecutive cycles (grey), (b) LRS and HRS values measured between 0 and 0.1 V, (c) SET and RESET voltage distribution. limitation of the current passing through the cell by setting the proper current compliance limit (Icc ) is required to prevent a fast degradation and a not reversible breakdown of the device. During the forming Icc is fixed at 150 µA. After forming, a bipolar resistive switching is obtained, with the SET process in positive polarity (0 → 2 → 0V, Icc of 150 µA) and the RESET in negative (0 → −2 → 0V). The switching parameters are extracted from the I-V characteristic analysis, reporting a stable HRS and LRS over cycles (Figure 2b) with a HRS/LRS ratio higher than 600. The distribution of the Vset and Vreset with respect to the mean values Vset mean '1 V and Vreset mean '0.7 V are presented in Figure 2c, resulting of ±0.2 V and ±0.1 V, respectively. The sharp distributions confirm the high device performance reliability. Moreover, the HRS/LRS ratio between HRS and LRS defines a wide window of values in which the HRS can be tuned by accurate control of electrical parameters. The I-V curves show a clear difference in the transient current during SET and RESET operations (Figure 2a). A sharp change in current is visible in correspondence of Vset when the resistance changes from HRS to LRS in positive polarity, while current gradually decreases in negative polarity. After the first abrupt change in correspondence of Vreset , the resistance gradually decreases to reach a deeper HRS value along with the Vstop value. In VCM cells, this asymmetrical behavior can be explained considering the different internal dynamics that 6


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occur during SET and RESET transitions. The SET process 20,21,24 begins with a nucleation step, in which the CNF formation takes place by migration of O2− ions under the applied voltage, and continue with a growth step, resulting in an increase of the filament lateral size modulated by Icc . When the CNF is formed, the current is subjected to an abrupt increase until the Icc is reached. At this point, the circuit components for current limitation (i.e. transistor or resistance) regulate the voltage across the sample. Therefore, the LRS value depends on filament size and can be modulated by Icc , while the abrupt current variation at Vset makes the SET process not suitable for the resistance modulation by positive voltage control. The RESET transition 21,25 is governed by temperature and electrical field. When the applied voltage is sufficiently high, the current flowing through the CNF induces an increase of internal temperature by Joule-heating, which facilitates Vö-O2− recombination and determines a partial annihilation of the CNF. Once the insulating gap is formed in correspondence of Vreset , the current is suddenly reduced and the temperature decreases. The result is a slow self-limiting carrier migration, which leads to a gradual increase of the gap dimension and HRS value. The maximum voltage value defines the final HRS. It has been widely accepted that HRS can be limited by the maximum applied RESET voltage amplitude Vstop . 32,41,42 However, the voltage stimuli duration can also play an important role on the control of the switching resistance. Therefore, it is important to evaluate the control of HRS by means of both RESET voltage sweep and pulse mode to have a clear understanding on the Reset kinetic mechanism.

HRS modulation by DC voltage sweep The study of RESET dynamics in DC voltage sweep mode allows to understand the filament rupture dynamics and the transport mechanism involved in the switching kinetics.

Ten

consecutive DC cycles have been performed for different Vstop values, varying from -2 V to -1.3 V (step of 0.1 V). Figure 3a reports a representative cycle for each Vstop . The HRS value changes over three orders of magnitude from 30 MΩ at Vstop of -2 V, to 100 kΩ for -1.3 V 7



(a)

(b)

1E-3

Current (A)

1E-4 1E-5

1E-7 1E-8

-2

-1

(c)

0 Voltage (V)

1

-0.9 V

-0.2 V

-2.0 V

TiN

TiN

TiN

Ti

Ti

Ti

TiOx

O

2-

Vö

2-2V -1.9V -1.9 -1.8V -1.8 -1.7V -1.7 -1.6V -1.6 -1.5V -1.5 -1.4V -1.4 -1.3V -1.3

1E-6

Pt

Vö

Vö

HfO2

Pt

Pt

2

(d)

1.6

~ 1.9 ~ 1.7

-12 ~ 2.0

1.2

0.8

0.8

1.0 0.6

0.4

~ 2.2

-14 ~ 2.8 -0.4

1.2

Junction Barrier (eV)

-10

1.4

Switching Distance (nm)

-8 ln(|Current|)

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0.4 0.2

0.0

-0.2

0.0

0.2 0.4 ln(|Voltage|)

0.6

0.8

1E3 1E4 1E5 1E6 1E4 1E5 1E6 Resistance (Ω) Resistance (Ω)

0.0

Figure 3: (a) I-V characteristic in logarithmic scale, a representative cycle for each Vstop is reported; (b) Graphical representation of the conduction mechanism and internal CNF dynamics during RESET; (c) RESET semi-cycle in ln(V)-ln(I) scale for a representative cycle with Vstop = −2 V, the consecutive resistance states are interpolated by linear fit and the slopes are reported; (d) Switching distance (blue) and Pt/HfO2 junction barrier (red) evaluation from Schottky-diode conduction mechanism formula. Vstop (further details in S2). The Vreset remains constant at ∼-0.7 V and is not influenced by the Vstop value. In fact, since the SET operation is kept at 2 V and 150 µA Icc for all the measurements, one can assume that CNFs with comparable dimensions are created over consecutive cycles, which require comparable Vreset values to be ruptured. During the forming process, the O2− migration from HfO2 is assisted by the positive bias. Due to the low energy required for Ti oxidation (∆G value of -883.3 kJ/mol), 43,44 the Vö concentration at the Ti/HfO2 interface increases and a thin layer of TiOx is formed at the interface region. The presence of the Ti scavenging layer define the formation of a conicshape CNF, with the larger part at the Ti/HfO2 interface. The rupture/reconstruction of 8


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filament takes place at the narrow part close to the inert BE. 25 The formation of a conductive path in the oxide alters the initial potential-barriers created by the junction of materials with different work functions. 23 The Ti/HfO2 contact can be described as an Ohmic-like contact due to high Vö concentration, while the HfO2 /Pt can be considered as a Schottkylike contact, because of the narrow filament size and the high Pt barrier potential. Figure 3b shows a schematic representation of the CF evolution during the RESET. When a negative voltage is applied, the ion drift is modulated by the TiOx reduction, until the Vö-O2− recombination near the narrow CNF side creates the insulating gap. The CNF broken part increases the potential barrier at HfO2 /Pt interface, forcing the carrier transport through the oxide. Therefore, the ruptured CNF region can be considered as a bottleneck point, in which the electron transport inhibition through the potential barrier is related to thickness and width of the gap. 45 The modification of the CNF region is evident in the representation of the RESET semi-cycle in ln(|I|)-ln(|V |) scale (Figure 3c). After the first abrupt change at Vreset , one can observe that quantized resistance states are achievable by increasing the maximum negative applied voltage, demonstrating the gap amplitude increase. Such steplike function is typically related to the existence of preferred atomic-scale re-arrangements of the filament. 46,47 Moreover, the linear fits on the multi-level HRS values reported in Figure 3c show slopes of ∼2, revealing that the transport mechanism is attributed to the high number of injected carriers rather than the thermally generated carriers from the bulk oxide. 48 In order to further understand the conduction mechanism responsible for charged carrier transport, different electrode-limited conduction mechanisms have been evaluated. Among them, the best accordance between data and conduction model is obtained for the Schottky transport. p The RESET semi-cycles for the different Vstop are represented in ln(|I|)- |V | scale and the HRS is fitted (fitting procedure described in S3), considering the Schottky equation: " JSD = A∗ T 2 exp

−q(ΦB −

9

p

qE \ 4π0 r ) kT


# (1)


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Where A∗ is corrected Richardson’s Constant, q the elementary charge, r is the oxide permittivity (r = 25 for HfO2 49 ), T is the temperature during the switching operations 21 and ΦB is the barrier height. The current flux is evaluated depending on the active area of the device defined by the VIA opening (5 µm) and the electric field is defined as E = V /dSW , where the switching distance (dSW ) is the portion of CNF that has been broken during RESET. From the linear fits of the HRS, ΦB and dSW are extracted through intercept and slope respectively, as: kT · intercept q

(2)

q3 1 · 2 (kT ) 4π0 r slope2

(3)

φB = − dSW =

In Figure 3d, the φB and dSW values are plotted with respect to the measured HRS at different Vstop . The potential barrier undergoes a small increase from '1 eV for HRS values in the order of 10 kΩ to 1.1 eV for HRS in the order of 10 MΩ, which is in line with the range of value reported in literature 49,50 . The constant value of barrier potential demonstrates that the resistance variation is determined by the CNF evolution and not by a structural variation at Pt/HfO2 interface. The dSW increase with HRS from 0.6 nm for the -1.3 V Vstop to 1.2 nm for the -2 V Vstop is consistent with the correlation between the maximum applied negative voltage and the insulating gap dimension. Moreover, the saturation in dSW trend is a confirmation of self-limiting migration process due to the temperature reduction after the RESET.

HRS modulation by pulses The impact of time on the energy provided to the system for RESET can alter the switching kinetics, resulting in partial not-retainable states. To inspect the response of (Pt/HfO2 /Ti/TiN) devices to pulse stimulation, different tests were performed. In particular the effect of pulse timing, positive voltage amplitude (Vpos ) and negative voltage amplitude (Vneg ) are studied (Figure 4) through endurance pulse measurements. For the evaluation of each parameter 10


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(a)

1E-7

Pulse Width Timing (s)

1E-6

5E-6

1E-5

1E-4

Resistance (Ω)

1E+7 1E+6 1E+5 1E+4 1E+3

2 E3

0

(b)

4 E3 6 E3 Cycle (n)

8 E3

Positive Voltage Amplitude (V)

1

1.1

1.2

1.3

1 E4

1.4

Resistance (Ω)

1E+7 1E+6 1E+5 1E+4 1E+3

0

(c)

3 E3 2 E3 Cycle (n)

1 E3

-1.9

4 E3

Negative Voltage Amplitude (V)

-1.8

-1.7

-1.6

5 E3

-1.5

1E+7 Resistance (Ω)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E+6 1E+5 1E+4 1E+3

0

1.5 E3

3 E3 4.5 E3 Cycle (n)

6 E3

7.5 E3

Figure 4: Pulse modulation effect on the resistance values: (a) Pulse width variation endurance: pulse width is decreased from 100 µs to 100 ns, reading every 50 cycles,. Vpos and Vneg are kept constant at 1.4 V and -2 V, respectively; (b) Vpos variation endurance: Vpos is increased from 1 to 1.4 V with 0.1 V steps and Vneg is fixed -2V, reading every 50 cycles; (c) Vneg variation endurance: Vpos is fixed at 1.4 V and Vneg varies from -2 to -1.4 V with 0.02 V steps, reading every 5 cycles.

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effect, the endurance measurements consist of consecutive positive (SET) and negative (RESET) pulses, in which the Icc in positive polarity is limited by an external transistor at 150 µA (setup details in S1). Resistance reading is performed by a voltage ramp between 200 mV and 250 mV and reading periodicity is user-defined. Figure 4a shows the impact of pulse width on the HRS and LRS. The two resistance states do not show any remarkable dependency with respect to the pulse duration. Only a slight HRS reduction is visible at small pulse range of 100 ns, which is caused by a pulse shape distortion for high frequency input stimuli in our measurement setup. For the pulse voltage variation analysis, the pulse width is fixed at 1 µs. Concerning the effect of voltage amplitude, HRS and LRS trends are slightly influenced by Vpos variation from 1 V to 1.4 V (Figure 4b), while a strong impact of Vneg on HRS is visible (Figure 4c). Different distinguishable HRS multi-states in the wide operating window of ∼ 103 (30 MΩ - 10 kΩ) can be achieved by the precise control of pulse negative amplitude. A voltage variation as small as ∆V≤0.05 V is sufficient to determine a resistance change, making these devices extremely interesting for the fine control of several multi-states, whose repeatablility and non-volatility are fundamental requirements. To evaluate the repeatability of the multi-state, an endurance test is considered. During the test, a set of 250 cycles with a reading periodicity of 5 is performed for each Vneg from -2 V to -1.3 V with steps of 0.05 V. The cumulative probability distributions for the 50 HRS for each Vneg are reported in Figure 5a, showing low cycle to cycle variability, which decreases for lower HRS. The non-volatility of the multi-states programmed by pulses is proved by retention measurements for six intermediate states corresponding to -1.9V, -1.8 V, -1.7 V, -1.6 V, -1.5 V and -1.4 V (Figure 5b). The states have a good stability over time and no drift is registered in 2 hours of measurements. Moreover, the retention properties of the intermediate states do not show a dependency on the resistance value. To study the filament evolution under the effect of negative pulses, the current during the negative pulses with different Vneg has been measured. Figure 5c shows the current transient trend as a function of time. On the pulse rising, the device is in LRS and the current

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increases accordingly to the voltage amplitude until the RESET point is reached and it is subjected to a sharp change. One can notice that the |Vneg | increase leads to a current change which is more abrupt and to a deeper HRS, while gradual resistance variation is visible in correspondence of pulses with small amplitude. In Figure 5d the currents I0 and I8µs as a function of Vneg are reported, where I0 is evaluated as the maximum current reached during the pulse rise transient and I8µs is the current measured at 8 µs, when the RESET operation is completed. Since the RESET process is regulated by two main factors, which are temperature and electric field, it can be simplified in two consecutive regimes. 11,32 During the early stage of RESET, the pulse rise determines a fast increase in temperature inside the filament, which is proportional to the current passing through the device. The maximum in transient current (I0 ) shows a direct proportionality to the negative voltage absolute value, as it is visible in Figure 5d. The rupture point of conic shape filament in the thinner point and the gap formation are modulated by temperature. When the amplitude of pulses is small and the temperature does not reach high values, the ion lower diffusion determines a partial rupture of the CNF, where a part of the Vö does not recombine and remains in the filament region close to the BE. The current passing through the partially ruptured filament remains higher also when the RESET operation is finished, as it is visible in the change of I8µs , whose increase corresponds to the change of regime. When the thermal energy provided by the pulses is higher, a neat gap with fewer defects in CNF area is obtained. The gap amplitude increases for higher Vneg due the ion drift and the Vö- O2− recombination along the filament axis. From Figure 5d, one can notice that the current I8µs is initially high and a sudden decrease is registered when the gap becomes neat. The HRS evolution trend as a function of Vneg is inspected considering the endurance measurement represented by descriptive statistics in Figure 5e. Two different regimes in HRS gradual change are distinguishable: (i) a linear resistance variation in the Vneg interval between -2 V and ∼ -1.65 V, in which the HRS passes from 30 MΩ to 100 kΩ, and (ii) an asymptotic decrease from ∼ -1.6V to -1.3V, where the resistance tends toward 10 kΩ. Fig-

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(a)

-1.30 V

-1.75 V

-2.00 V

(b)

-1.4 V

-1.7 V

-2.0 V

1E+7

0.8

Resistance (Ω)

Cumulative probability

1.0

0.6

1E+6

0.4

1E+5

0.2

1E+4

0.0

(c)

1E+4

1E+5 1E+6 Resistance (Ω)

1E+7

0 1E+3

Current (A)

-2E-4 Current (A)

I8μs

-6E-4

-2.5V

-8E-4

I0 -2

0

(e) 1E+7 1E+6 1E+5

Linear Variation

2

8E-2 6E-2 4E-2 2E-2

-1.7V

4

6 8 Time (μs)

10

12

0 14

-1.50

(f)

Median, 1st and 3rd quartiles HRS mean value

Asymptotic Exponential Decrease

3E+7

Resistance (Ω)

-1E-3

7E+3

Current I0 Current I8μs

1E-3

-4E-4

3E+3 5E+3 Time (s)

(d)

0

Resistance (Ω)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1E+4

y=a+b*x

R = 0.9965 2

y=a-b*c^x

2E+5

R = 0.8927 2

2E+7 1E+5 1E+7

0

-2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 Reset Pulse Amplitude (V)

-1.75 -2.00 -2.25 -2.50 Reset Pulse Amplitude (V)

Linear Variation

Exponential Decrease

-2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 Reset Pulse Amplitude (V)

0

Figure 5: (a) Cumulative probability distribution, during the measurement Vneg decreases from -2 V to -1.3 V and pulse width is fixed to 1 µs; (b) retention on 6 different HRS multistates, reading is performed every 2 minutes; (c) current evaluation under different reset pulses, evaluated by the insertion of a series resistance in the testing setup (SI 1).The choice of 10 µs pulse duration is defined to minimize the parasitic effects which occur in the I measurement for faster pulses; (d) Trends for the maximum current (I0 ) and the current after reset (I8µs ) measured in correspondence of 8 µs respect to the Vneg ; (e) Descriptive statistics for 250 consecutive cycles for each Vneg , with a reading period of 5; (f) Mean values and relative errors for each Vneg extracted from Figure (e). Two regimes are distinguishable: a linear trend (red) in the range [-2;-1.65] V and a decreasing exponential trend (blue) in the range [-1.6;-1.3] V.

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ure 5f displays the linear and exponential fits performed on the mean value and relative errors extracted on 50 HRS values for each Vneg data set.

HRS modulation by pulse trains 1.50 0.75 0.00 -0.75 -1.50 -2.25

(b) Pulse Amplitude

1E+7

Resistance (Ω)

Pulse Voltage(V)

(a)

1E+6 1E+5 1E+4

0

20

(c)

40 60 Pulse (n)

1E+3

80

dep pot

0

82

163

(d)

1E+7

244 325 Pulse (n)

406

Resistance (Ω)

1E+7

Resistance (Ω)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E+6

1E+6

1E+5

1E+5

1E+4 Read Resistance

1E+3 0

20

first-third quartiles median

1E+4

40 60 Pulse (n)

80

0

10

20

30

40 50 Pulse (n)

60

70

80

Figure 6: (a) Schematic representation of the voltage stimuli used for a DPC, consisting in 81 negative pulses (Vneg from -1.2 V to -2 V with step 0.01 V and pulse width of 1 µs) and one positive pulse (Vpos of 1.4 V and pulse width of 100 µs); (b) First six representative consecutive DPCs of the 100 cycles used in Figure(d); (c) Example of resistance gradual control during the DPC, reading is performed after each pulse; (d) Statistical analysis on 100 DPC, for a total of 8.2×103 consecutive pulses. In the graph, the grey dots correspond to the median value for each resistance measurement, while the red area encloses the values between the first and third quartiles. Taking advantage of the precise control of resistance by negative pulse amplitude modulation, the plasticity properties of our devices were tested by pulse train stimulation. In biology, long-term changes in synaptic strength (plasticity) involve the migration of Na+ and Ca2+ ions by electrochemical reactions due to the neuron excitatory and inhibitory spikes. 51 In this case, instead, the resistance change takes place through the modulation of the CNF gap inside the HfO2 by O2− ions migration under electrical stimuli. In particular, depres15



sion is performed applying a train of pulses with increasing amplitude (-1.2 V → -2 V, step 0.01 V), while potentiation is performed by applying a positive pulse of 1.4 V, as represented in Figure 6a. After each pulse the resistance is measured by a reading ramp at 0.1 V and the depression-potentiation cycle (DPC) is repeated. Figure 6c shows a representative DPC, where an analog modulation of resistance is obtained during the depression step, while a digital control is adopted for the potentiation. Negative voltage amplitude, voltage range and steps between consecutive pulses were targeted in order to reach the optimum in resistance control and DPC to DPC variability. With a view to the neuromorphic applications, one could comment that the unidirectional analog resistance control implies constraints related to the implementation of bi-directional updates. However, online training is still attainable, by the coupling of two memory devices in order to have potentiation and depression. Similar architectures have been widely employed in the development of phase change memories (PCM)-based networks. 52 The device coupling determines a slight reduction in the scalability of the neural network, but guarantees complete symmetricity in the device training. Consecutive DPCs were performed in order to study the analog resistance variability over several depression procedures. The resistance evolution was evaluated over 100 consecutive DPCs, for a total of 8.2×103 pulses (the first six depression-potentiation are reported as an example in Figure 6b). A better understanding of cycling impact on resistance variability is achieved by the evaluation of data dispersion around the median value of resistance on 100 reading performed on consecutive depressions. The resistance distribution can be found in Figure 6d. The minor resistance variability is recorded in the region between pulses #65 and #81, which corresponds to the Vneg interval of [-1.85;-2] V, indicating that the maximum gap saturation region is reached. A crucial point in the device performance is the definition of the number of achievable states in the programming window. To this purpose, the resistance variation between two consecutive pulses is evaluated as ∆R = Rpulsei − Rpulsei−1 . From Figure 7a), in which the ∆R values depending on the resistance are presented, it is evident that the higher pulse

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(a)

(b) 3.2E+7

2E+6

1E+6

1E+4

2.4E+7

SUB-THRESHOLD REGION

2.0E+7

45E-6 LINEAR REGION

37E-6 32E-6

1.6E+7

22E-6

1.2E+7 8.0E+6

SATURATION REGION

4.0E+6

0

52E-6

Resistance Conductance

2.8E+7 Resistance (Ω)

Resistance Variation (Ω)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


7E-6 0

0 1E+5 1E+6 1E+7 Resistance (Ω)

15E-6

Conductance (S)

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0

20

40 60 Pulse (n)

80

Figure 7: (a) Resistance variation (∆R) as a function of the read resistance (Rpulsei ) on the resistance mean values over 100 consecutive DPCs; (b) Resistance (red) and Conductance (blue) trend in linear scale. to pulse variability is registered in the 10-20 MΩ region. For higher resistance values ∆R decreases, indicating that the saturation region has been reached and the HRS has become constant. The maximum obtained ∆R variation of 2 MΩ defines the resolution between different resistance states of our devices. Therefore, considering a resistance window of ∼30 MΩ, minimum 15 significantly distinct resistance levels are achievable. One should mention that this method provides a conservative estimation of the pulse to pulse variability, which can be improved by further calculation in order to reduce the discrete level dimension. 36 Finally, it is interesting to compare the resistance and conductance trend as a function of the pulse number in linear scale. Consistently to the proposed pulse CNF kinetics, in Figure 7b the three resistance regimes are distinguishable: (i) sub-threshold region, in which the filament is partially broken and the resistance decrease rate is small; (ii) linear region, where the major analog resistance dynamics is centered; and (iii) saturation region, where the gap dimension saturates. The resistance sub-threshold region catches particular attention for the conductance trend: the highest density of discrete conductance levels is visible, in accordance with the correspondence between fine analog conductance control and dimension of the programming window. In fact, several works report that the number of discrete conductance states is inversely proportional to the dynamic range of variation. 36,53 In this interval of values of

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reduced resistance window (102 ), the conductance presents a linear variation, which is fundamental request to obtain robust learning algorithms for memristor-based neural network applications. 7,54 Conversely, the region where the conductance reaches the saturation value corresponds to the highest resistance variation, characterized by a linear regime with more than 10 different resistance states in the range 2-26 MΩ. The control of CNF gap dimension defines a linear resistance modulation in this region, where the defined states can be used for multi-bit storage information with low power consumption. To summarize, a quantitative comparison with similar literature works is reported in Table 1, where most used figures of merit for gradual resistance control in HfOx-based ReRAM are listed: operating window, linear control, retention of intermediate states, and depression pulse amplitude (to be used as an index of power consumption). As it can be clearly seen, devices exhibiting large operating windows are typically bad performing in terms of retention of intermediate states and power consumption. Conversely, literature works with high retention and low power consumption exhibit limited operating window and no linear control. Therefore, the here reported findings represent an important achievement in the perspective of low power neuromorphic applications and multi-bit storage. Table 1: comparison for the performances in gradual resistance control for metal-oxide based devices, with particular focus on HfOx-based devices, considering the most used figures of merit (i.e. operating window, linear resistance control, retention of intermediate states and power consumption).

32 35 53

55 37 34 36

this work

device depression stuck stimuli width HfO2 ramping 200 ns HfO2 /Ta ramping 100 ns HfO2 /Ti identical 1-100 µs +Al2O3 100 µs HfO2 ramping 100 µs HfO2 /Al:TiO2 identical 70 ms Alx Oy /TiO2 ramping 100 ns HfO2 /Ti identical 100 µs HfO2 /Ti ramping 1 µs

pulse amplitude -2 to -4.1 V -1.05to-1.17 V -1.1 V -1 V 1 to 1.6 V -3 V 1 to 2 V -0.7 V -1.2 to -2 V

18

resistance operating window range 103 1kΩ-30 MΩ 4 0.6-2.5 kΩ 10 5-20 kΩ 3 15-50 kΩ 50 0.2-10 kΩ 4 0.7-2.5 kΩ 20-120 kΩ 50 0.7-2.5 kΩ 4 2 kΩ-35 MΩ 103


linear retention control inter.states yes only in DC no 104 s no no yes no no no yes no 8h no 103 s yes 2h

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Conclusion In this work, the analog resistance modulation for (Pt/HfO2 /Ti/TiN) devices was explored under the effect of different input stimuli and correlated to the internal dynamics responsible of the switching. In particular, the gradual nature of RESET process for our devices suggested the control of the negative voltage amplitude, to obtain the best response in terms of number of states and operating window dimension. Fifteen distinct states over a resistance window of 103 were achieved, with good cycle-to-cycle and device-to-device reliability. The intermediate states show narrow distribution over consecutive programming pulses, linear variation and non-volatility. Through the study of DC RESET dynamics for different Vstop values, a switching kinetics based on the formation/rupture of a Vö based CNF was proposed, which is characterized by a conic shape filament with the narrower part at the Pt/HfO2 interface. Schottky mechanism defines the carrier transport inside the device during RESET, indicating that the increase of the voltage amplitude results in an increase of the insulting gap dimensions from 0.6 nm to 1.2 nm depending on Vstop . The study was then extended by considering pulse modulation and the impact of internal temperature and electric field on the HRS value. Three different regimes for resistance analog variation were defined, which correspond to the sub-threshold, the linear and the saturation regions. The two edge regimes are related to not complete filament rupture and maximum gap creation, respectively, while in the central region the resistance can be modulated linearly. Finally, analog depression by a train of 81 pulses and binary level potentiation cycles demonstrated the synaptic ability of our devices. An estimation of the number of discrete resistance states, based on the maximum R variability between consecutive pulses, and the DPC to DPC variability are analyzed considering 102 consecutive DPC. The obtained linear variation through a wide operating window, the good reliability and stability over time of the intermediate states, and the repeatability on a high number of consecutive depressions are among the main current requests for the realization of strong and reliable neuron-inspired technologies.

19



Acknowledgement The authors thank the staff of the center of micro-nano technology (CMi) at the EPFL, for providing technical support during the device fabrication. The authors acknowledge also Mr. Igor Krawczuk for the development of the testing code used during the pulse measures.

Supporting Information Available PDF file, including: Electrical measurement setup, HRS estimation for different Vstop values, fitting procedure for the DC cycles.

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Analog Control of Retainable Resistance Multistates in HfO2 Resistive

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