# Intrinsic RESET speed limit of valence change memories

M. von Witzleben  Institut für Werkstoffe der Elektrotechnik 2, RWTH Aachen
University, Sommerfeldstraße 24, D-52074 Aachen, Germany  Peter Grünberg
Institut 7, Forschungszentrum Jülich and JARA-FIT, Wilhelm Johnen Straße,
D-52428 Jülich, Germany  Corresponding author<EMAIL_ADDRESS>S.
Wiefels  Peter Grünberg Institut 7, Forschungszentrum Jülich and JARA-FIT,
Wilhelm Johnen Straße, D-52428 Jülich, Germany  A. Kindsmüller  Institut für
Werkstoffe der Elektrotechnik 2, RWTH Aachen University, Sommerfeldstraße 24,
D-52074 Aachen, Germany  P. Stasner  Institut für Werkstoffe der
Elektrotechnik 2, RWTH Aachen University, Sommerfeldstraße 24, D-52074 Aachen,
Germany  F. Berg  Institut für Werkstoffe der Elektrotechnik 2, RWTH Aachen
University, Sommerfeldstraße 24, D-52074 Aachen, Germany  F. Cüppers  Peter
Grünberg Institut 10, Forschungszentrum Jülich and JARA-FIT, Wilhelm Johnen
Straße, D-52428 Jülich, Germany  S. Hoffmann-Eifert  Peter Grünberg Institut
10, Forschungszentrum Jülich and JARA-FIT, Wilhelm Johnen Straße, D-52428
Jülich, Germany  R. Waser  Institut für Werkstoffe der Elektrotechnik 2, RWTH
Aachen University, Sommerfeldstraße 24, D-52074 Aachen, Germany  Peter
Grünberg Institut 7, Forschungszentrum Jülich and JARA-FIT, Wilhelm Johnen
Straße, D-52428 Jülich, Germany  Peter Grünberg Institut 10, Forschungszentrum
Jülich and JARA-FIT, Wilhelm Johnen Straße, D-52428 Jülich, Germany  S. Menzel
Peter Grünberg Institut 7, Forschungszentrum Jülich and JARA-FIT, Wilhelm
Johnen Straße, D-52428 Jülich, Germany  U. Böttger  Institut für Werkstoffe
der Elektrotechnik 2, RWTH Aachen University, Sommerfeldstraße 24, D-52074
Aachen, Germany

###### Abstract

During the last decade, valence change memory (VCM) has been extensively
studied due to its promising features, such as a high endurance and fast
switching times. The information is stored in a high resistive state (logcial
‘0’, HRS) and a low resistive state (logcial ‘1’, LRS). It can also be
operated in two different writing schemes, namely a unipolar switching mode
(LRS and HRS are written at the same voltage polarity) and a bipolar switching
mode (LRS and HRS are written at opposite voltage polarities). VCM, however,
still suffers from a large variability during writing operations and also
faults occur, which are not yet fully understood and, therefore, require a
better understanding of the underlying fault mechanisms. In this study, a new
intrinsic failure mechanism is identified, which prohibits RESET times
(transition from LRS to HRS) faster than 400 ps and possibly also limits the
endurance. We demonstrate this RESET speed limitation by measuring the RESET
kinetics of two valence change memory devices (namely Pt/TaOx/Ta and
Pt/ZrOx/Ta) in the time regime from 50 ns to 50 ps, corresponding to the
fastest writing time reported for VCM. Faster RESET times were achieved by
increasing the applied pulse voltage. Above a voltage threshold it was,
however, no longer possible to reset both types of devices. Instead a unipolar
SET (transition from HRS to LRS) event occurred, preventing faster RESET
times. The occurrence of the unipolar SET is attributed to an oxygen exchange
at the interface to the Pt electrode, which can be suppressed by introducing
an oxygen blocking layer at this interface, which also allowed for 50 ps fast
RESET times.

##  1 Introduction

Among other emerging memory technologies, valence change memory (VCM) can not
only be used as binary storage class memory, but also to perform in-memory
calculations or to realize neuromorphic applications [1, 2, 3, 4]. In the
binary mode, the information is encoded in a high and a low resistive state
(HRS and LRS). These two states can be programmed with electrical stimuli. The
transition from the HRS to LRS is referred to as SET and the opposite
transition as RESET. A VCM device usually consists of a mixed electronic-ionic
conducting layer (e.g. TaOx or ZrOx), sandwiched between two asymmetric
metallic electrodes [5, 6, 7, 8]. One of the two electrodes is inert (e.g. Pt)
and referred to as active electrode, whereas the opposite electrode is oxygen
affine (e.g. Ta). The devices are programmed by applying electrical stimuli,
during which an n-conducting filament consisting of mobile donors is either
formed (SET) or ruptured (RESET). Spectroscopic studies have identified these
mobile donors as oxygen vacancies [9, 10, 11, 12, 13]. Especially for TaOx-
based devices also a movement of metallic cations was observed [14, 15, 16].
During the SET, a negative voltage is applied to the active electrode
(attracting mobile donors) and a positive voltage during the RESET (repelling
mobile donors). As the voltages required for the SET and RESET have opposite
signs, this corresponds to a bipolar switching mode.

For the binary switching mode, a high endurance of up to 1012 cycles [17, 18]
and writing times below 1 ns[19, 20, 21, 22, 23, 24] have been reported. A
successful market launch also requires high storage densities and,
consequently, the integration of VCM devices into 3D structures [25]. Due to
the presence of Joule heating during the SET [26, 27] and during the RESET
operation [28], the writing time depends strongly non-linearly on the applied
voltage[29, 30]. This non-linearity allows VCM devices to overcome the
voltage-time-dilemma[31], which describes the necessity for high data
retention during the read-out (at low voltages) and fast writing times (at
high voltages) [32]. Programming VCM devices with shorter electrical stimuli
also enhances the devices’ endurance [33, 34]. Calculations and simulations
show that for nanoscale devices faster writing times of 1 ps are possible
[35]. Sub-nanosecond switching times are still realizable, if the VCM devices
were integrated into nanoscale crossbar array structures [36]. Also, first
neuromorphic applications have been demonstrated on a sub-nanosecond
timescale: Ma et al. recently demonstrated spike timing-dependent plasticity
(STDP) in memristive devices with 600 ps pulses [37]. Concepts of GHz deep
neural networks were developed, which are potentially faster than today’s CPUs
and GPUs by a factor of 30,000 [38]. Most applications in the GHz regime
require, consequently, fast writing times. So far, the speed limit was always
attributed to the electrical charging of the devices, assuming that the
intrinsic speed limit is only limited by the attempt frequency of the mobile
donors in the THz domain [35].

Recently, we have shown that 50 ps fast SET times can be achieved for TaOx\-
and ZrOx-based VCM devices [39], which corresponds to the limitation of the
experimental setup. We also demonstrated that the SET kinetics are mainly
delayed by the electrical charging time in the sub-nanosecond regime and not
by intrinsic processes, such as the migration of ions or the heating of the
filamentary region [40]. The fast heating results from the narrow filament,
which has only a diameter in the range from 1 nm to 3 nm [41]. While the SET
kinetics have been studied quite extensively, studies investigating possible
intrinsic RESET speed limits are rare. Most studies show only 10 or fewer
successful RESET operations [21, 19, 20] and are not discussing possible RESET
speed limitations. Only Wang et al. studied RESET kinetics in dependence on
the applied voltage in the sub-nanosecond regime and observed a lower change
in resistance at shorter pulse widths than 800 ps [22]. At pulse widths below
200 ps the VCM device switched randomly between the HRS and LRS. They explain
this observation with a lower heating of the filamentary region during the
RESET at shorter pulse widths than 800 ps. Their argumentation, however, does
not account for the random switching between the LRS and the HRS.

In this study, we propose a different failure mechanism limiting the RESET
kinetics in the sub-nanosecond regime: For this purpose, we focus on the RESET
kinetics in the regime from 50 ns to 50 ps and show that they are
intrinsically limited by the presence of a unipolar switching mode [42, 43].
Different to previous studies, we also acquired a much larger dataset to
demonstrate the reproducibility of successful RESET operations. At slower
timescales (above 700 ps) the RESET kinetics depend exponentially on the
applied voltage, which was already demonstrated in other studies [28, 44, 45,
46, 47]. By increasing the applied voltage we could successfully reset the
TaOx-based device within 670 ps at a voltage of 1.6 V and the ZrOx-based
device within 480 ps at an voltage of 1.8 V. At higher voltages, the devices
could not be driven to the HRS. Instead of an increase in resistance, a
unipolar SET could be observed, decreasing the device’s resistance and,
thereby, preventing faster RESET times.

This unipolar switching mode has already been observed for TaOx\- [48] and
ZrOx-based devices [49], but has never been considered as failure meachanism
for neither the RESET kinetics, nor the endurance. It can be triggered by
applying a positive voltage to the active electrode, with a higher amplitude
compared to the RESET. This could result in a higher heating of the
filamentary region than during the bipolar SET and RESET, which in turn could
initiate thermo-diffusion of the mobile donors (also referred to as
thermophoresis) [50]. To protect the device from damage, a current compliance
is crucial during the unipolar SET, which also exhibits abrupt threshold
switching. This switching mode was strongly investigated in the years up to
2013 in the hope of achieving a similar performance as for the bipolar
switching mode. However, the current compliance to achieve the unipolar SET,
has to be in the range of 1 mA [51], which increases the power consumption and
the devices’ degradation during cycling. To our knowledge, the highest
measured endurance of a unipolar switching mode amounts to only 106 cycles
[52], being far worse than the endurance of the bipolar switching mode (1012
cycles [17]). As this mode prohibits faster RESET times and only achieves a
poor performance with regard to power consumption and endurance, and also
limits the writing time, it constitutes a failure mechanism.

The kinetics of this unipolar SET are also investigated in the time regime
from 250 ps to 50 ps. We demonstrate that this unipolar SET event can be
conducted within 50 ps. From the RESET and unipolar SET kinetics, we derive
voltage programming windows, from which the intrinsic RESET speed limitation
can be derived. Finally, we suppressed the oxygen exchange at the Pt
electrodes with a 1.0 nm thin Al2O3 layer, which also allowed for 50 ps fast
RESET times for both devices, which is - to our knowledge - the fastest
reported RESET time of redox based random access memories (ReRAMs).

##  2 RESET kinetics

The RESET and unipolar SET kinetics measurements were conducted on a
Pt/TaOx/Ta and a Pt/ZrOx/Ta device. Both devices have a size of $2\times 2$
µm2 and were also used in [39], showing that the SET operation can occur
within 50 ps. The 30 nm thick Pt bottom electrode serves as active electrode.
The film thickness of the TaOx and the ZrOx amounts to 5 nm and the film
thickness of the Ta top electrode to 20 nm. Further information are given in
the methods section. In recent publications, we have shown that devices with
these material stacks have an endurance of at least 106 cycles [53, 54].

(a)

(b)

(c)

Figure 1: (a) Illustration of experimental setup. The pulse generator is
connected to the AC port (orange) of the bias tee and the SMU to the DC port
(green). The combined output of the bias tee (DC + AC) is connected to the Pt
bottom electrode of the VCM device. The current response is measured with an
oscilloscope, connected at the Ta top electrode. (b) Measurement procedure to
determine the RESET kinetics in the range from 50 ns to 400 ps. Read
operations are indicated in blue, SET operations in green and RESET operations
in red. All voltages are applied to the Pt active electrode. The green and
orange shaded areas mark the part measured at the DC and the AC port of the
bias tee, respectively. (c) I(V) characteristics of both devices (sweep rate:
0.5 V/s). Reprinted from [39], with the permission of AIP Publishing.

The experimental setup is sketched in Fig. 1(a) and is explained in detail in
[39]. A pulse generator is connected to the alternating current (AC) port and
a source measure unit (SMU) to the direct current (DC) port of a broadband
bias tee. The combined DC + AC port of the bias tee is connected to the Pt
bottom electrode of the VCM device, to which all indicated voltages in this
paper were applied. Finally, the current response is measured with a real-time
oscilloscope at the Ta top electrode. More information on the experimental
setup is given in the methods section. The I(V)-characteristics of both
devices are shown in Fig. 1(c).

To achieve proper impedance matching, both devices were integrated into
coplanar waveguide (CPW) structures, consisting of three parallel stripes
(ground-signal-ground, GSG). These CPW structures have gained more attention
in recent years, as they can be used to realize radio frequency (RF) switches
with memristive devices [55, 56]. Recently, we have shown for the TaOx-based
device that the electrical charging occurs within less than 80 ps, if the
device is integrated in a proper CPW structure [40]. The scattering parameters
of both devices are shown in the supplementary Fig. S1. For these scattering
parameters the devices’ charging times were derived in the supplementary Fig.
S2, showing that the ZrOx-based device can even be charged within less than 70
ps.

The measurement procedure to determine the RESET kinetics on the timescale
from 50 ns to 400 ps is depicted in Fig. 1(b). At the beginning of every
cycle, the devices were driven to the LRS (ranging from 1.0 k$\Omega$ to 3.0
k$\Omega$) by using a voltage sweep with an amplitude of -1.2 V at a sweep
rate of 0.5 V/s. To protect the devices from damage a current compliance of
100 µA was used. The devices’ resistance was measured at a voltage of -0.2 V
before and after the application of the pulse and is referred to as
$R_{\mathrm{PRE}}$ and $R_{\mathrm{POST}}$, respectively. The RESET pulses’
amplitudes were adjusted between 1.2 V and 1.6 V111This is the effective pulse
voltage seen by the device. The pulses emitted by the pulse generator only
have half the amplitude. As the 50 $\Omega$ transmission line is terminated
with a high ohmic VCM device (even the resistance of the LRS is much larger
than 50 $\Omega$), the voltage at the device effectively doubles. This is due
to the overlap of incoming pulse and the reflected pulse at the VCM device
(see also supplementary section S.1 or [40]). At the end of each cycle, the
device was driven to the HRS by applying a voltage sweep with an amplitude of
1.6 V at a sweep rate of 0.5 V/s. The pulse width was reduced with every
increase in amplitude to reduce the stress on the device.

(a)

(b)

(c)

Figure 2: (a) Current response to a pulse with an amplitude of 1.6 V, applied
to the TaOx-based device. The horizontal dotted lines mark the maximum
current, the half value current, and the minimum current (top to bottom). The
determined RESET time is denoted by the vertical dotted lines. On the lower
right, the change in resistance is indicated. (b) Current response to a pulse
with an amplitude of 1.8 V, applied to the ZrOx-based device. The additional
horizontal dotted line indicates the zero current baseline. (c) Reset times
$t_{\mathrm{RESET}}$, plotted against the applied voltage.

Two exemplary current responses to the applied voltage pulse are shown Fig.
2(a) and (b) for the TaOx and ZrOx-based device, respectively. In both cases,
the current increases rapidly at the beginning of the pulse and decreases,
subsequently, to values between 400 µA to 500 µA, which corresponds to the
RESET. The contribution of the capacitive current is negligible. This can be
seen at the end of the pulse applied to the ZrOx-based device in Fig. 2(b).
The negative current peak corresponds to the capacitive current and is much
smaller than the current peak at the beginning of the pulse. The RESET time
$t_{\mathrm{RESET}}$ is defined as the time difference between the time at
which the current surpasses 20 % of the maximum current at the beginning of
the pulse (first vertical dotted line in Fig. 2(a) and (b)) and the time at
which the current reaches its half value (second vertical dotted line). The
half value of the current $\Delta I$/2 is defined as half the current
difference between the minimum and the maximum current $\Delta I$ (see
illustrations in Fig. 2(a) and (b)). A similar definition was used in our
previous publications [28, 45].

In case of the current response of the TaOx-based device in Fig. 2(a), a 10 ns
pulse with an amplitude of 1.6 V was applied. During this pulse the device’s
resistance increased from 1.39 k$\Omega$ to 18.2 k$\Omega$ and a RESET time of
670 ps was determined. By using higher pulse amplitudes, faster RESET times
could be possible. Increasing the pulse amplitude to 1.8 V, however, resulted
in dielectric breakdown and the device’s resistance started to decrease. This
is shown in the supplementary Fig. S3. All determined RESET times
$t_{\mathrm{RESET}}$ are shown in Fig. 2(c) in dependence of the applied
voltage. Up to a voltage of 1.6 V, the RESET time depends strongly non-
linearly on the applied voltage, which was expected. At a voltage of 1.8 V
(only values for ZrOx) the kinetics start to bend towards slower RESET times,
which is attributed to the influence of the pulse generator’s rise time
($\approx$ 360 ps).

To decrease the influence of the pulse generator’s rise time, the RESET
kinetic measurements in the range from 250 ps to 50 ps were conducted with a
faster pulse generator, having a rise time of only $\approx$ 35 ps. The
measurement cycle is sketched in Fig. 3(a), and is almost identical to the
previous (Fig. 1(b)), only the applied RESET pulse has changed. The pulse
amplitude was once chosen to 1.6 V and once to 2.2 V. As in [39], the pulse
width was increased from 50 ps to 250 ps in steps of 5 ps. Each cycle was
repeated 10 times222The measurement cycles of the ZrOx-based device at a
voltage of 1.6 V were repeated 20 times to achieve a smooth line of
$R_{\mathrm{Post}}$/$R_{\mathrm{PRE}}$..

(a)

(b)

(c)

Figure 3: (a) Measurement procedure to determine the RESET kinetics in the
range from 250 ps to 50 ps. (b) Exemplary result for the TaOx-based device at
a voltage of 1.6 V. The boxplots indicate the scattering of the ratio
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ at a specific full width half maximum
(FWHM). The red bar indicates the median value. (c) Median values of all
measurements. The solid and dotted lines indicate the results of the TaOx and
ZrOx-based devices, respectively. The pulse amplitude amount to 1.6 V (blue)
and 2.2 V (orange). The solid blue line in (c) represents the median values of
(b).

An exemplary measurement on the TaOx-based device at a voltage of 1.6 V is
shown in Fig. 3(b). The ratio of the resistance before $R_{\mathrm{PRE}}$ and
after $R_{\mathrm{POST}}$ the pulse’s application is plotted as boxplot
against the FWHM of the applied pulse. The red bar marks the median. As
expected, the ratio $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ increases with
increasing FWHM. The median of $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$,
however, remains below 1.5 for all FWHMs, which means that no successful RESET
occurs in this time interval333For a successful RESET operation the ratio of
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ should be greater than 3 [54]. The
median values of $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ of all four
measurements are shown in Fig. 3(c). The corresponding boxplots can be found
in the supplementary Fig. S4. As the ratio
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ does not yield any information about
the absolute resistance values, the $R_{\mathrm{POST}}$ values are shown in
the supplementary Fig. S5. The initial resistances $R_{\mathrm{PRE}}$ were
always in the range from 1.0 k$\Omega$ to 2.5 k$\Omega$.

At 1.6 V, the ratio $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ of the ZrOx-based
device (dashed blue line in Fig. 3(c)) also remains below 2.0 for all FWHMs,
indicating that the ZrOx-based device cannot be driven to HRS within 250 ps.
At an amplitude of 2.2 V, $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ of the TaOx-
based device (solid orange line in Fig. 3(c)) remained near unity for all
FWHMs, while $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ of the ZrOx-based device
(dotted orange line in Fig. 3(c)) decreased with increasing FWHM.
Consequently, it is not possible with both devices to achieve RESET times
faster than 250 ps by increasing the pulse amplitude. The decrease in
resistance of the ZrOx-based device at 2.2 V indicates the presence of a
unipolar switching mode.

##  3 Unipolar SET kinetics

The measurement procedure to determine the unipolar SET kinetics is depicted
in Fig. 4(a). Different to the measurement procedures of the RESET kinetics,
the device is driven to the HRS at the beginning of the measurement cycle by
applying a voltage sweep with an amplitude of 1.6 V. The resulting resistance
values were again in the range from 10 k$\Omega$ to 30 k$\Omega$. At the end,
it is driven to the LRS with a voltage sweep of -1.2 V. The sweep rate (0.5
V/s) and the current compliance during the SET sweep (300 µA) are identical to
the values chosen in the RESET kinetics. The pulse amplitude was again varied
from 50 ps to 250 ps and the amplitude from 1.6 V to 5.0 V. As the unipolar
switching mode has a large variabilty for TaOx\- [57] and ZrOx-based devices
[58, 49], this cycle was repeated at least 10 times444The exact numbers are
listed in Table S1 of the supplementary information., until smooth curves were
achieved for $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$.

(a)

(b)

(c)

(d)

Figure 4: (a) Measurement procedure to determine the unipolar SET kinetics in
the range from 250 ps to 50 ps. (b) Exemplary result for the TaOx-based device
at a voltage of 3.2 V. (c) Median values of all measurements. The solid and
dotted lines indicate the results of the TaOx and ZrOx-based devices,
respectively. The pulse amplitude amount to 1.6 V (blue), 2.2 V (orange), 3.2
V (green), and 5.0 V (red). The solid green line in (c) represents the median
values of (b).

An exemplary measurements is shown in Fig. 4(b), in which voltage pulses with
an amplitude of 3.2 V were applied to the TaOx-based device. A short FWHMs,
the ratio $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ remains near unity,
indicating that the resistance of the device does not change during the
pulse’s application. At FWHMs of about 95 ps,
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ drops towards zero, indicating that the
device was successfully driven to the LRS by applying a positive voltage pulse
to the active Pt electrode. As the device is also driven to the HRS with a
positive voltage pulse, this corresponds to a unipolar SET. At longer FWHMs,
the measurement was aborted to prevent the device from damage.

This measurement procedure was repeated at different amplitudes (from 1.6 V to
5.0 V) for the TaOx\- and ZrOx-based devices. The median values are plotted in
Fig. 4(c). The boxplot representation of
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ and the absolute values of
$R_{\mathrm{POST}}$ are shown in the supplement Fig. S6-S9. Similar to our
previous study, we defined the unipolar SET time, as the time, at which
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ reaches a value below 0.5 [39]. This
threshold is indicated as horizontal dashed line in Fig. 4(c).

The resulting unipolar SET times are shown in Fig. 4(d) in dependence of the
pulse voltage. The unipolar SET kinetics have similar fast switching times
compared to the bipolar SET kinetics from [39]. Only the voltage has been
shifted to higher absolute values. The fastest unipolar SET time amounts to 50
ps, which is - to our knowledge - the fastest unipolar SET measured in ReRAM
devices. The fastest reported unipolar SET time, so far, amounts to 16 ns
[59]. As the TaOx-based device did not switch at a pulse width of 50 ps an
amplitude of 5.0 V to the LRS, a single measurement cycle with a pulse width
of 50 ps and an amplitude of 7.1 V was repeated, during which the TaOx-based
device switched to the LRS. Exemplary measured current transients, during
which a unipolar SET time of 50 ps was realized, are shown in Fig. S10 of the
supplementary information for both devices. The endurance of the unipolar
switching mode was also tested. The TaOx and the ZrOx-based device reached an
endurance of 104 cycles and 3590 cycles, respectively. The description of the
measurement procedure and the results are shown in the supplementary Fig. S11.
Usually, current compliances are required to realize unipolar switching modes
[51]. In this study, the FWHM of the electrical stimuli is much shorter than
state-of-the-art current compliances (often operating at time-scales above 1
µs[60]) and, therefore, the unipolar switching mode can be realized without
current compliance.

##  4 Intrinsic RESET speed limitation

Although fast switching times are usually considered as promising feature, our
interpretation of the fast unipolar SET time is that it should be considered
as failure mechanism. At higher voltage amplitudes, the unipolar SET occurs
faster than the RESET and, thereby, prohibits fast bipolar switching in both
directions. This RESET speed limitation is illustrated in the following with
RESET programming windows. These windows were estimated with the results from
the RESET and the unipolar SET kinetics. As mentioned in the introduction, the
unipolar switching mode observed in ReRAM devices, has less promising
attributes with regards to endurance and switching power compared to the
bipolar switching mode.

The results from the RESET kinetics (Fig. 2(c)) and the results from the
unipolar SET kinetics (Fig. 4(d)) are plotted in Fig. 5. The red points mark
the measured RESET times and the green points the measured unipolar SET times.
The red and green shaded areas mark the voltage-time combinations at which
either a RESET or a unipolar SET event is triggered. The green and red lines,
encircling the red and green shaded area, are drawn by the eye. Their
intersection is an estimate of the fastest possible RESET time, demonstrating
that the presence of the unipolar switching mode intrinsically limits faster
RESET times. In case of the TaOx-based device, this intersection occurs at 510
ps and in case of the ZrOx-based device at 400 ps, which marks their intrinsic
RESET speed limit. It has, however, to be noted that this RESET programming
window will vary from device to device and possibly also from cycle to cycle
due to the high variability of the unipolar SET. This might also be the origin
of the random switching between the HRS and the LRS in the results of Wang et
al. [22]. In the sub-100 ps regime the measured unipolar SET events are also
influenced by the electrical charging of the devices. At slower timescales,
the unipolar SET is assumed to be time-independent.

(a) TaOx-based device

(b) ZrOx-based device

Figure 5: RESET programming window (a) for the TaOx and (b) for the ZrOx-based
device. The red points mark the measured RESET times from Fig. 2(c) and the
green points the measured unipolar SET times from Fig. 4(d). The red and green
areas (drawn by the eye) mark time-voltage combinations, at which either a
RESET or a unipolar SET is triggered.

##  5 Discussion

From Fig. 5, two possibilities to achieve faster RESET times can be derived:

  1. 1.

Lowering the RESET voltage

  2. 2.

Suppressing the unipolar switching mode

Torrezan et al. achieved 120 ps fast RESET times with a TaOx-based device
[21]. The I(V) characteristics of their devices show that the RESET sets in at
about 0.35 V [61]. In contrast, the RESET of the devices used in this study
sets in above 0.5 V (see Fig. 1(c)). The device stack of both devices is very
similar ([21]: Pt(20 nm)/TaOx(7 nm)/Ta(30 nm), this work: Pt(30 nm)/TaOx(5
nm)/Ta(20 nm). We therefore, assume that different fabrication processes are
responsible for the lower RESET voltage.

Suppressing the unipolar SET or mitigating its impact on the bipolar RESET
kinetics requires a better understanding of the underlying physical processes.
The abrupt nature of the unipolar SET results from a thermal runaway (similar
to the bipolar SET) [42]. This thermal runaway, however, does not necessarily
lead to a permanent change in resistance. Especially TaOx also exhibits
threshold switching [62]. The sudden current increase, may initiate an oxygen
exchange between the oxide and the active Pt electrode, which leads to a
permanent change in the device’s resistance. Such an exchange was also
observed in the so-called “eightwise” switching mode, which has been observed
in many transition metal oxides [63, 64, 65, 66], including TaOx-based devices
[46]. This oxygen exchange could also be the origin of the permanent decrease
in resistance during the unipolar SET, and could be suppressed in other
studies by introducing an oxygen blocking layer such as C [46] or Al2O3 [64,
66].

To test if an oxygen exchange also occurs during the unipolar SET between the
oxide and the active Pt electrode, we introduced a 1.0 nm thick Al2O3 layer
between the active Pt electrodes and the oxides, resulting in a Pt(30
nm)/Al2O3(1.0 nm)/TaOx(5 nm)/Ta(20 nm) and a Pt(30 nm)/Al2O3(1.0 nm)/ZrOx(5
nm)/Ta(20 nm) stack (referred to as Al2O3/TaOx and Al2O3/ZrOx device,
respectively). We tested to reset both devices with 50 ps pulses. The
measurement cycle is similar to the one from Fig. 3(a), only that this time
the pulse width was fixed at 50 ps and the pulse amplitude was chosen to 5.0 V
and 4.0 V for the Al2O3/TaOx and the Al2O3/ZrOx device, respectively. This
measurement cycle was repeated 100 times for each device.

The results for $R_{\mathrm{PRE}}$ and $R_{\mathrm{POST}}$ of the Al2O3/TaOx
and the Al2O3/ZrOx device are shown in Fig. 6(a) and (b), respectively. During
most cycles the devices switched to a higher resistance value after the
application, showing that the additional Al2O3 layer improves the feasibility
of fast RESET operations. As shown in Fig. 4(c) the devices without additional
Al2O3 already started to switch to the LRS at a pulse amplitude of 5.0 V (red
lines). To our knowledge, this is the first time that a 50 ps fast RESET
process has been demonstrated for a ReRAM device. Two exemplary current
responses are shown in Fig. 6(c) and (d) for the Al2O3/TaOx and Al2O3/ZrOx
device, respectively. The FHWM of 50 ps has been preserved in both cases.

(a) Al2O3/TaOx device, $V=5.0$ V, FWHM = 50 ps

(b) Al2O3/ZrOx device, $V=4.0$ V, FWHM = 50 ps

(c) Al2O3/TaOx device, $V=5.0$ V, FWHM = 50 ps

(d) Al2O3/ZrOx device, $V=4.0$ V, FWHM = 50 ps

Figure 6: Histograms of $R_{\mathrm{PRE}}$ and $R_{\mathrm{POST}}$ for the (a)
Al2O3/TaOx and (b) Al2O3/ZrOx device. Exemplary current responses during the
RESET of the (c) Al2O3/TaOx and (d) Al2O3/ZrOx device. The change in
resistance is indicated on the upper right.

The devices did, however, also remain in the LRS sometimes, indicating that
the 1.0 nm thick Al2O3 layer might only partially prohibit the oxygen exchange
at the Pt active electrode and the remaining oxygen exchange might prohibit
successful RESET operations. A similar observation was made by Zhang et al.,
who have placed an Al2O3 layer at the active electrode of a TiOx-based device
to suppress the oxygen exchange at the active interface [64]. Their approach,
however, only worked for Al2O3 layers thicker than 2 nm. Further studies with
different oxygen blocking layers or different active electrodes are,
consequently, necessary to achieve better control over the RESET process at
these fast timescales.

Another aspect of the unipolar SET is that it might limit the endurance of VCM
based devices. During endurance measurements on ZrOx and TaOx-based devices,
with very similar device fabrication, we observed that the devices were
usually trapped in the LRS [67, 54], which might have been triggered by a
unipolar SET event. An exemplary endurance measurement from [54], during which
a ZrOx-based device got trapped in the LRS is shown in Fig. 7. In [67] the
endurance limitation of TaOx-based devices was referred to as “RESET Failure”,
which is characterized by an abrupt current increase during a RESET sweep.
Afterwards, the devices were stuck in the LRS. This abrupt current increase is
also observed during the unipolar SET, only that it is usually controlled with
a current compliance [51].

Figure 7: Exemplary endurance measurement on a Pt(30 nm)/ZrOx(5 nm)/Ta(20 nm)
device. The device got irreversibly stuck in the LRS after about 2.8$\cdot
10^{5}$ cycles.

##  6 Conclusion

In this study, we have demonstrated that the RESET kinetics of VCM-based
devices are intrinsically limited by the coexistance of a unipolar switching
mode. Therefore, the RESET kinetics of a TaOx and a ZrOx-based device were
investigated in the regime from 50 ns to 50 ps. RESET times down to 480 ps
could be achieved by increasing the voltage amplitude of the RESET pulse. At
higher amplitudes, a unipolar SET event was triggered which prohibits faster
RESET times and rather decreases the devices’ resistances. The unipolar SET
kinetics were subsequently measured, showing that the unipolar SET can occur
within 50 ps. We attribute the unipolar SET event to a thermal runaway, which
followed by an oxygen exchange between the oxide and the active Pt electrode.
This oxygen exchange could be partially suppressed by introducing a 1.0 nm
thick Al2O3 layer between the oxide and the active electrode. With these
devices 50 ps fast RESET operations could be repeated, but only
stochastically. We also show, with the data from previous publications, that
the occurrence of the unipolar SET limits the endurance of both devices. As
the unipolar switching mode has less promising attributes than the bipolar
switching mode, the unipolar SET needs to be treated as failure mechanism and
further strategies should be developed to suppress its occurrence.

## Methods

Device fabrication and structure: As substrate served a Si-wafer ($\rho>10$
k$\Omega$cm). The top of the wafer was oxidized resulting in a 430 nm thick
SiO2 layer. All deposition steps were conducted by means of RF magnetron
sputtering. The $2\times 2$ µm2 devices were structured with optical
lithography. More details on the device fabrication can be found in [68] and
[69] for the TaOx\- and the ZrOx-based device, respectively. The 1.0 nm Al2O3
layer was grown by atomic layer deposition (ALD), using trimethylaluminum
(TMA) and a remote RF oxygen plasma source [64, 66]. This process ensures a
uniform and dense Al2O3 layer on the sample surface.
The devices were formed with a voltage sweep with an amplitude of -4.0 V at a
sweep rate of 0.5 V/s, applied to the active Pt electrode. A current
compliance of 100 µA was used during the forming. Both devices were integrated
into a coplanar waveguide structure, having a length of 590 µm. The center
signal stripe has a width of 100 µm and a spacing of 60 µm to the outer
grounded stripes. At the center the inner conductor is tapered to 2 µm,
matching the dimensions of the $2\times 2$ µm2 devices. More information and
illustrations of this structures are given in [40].

Electrical characterization: The experimental setup is sketched in Fig. 1. The
voltage sweeps and read-outs were conducted with a Keithley 2634B SMU. Two
pulse generators were used: pulses with a pulse width above 1.0 ns were
applied with a Picosecond 2600C pulse generator (rise time $\approx 360$ ps)
and pulses between 250 ps and 50 ps with a customized pulse generator from the
Sympuls GmbH (rise time $\approx 35$ ps). It has a fixed pulse amplitude of
5.0 V (at 50 $\Omega$), which was adjusted with fixed broadband attenuators.
The current responses of the pulse were measured with a Tektronix DPO73304D
real-time oscilloscope, having a bandwidth of 33.0 GHz and a sample rate of
100 GS/s. The devices were connected with GSG Z-probes from FormFactor. All
components of the setup (except of the oscilloscope) have a bandwidth of 40
GHz. The measurement procedure is more explicitly described in [39].

## Acknowledgements

This work was supported in part by the Deutsche Forschungsgemeinschaft under
Project SFB 917 and in part by the Federal Ministry of Education and Research
(BMBF, Germany) in the Project Neuro-inspirierte Technologien der künstlichen
Intelligenz (NEUROTEC) under grants 16ES1134 and 16ES1133K. It is based on the
Jülich Aachen Research Alliance (JARA-FIT).

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##  Appendix S Supplementary Information

###  S.1 Electrical charging time

In [1], we have demonstrated for the TaOx-based device a charging time of 77.1
ps by using its scattering parameters. In Fig. S1, we have plotted the
scattering parameters of both, the TaOx and ZrOx-based device. The forward
reflection $S_{11}$ is shown in (a) and the forward transmission $S_{21}$ in
(b). They were measured with a HP8722ES vector network analyser (VNA) in the
frequency range from 50 MHz to 40 GHz at a power of -3 dBm. The VNA was
calibrated using the SOLT (short-open-load-trough) method with a calibration
substrate (FormFactor CSR-8 100-250). Both devices were driven to the HRS
prior to the frequency domain measurements and show a similar trend over the
entire frequency range. Both are insulating at low frequencies and become
transparent at higher frequencies. This is due to the capacitance of the VCM
stack, which acts as high pass filter.

(a)

(b)

Figure S1: Absolute values of the (a) forward reflection $S_{11}$ and (b) the
forward transmission $S_{21}$ of the TaOx (blue) and ZrOx-based (orange)
device.

From the scatterings parameters, we determined the electrical charging time,
by using the method described in [1]. The voltage at the device
$V_{\mathrm{DUT}}(t)$ is the sum of the applied signal $V_{\mathrm{P}}(t)$ and
the reflected signal $v_{1}^{-}(t)$, minus the transmitted signal
$v_{2}^{-}(t)$:

$V_{\mathrm{DUT}}(t)=V_{\mathrm{P}}(t)+v_{1}^{-}(t)-v_{2}^{-}(t).$ (1)

An 250 ps pulse with an amplitude of 0.8 V was used as $V_{\mathrm{P}}(t)$,
having a rise time of about 35 ps (10 %-90 %). The reflected and transmitted
signals were calculated by building the Fourier transform of
$V_{\mathrm{P}}(t)$, multiplying it with $S_{11}$ for the reflection or with
$S_{21}$ for the transmission, and finally building the inverse Fourier
transform of this product:

$v_{1}^{-}(t)=\mathcal{F}^{-1}\left(\mathcal{F}(v_{1}^{+}(t))\cdot
S_{11}(f)\right),$ (2)

$v_{2}^{-}(t)=\mathcal{F}^{-1}\left(\mathcal{F}(v_{1}^{+}(t))\cdot
S_{21}(f)\right).$ (3)

The results for $V_{\mathrm{DUT}}(t)$ of both devices are shown in Fig. S2,
showing that both devices can be charged in less than 80 ps (10 %-90 %).
Please note that $V_{\mathrm{DUT}}(t)$ rises to twice the amplitude of
$V_{\mathrm{P}}(t)$, which is due to the superposition of the incoming and
reflected pulse. For this reason, we indicated always twice the pulse’s
amplitude in the main text.

Figure S2: Calculated voltage at the device $V_{\mathrm{DUT}}(t)$ after the
application of 250 ps pulse with an amplitude of 0.8 V for the TaOx (blue) and
ZrOx-based (orange) device. The dotted vertical lines indicate the charging
times (10 %-90 %).

###  S.2 RESET failure of TaOx-based device at $V$ = 1.8 V

The current response of the TaOx-based device to a 4 ns pulse with an
amplitude of 1.8 V is shown in Fig. S3. The devices was driven to a LRS of
1.31 k$\Omega$ before the pulse’s application. Although, a positive voltage
pulse (applied to the active Pt electrode) should drive the device to the HRS,
the device’s resistance decreased to 990 $\Omega$, remaining in the LRS. Also,
the current was significantly higher than during pulses with lower amplitude.
At a pulse amplitude of 1.6 V (see Fig. 2(a) of the main text), the maximum
current amounted to approx. 1.5 mA and then decreased abruptly. In the case of
1.8 V it remained constantly at approx. 3 mA. This current increase can be
explained by the occurrence of a unipolar SET event, which in this case
prohibits a successful RESET operation. In a previous study on the RESET
kinetics of a similar TaOx-based device, only a small linear dependence of the
maximum current on the applied voltage was observed [2]. The observed current
increase from 1.5 mA to 3.0 mA can, therefore, not be explained by the
increase of voltage from 1.6 V to 1.8 V.

Figure S3: Current response of the TaOx-based device to a 4 ns with an
amplitude of 1.8 V.

###  S.3 RESET kinetics

Fig. 3(c) of the main text shows the median values of the ratio
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ of the TaOx\- and ZrOx-based device,
which measured during the RESET kinetics in the time regime from 250 ps to 50
ps. Two pulse amplitudes were used (1.6 V and 2.2 V). The boxplot
representation was only shown for the TaOx-based device at 1.6 V in Fig. 3(b).
The boxplot representation of the other three measurements is shown in Fig.
S4. As the ratio $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ does not yield any
information about the absolute resistance values, the boxplots of
$R_{\mathrm{POST}}$ are shown in Fig. S5. The $R_{\mathrm{PRE}}$ values were
always in the range between 1.0 k$\Omega$ and 2.5 k$\Omega$.

(a) TaOx-based device, $V=2.2$ V.

(b) ZrOx-based device, $V=1.6$ V.

(c) ZrOx-based device, $V=2.2$ V.

Figure S4: Boxplots of $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ values of the
RESET kinetic measurements shown in Fig. 3(c) of the main text. The red bar in
the boxplot marks the median.

(a) TaOx-based device, $V=1.6$ V.

(b) TaOx-based device, $V=2.2$ V.

(c) ZrOx-based device, $V=1.6$ V.

(d) ZrOx-based device, $V=2.2$ V.

Figure S5: Boxplots of $R_{\mathrm{POST}}$ values of the RESET kinetic
measurements shown in Fig. 3(c) of the main text.

###  S.4 Unipolar SET – Kinetics

Fig. 4(c) of the main text shows the median values of the ratio
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ of the TaOx\- and ZrOx-based device,
which measured during the unipolar SET kinetics in the time regime from 250 ps
to 50 ps. Four different pulse amplitudes were used, ranging from 1.6 V to 5.0
V. The boxplot representation was only shown for the TaOx-based device at 3.2
V in Fig. 4(b). The boxplot representation of the other measurements on the
TaOx\- and ZrOx-based device are shown in Fig. S6 and Fig. S7, respectively.
The boxplots of $R_{\mathrm{POST}}$ are shown in Fig. S8 and Fig. S9 for the
TaOx\- and the ZrOx-based device, respectively. The $R_{\mathrm{PRE}}$ values
were always in the range between 10 k$\Omega$ and 30 k$\Omega$. The
measurement cycle was repeated at least 10 times and until smooth lines for
$R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ were achieved. The number of conducted
cycles are listed in Table S1. In Fig. S10 transient current responses to 50
ps long pulses are shown for both devices. The devices switched from the HRS
to the LRS during theses pulses.

(a) $V=2.2$ V.

(b) $V=5.0$ V.

Figure S6: Boxplots of $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ values of the
unipolar SET kinetics measurements (shown in Fig. 4(c) of the main text),
conducted on the TaOx-based device.

(a) $V=1.6$ V.

(b) $V=2.2$ V.

(c) $V=3.2$ V.

(d) $V=5.0$ V.

Figure S7: Boxplots of $R_{\mathrm{POST}}$/$R_{\mathrm{PRE}}$ values of the
unipolar SET kinetics measurements (shown in Fig. 4(c) of the main text),
conducted on the ZrOx-based device.

(a) $V=2.2$ V.

(b) $V=3.2$ V.

(c) $V=5.0$ V.

Figure S8: Boxplots of $R_{\mathrm{POST}}$ values of the unipolar SET kinetics
measurements (shown in Fig. 4(c) of the main text), conducted on the TaOx-
based device.

(a) $V=1.6$ V.

(b) $V=2.2$ V.

(c) $V=3.2$ V.

(d) $V=5.0$ V.

Figure S9: Boxplots of $R_{\mathrm{POST}}$ values of the unipolar SET kinetics
measurements (shown in Fig. 4(c) of the main text), conducted on the ZrOx-
based device.

Table S1: Number of conducted cycles Device | Voltage [V] | No. of cycles
---|---|---
TaOx | 2.2 | 100
TaOx | 3.2 | 300
TaOx | 5.0 | 100
ZrOx | 1.6 | 300
ZrOx | 2.2 | 300
ZrOx | 3.2 | 500
ZrOx | 5.0 | 100

(a) TaOx, $V=7.0$ V

(b) ZrOx, $V=5.0$ V

Figure S10: Current responses of the (a) TaOx\- and (b) the ZrOx-based device
to the application of a 50 ps pulse. The devices’ resistances before
$R_{\mathrm{PRE}}$ and after $R_{\mathrm{POST}}$ the application of the pulse
are indicated on the upper right, showing that the device switched from the
HRS to the LRS during the pulse’s application.

###  S.5 Unipolar SET – Endurance

The measurement procedure to test the devices’ endurance is sketched in Fig.
S11(a). All applied voltages were positive (including the read-out). At the
beginning of each cycle, the device is driven into the HRS with a positive
voltage sweep with an amplitude of 1.3 V for the TaOx\- and of 1.2 V for the
ZrOx-based device. The amplitude was reduced compared to the measurement in
the main text to reduce the stress onto the devices. To reduce the measurement
duration, the sweep rate was also accelerated from 0.5 V/s to 2.5 V/s. The
devices were then driven into the LRS with a positive voltage pulse. For the
TaOx-based device, the pulse width was chosen to 70 ps and the pulse amplitude
to 5.0 V. For the ZrOx-based device, the pulse width was chosen to 50 ps and
the pulse amplitude to 7.1 V. The devices’ resistances were read at a voltage
of 0.5 V, before $R_{\mathrm{PRE}}$ and after $R_{\mathrm{POST}}$ the pulse’s
application.

(a) Sketch of endurance measurement.

(b) TaOx

(c) ZrOx

Figure S11: (a) Sketch of the pulse sequence for the endurance measurement.
Resulting values for $R_{\mathrm{PRE}}$ (blue) and $R_{\mathrm{POST}}$
(orange) are shown in (b) and (c) for the TaOx\- and ZrOx-based device,
respectively.

The results are shown in Fig. S11(b) and (c) for the TaOx\- and ZrOx-based
device, respectively. The measurement of the TaOx-based device was aborted
after 104 cycles. The $R_{\mathrm{PRE}}$ and $R_{\mathrm{POST}}$ were always
separated by an order of magnitude and an even higher endurance may be
possible. The ZrOx-based device got stuck in the HRS after 3590 cycles. Until
then, the $R_{\mathrm{PRE}}$ and $R_{\mathrm{POST}}$ were also separated by
one order of magnitude. The device could, however, be driven back to the LRS
with a negative voltage sweep and was again operational. Further adjustments
of the pulse width and amplitude may result in an higher endurance, but this
is beyond the scope of this study.

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