Strong electron correlation effects in non-volatile
electronic memory devices
M. J.
Sánchezk ,
∗ Correlated
Isao H. Inoue∗,† , M. J. Rozenberg‡,§ , S. Yasuda†,¶ ,
M. Yamazaki†,∗∗ , T. Manago†,∗∗ , H. Akinaga†,∗∗ , H. Takagi†,¶ , H. Akoh∗,† and Y. Tokura†,††
Electron Research Center (CERC), National Institute of Advanced Industrial Science and Technology (AIST),
Tsukuba 305-8562, Japan. Tel: 81–29–861–5133, Fax: 81–29–861–2663, Email: i.inoue@aist.go.jp
† Research Consortium for Synthetic Nano-Function Materials Project (SYNAF), AIST, Tsukuba, Japan
‡ Laboratoire de Physique des Solides CNRS, Université Paris-Sud, France
§ Departamento de Fı́sica Juan José Giambiagi, FCEN, Universidad de Buenos Aires, Argentina
¶ Department of Advanced Materials Science, University of Tokyo, Kashiwa, Japan
k Centro Atómico Bariloche, Argentina
∗∗ Nanotechnology Research Institute (NRI), AIST, Tsukuba, Japan
†† Department of Applied Physics, University of Tokyo, Tokyo, Japan
Abstract— We propose a theoretical domain-tunneling (DT)
model of the resistance switching phenomenon that is often
experimentally observed in metal–semiconductor–metal sandwich
structures which is considered as a possible non-volatile memory
devices. The DT model is incorporated with a metal-insulator
transition due to strong electron correlations at the semiconductor/metal interface. We have also prepared experimentally a
Pt/NiO/Pt test device and have observed the resistance switching.
The calculated results of the DT model are compared to the
experimental results, manifesting that this sandwich structure
could be the realisation of a novel strongly correlated electron
device.
I. I NTRODUCTION
Minute variation in a carrier density can drive a drastic and
qualitative change in a ground state of the correlated electron
system. To establish a method of a critical control of the carrier
density at the boundary of phase competitions is a pressing
challenge in the interdisciplinary field among the modern
condensed-matter physics and semiconductor technologies.
It has long been believed to enable a fine tuning of the
carrier density in materials without causing a disturbance to the
underlying lattice [1]–[3] by simply employing techniques of
field-effect doping methods: e.g., the electrostatic (capasitive)
charging and/or electrodynamic carrier injection, We have
been investigating on the possibility of the two methods for
the research of transition metal oxides (TMOs), which are a
bustling repository of the strong correlation phenomena [4].
One of our methods is a capacitive (electrostatic) charging
of a single crystal of TMOs through a thin dielectric film (gate
insulator) deposited on the top of the crystal [5], [6]. The other
method is to inject/extract carriers rather dynamically through
a barrier at metal/TMO junctions. The two methods are now
versatile and are expected to be applicable for a large class of
systems under current heavy experimental investigation.
In this paper, we focus on the latter part. Our recent results
of theoretical as well as experimental works on the dynamical
injection/extraction of carriers are reported.
II. T HEORETICAL APPROACH
A. Essence of the domain-tunneling (DT) model
The target of our model is a simple sandwich structure of a
semiconductor with two metal electrodes. Quite surprisingly,
some of them toggles the two-terminal resistance in several
orders of magnitude and in a nonvolatile manner by applying
an electric pulse [7]–[19]. The research on the two-terminal
nonvolatile resistance switching has recently caused an upsurge of the development research of the so-called resistance
random access memory (RRAM). This is believed to be a next
generation electronic application.
It is worth while to note here that the research of the bistable
switching in Schottky contacts [20]–[23] also has a long
history since 1970 for the ZnSe/Ge heterojunction [24] and
GaAs/Si [25]. In this system, the imperfection of the junction
caused by the forming process is believed to play an important
role. In addition, there are other classes of sandwiches showing
the similar resistance switching, which however is rather due to
a structural phase transition and/or due to a thermodynamical
effect. Typical example of the former is the wide-ranging work
on the phase transition memory (amorphous matrix forming
a crystalline filamentary path) such as “ovonics” [26], and
an example of the latter is a sandwich structure where the
filaments of metal atoms are unequivocally recognized [27],
[28].
We have introduced a theoretical model for the resistance switching from a viewpoint of the dynamical injection/extraction of carriers through an energetic barrier between
the metal electrode and the semiconductor matrix. The model
seems quite applicable to some of the examples listed above.
In the model, we have assumed that the “semiconductor” part
is composed of an insulating (and inert) medium with a nonpercolating structure of charged domains [29]–[31] (Fig. 1).
A possible conduction path is a kind of one-dimensional
“filament” connecting the domains by quantum tunnelling,
thus, this is called a “domain tunnelling (DT) model.”
Top Electrode
charged region
V (arb. units)
(a)
(b)
(defects, dislocation,
Impurities, phase
separation, etc)
8
-0.2
0
-8
0
600000
I (carr/uot)
Electroforming
insulating
medium
or “filament”
3000
4000
5000
6000
0
1000
2000
3000
4000
5000
6000
0
1000
2000
3000
4000
5000
6000
0
(e)
(d)
Top Electrode
Top Domains
model
Middle Domains
I (carr/uot)
(c)
2000
-600000
Bottom Electrode
conduction path
1000
0
-2000
-4000
time (uot)
Bottom Domains
Bottom Electrode
Fig. 1.
(a) The semiconductor part is assumed to be composed of an
insulating (and inert) medium with a non-percolating charged domains. (b)
By applying a large electric field for a sufficiently long period of time, the
semiconductor is “electroformed”. We think the domains are more charged
by this electroforming. (c) A possible conduction path is a kind of onedimensional “filament” connecting the regions of charge inhomogeneity by
quantum tunneling (represented by arrows). (d) The amount of charge injected
to the domains from the electrode is not enough to dope whole of the domains.
However, the typical size of the domains near the interface is estimated to
be tens of nanometers [8], [32]. Thus, even small amounts of charge would
effectively modify their doping state. So, we have modeled the system as
composed of small domains near the electrodes (thick circles) and the rest.
(e) We set the number of top and bottom domains to be 40 and the number
of states that they hold to be 106 ; the sole central domain holds 109 states.
The actual number might be clarified by experiments such as in Ref. [11].
The number of states in the domains are such that produces carrier densities
of similar magnitude as those experimentally reported [10]. Carriers tunnel
between domains. The probability of charge transfer depends on phenomenological parameters such as the tunneling rates [7]. The mathematical definition
of the system using rate equations is described elsewhere [29].
The domain structure assumed in the DT model is motivated
from a universal aspect of strongly correlated TMOs: the
spatial inhomogeneity (or phase separation) at the nanoscale.
This has recently emerged as one of the most spectacular
properties of TMOs and possibly responsible for much of the
interesting physics that they display [33]–[36]. Clearly, the
origin of the inhomogeneity is the competition of the electronic
states that is brought about by the strong correlations in TMOs
[4]. In fact, in the DT model of the resistance switching, we
have proposed the doping driven (Mott) transition of the small
charged domains in the TMO materials [30].
B. Model simulation results
The basic switching behaviour obtained by the Monte Carlo
simulation of the DT model is demonstrated in Fig. 2. Details
of the calculation are described elsewhere [29], [30]. In this
report, we set our sight to the essence of the DT model.
The voltage pulses switch the system between two resistance
states corresponding to high and low current. This switching
property is directly related to the hysteresis in the currentvoltage (I–V ) characteristics.
Actually, in most of the systems which show the
pulse-induced resistance switching, the I–V characteristics
Fig. 2. Model simulation results. In the initial state, all small domains are
20 % filled and the center domain is 10 %. These occupations are consistent
with systems such as lightly Cr-doped SrZrO3 [9]. Top panel shows the
voltage protocol. An external dc voltage Vread is continuously applied
between the top and bottom electrodes and produces a carrier current. At
given time intervals of 1000 uot, voltage pulses of short duration (10 uot) are
applied. (1 uot = 1 unit of time = 1 Monte-Carlo step, in which the occupation
numper of all the domains are updated.) The middle panel shows the current at
the top electrode, and we see that positive voltage pulses cause sharp positive
current spikes while the negative pulses cause negative spikes. The bottom
panel also shows the current in a different vertical scale that reveals more
detailed behavior between the pulses.
show large hysterises. Among them, we are interested in
the hysteresis with a drastic transition1 from the highresistance to low-resistance state (usually denoted “Set”),
and that from the low-resistance to high-resistance state
(“Reset”); for example, Au/Ti/SrZr0.998 Cr0.002 O3 /SrRuO3 [9],
Ag/CeO2 /La0.67 Ca0.33 MnO3 [37], Ag/Bi2 Sr2 CaCu2 O8+y heterojunction [38], Pt/NiO/Pt [19], Al/“Rose Bengal”/ITO [39],
Al/DDQ/ITO [40], and Au/porus Si/p-type Si [41].
Typical hysteresis loop obtained using the DT model [30]
is shown in Fig. 3. Our result is in good qualitative agreement with the experimental observations; especially, we have
reproduced the sharp transition for both the Set and Reset.
C. Mechanism
In order to gain more insight on the mechanism for the
resistance switching we have examined the occupation of
the domains along the hysteresis cycle. Then, it has been
elucidated that the sharp switchings, Set and Reset, seen in the
hysteresis are originated in the Mott metal-insulator transition
(opening/closing of a correlation gap), which occurs only in
the electronic density of states of the top domains.
The transitions depend solely on the occupation of each top
domain, and not on that of each bottom domain for the set
of parameters which can reproduce the I–V characteristics of
1 The drastic transitions of “Set” and “Reset” are not necessary observed,
especailly when there is a large Schottky barrier between the metal electrode
and the insulator. This is because the change of the Schottky barrier width
due to the carrier injection becomes dominant for the hysteresis. We have also
done the model calculation for this case, and actually obtained the hysteresis
in the I–V characteristics [30] with no sharp transition, which is similar to
what is observed.
Reset
Set
conduction is dominated by such a narrow region as tens
of nanometers [8], [32], and even a small amount of doping
would effectively increase the carrier density of the domains
near the interface to the threshold of the strong correlation
effect. This is also comparable to the Coulomb blockade
phenomena in the nanoscale metal clusters.
III. E XPERIMENTAL APPROACH
A. Methods
Fig. 3. Current-voltage (I-V ) characteristics obtained using the DT model
[30]. The voltage protocol is −Vmax → 0 → Vmax → 0 → −Vmax and
the duration of the whole cycle is 3000 uot. Our result is in good qualitative
agreement with the experimental observations.
Fig. 3. Thus, we can safely say that the current switching is
controlled by a single electrode interface.
In fact, a model with small domains only on one of the two
interfaces would also have a parameter regime with similar
switching and hysteresis characteristics. In other words, the
presence of small domains at both interfaces is not strictly
required. The ocupation of the central domain is maintained
in a rather constant value; thus, it effectively acts as a buffer
that decouples the behaviors of the two interfaces. Increasing
the parameter which sets the number of available states in the
center domain, has the effect of reducing the variation of its
occupation level. However, it does not modify the switching
or hysteresis characteristics.
hopping or
tunneling
conduction
Reset
fuse blows!
(Mott transition)
Set
Fig. 4.
Schematic pictures of the “Set” and “Reset” actions elucidated
by our model calculation. The possible conduction path (a kind of one
dimensional “filament” connecting the regions of charge inhomogeneity by
quantum tunneling or hopping) is burnt at the interface preventing electric
current (“Reset”) and is then reconnected (“Set”). This is caused by the Mott
transition in only the small domains near either of the electrodes.
We have noted that a possible conduction path of these
systems is a kind of one dimensional “filament” connecting
the regions of charge inhomogeneity by quantum tunneling or
hopping. So, what is elucidated from our model calculation
is that the filament is ruptured near the interface when the
absolute voltage value exceeds the Reset threshold, and is
connected when the absolute voltage value exceeds the Set
threshold. This can be compared to a recoverable (or reconfigurable) electric fuse.
The schematic is depicted in Fig. 4. It is intriguing that
the macroscopic resistance switching is caused by such small
amount of carriers injected into TMOs. This is because the
To investigate the feasibility of the DT model for the real
sandwich structure, test devices were made of Ni oxides and
Pt electrodes on an oxidised silicon wafer as reported earlier
[19], [42]–[45]. (We express our Ni oxides NiO for simplicity,
but it is likely to be NiOx with x unequivalent to one.)
The polycrystalline NiO layer with a thickness of approximately 60 nm was prepared by the conventional rf magnetron
sputtering. During the deposition, the substrate temperature
was kept at 300◦ C in the Ar with 4 % oxygen atmosphere
of 0.67 Pa. Both the top and bottom Pt electrodes were also
prepared in the same sputtering chamber at room temperature
in 0.3 Pa of pure Ar atmosphere. The device is in the shape
of a 100 µm diameter column, which was patterned by the
standard photolithography and Ar ion milling.
The electroforming of as-deposited samples was then performed by applying dc voltage of 3–7 V. The Agilent 4156C
Precision Semiconductor Parameter Analyser with the conventional probing system was used to measure the dc electrical
properties of the device. All the measurement was performed
at room temperature.
B. dc properties
A typical I–V characteristic of the Pt/NiO/Pt device after
the electroforming treatment is shown in Fig. 5 (open circles).
In the high resistance state indicated by the arrows 1 and 6 in
Fig. 5, the current varies non-linearly with bias. The data is fit
well by the solid line which represents I = AH sinh(V /BH )
with AH = 26.7 × 10−6 A/V and BH = 664 mV.
Once the voltage bias reaches to 1.6 V, the current jumps
suddenly (arrow 2), and the system changes to the low resistance state (arrows 3 and 4). (In the experiment, the maximum
current is limited to 5 mA.) This switching transition (called
“Set”) can occur either side of the voltage bias; i.e., it can
be observed when the bias reaches to −1.6 V, It should be
noted that, before the Set transition at 1.6 V, the I–V curve
of the high resistance state does not show any hystereses for
repeated bias sweeps between −1.0 V and 1.0 V; in a similar
fashion, the I–V curve of the low resistance state after the Set
transition show no hysteresis for repeated bias sweeps between
−0.5 V and 0.5 V. That is, the two states are quite robust.
In the low resistance state, the current varies non-linearly
with the bias voltage. This is similar to the high resistance
state but the function is different. As in Fig. 5, the data
is fit by the dotted line sufficiently which represents I =
AL sinh−1 (V /BL ) with AL = 2.33 × 10−3 A/V and BL =
136 mV.
3
2
0
1
5
4
-4
Reset
-8
-2
-1
0
0.04
0.02
Set/Reset Voltage (V)
6
Set
Reset Current (A)
4
Pt (100nm)
NiO (60nm)
Pt (100nm)
-3
Current ( 10 A )
8
1
2
Bias Voltage ( V )
Fig. 5. Typical I–V characteristic of the Pt/NiO/Pt device after the electroforming treatment (open circles). The voltage bias protocol is indicated
by the numbered arrows. The I–V curve of the high resistance state can be
fit by I = AH sinh(V /BH ) (solid line), and the low resistance state by
I = AL sinh−1 (V /BL ) (dotted line). See text for details.
If we turn off the 5 mA current compliance, the low resistance state switches (arrow 5) to the initial high resistance
state, when the bias reaches to −0.7 V, This is called a “Reset”
transition. As with the Set transition, this Reset transition can
occur either side of the bias voltage. The Reset transition is
not as sharp as the Set transition, but it still looks very steep
in this quasi-static dc I–V measurement.
C. Set/Reset thresholds
We have repeated the dc I–V measurement for positive bias
voltage sweep as many as 50 times. The resistance alternates
between the high and low values as shown in Fig. 5 at every
Set and Reset transition. The Set and Reset voltages as well as
the Reset current (defined as a value of the current, when the
Reset transition occurs) for each switching cycle are plotted
in Fig. 6.
The Reset current shows a considerable variation, In contrast, the Reset voltage are fairly constant over the whole
switching cycle. It seems that this result is hardly explained
by a simple homogeneous conduction over the whole device.
Alternatively, a naive but reasonable explanation is provided
by assuming a filamentary conduction. In the filamentary
model, we can easily understand that the variation of the
Reset current is due to the different total cross-section of the
filament(s) penetrating the device. So, what is observed is the
rupture of each filament at a total-current-independent bias
voltage.
The Joule heating may be one of the reasons. Since it is
not an unreasonable assumption that the current density would
be identical in each of the filament(s), the lowest necessary
electric power (I × V ) per cross-section for the “Joule-heating
0
Set voltage
Reset voltage
4
2
0
20
40
Switching Cycle
Fig. 6. Reset current which is defined as a value of the current at the Reset
transition (top), as well as Set and Reset threshold voltages (bottom) plotted
for each switching cycle.
rupture of the filament” accounts for a constant threshold
value of the bias voltage independent of the total current.
However, the rupture of the filament does not seem to be due
to such a simple Joule heating. As already mentioned, we
have repeated the measurement of the I–V characteristics of
the low resistance state for V within the Reset voltage, but no
remarkable hysteresis usually concomitant to the local heating
has been observed. Moreover, we have also varied the dc bias
sweeping ratio from the order of 1 mV/sec to 1 V/sec, but the
Reset voltage has been almost kept to the unique constant
value.
With that in mind, we invoke the DT model; the filament
is like a string of beads made of “charge domains,” and one
of the domains (near the interface) becomes insulating when
it is “charged up” to a threshold value of the Mott transition.
The critical amount of charge Qreset normalised to the size of
the domain must be a proper value of the device. It depends
only on the bias voltage not a current, as it is Qreset /C =
Vreset where C is an effective capacitance of the charge domain
which reflects the physical size of it. Therefore, in the DT
model, Vreset does not depend on the amount of total current.
It should be also noted that the variation of the Set voltage
is possibly due to the different remnants of the ruptured
filaments, which makes the electrical field distribution inhomogeneous.
Consequently, we have had a good evidence that the DT
model with the Mott transition in the small domain can be
one of the possible accounts for the resistance switching
phenomenon seen in the Pt/NiO/Pt device.
IV. C ONCLUSION
We have seen that the resistance switching of some of the
metal–semiconductor–metal sandwich structures, especially
Pt/NiO/Pt system, which is concomitant to the hysteresis
in the I–V characteristics with the drastic Set and Reset
transitions, is the tangible application of the phase transition
of the charge domains located near the interface. The key
point is that the modulation of the electric field can inject
charge into the semiconductor matrix, and the doped charges
form the inhomogeneously charged regions in the systems,
which we call domains. The domains that receive the doped
charges are usually driven to get across a boundary between
two disctinct electonic phases, if each domain is a strongly
correlated electron system. These electronic phases, whatever
their particular nature is, would in general have very different
conductance properties, and thus lead to a resistance switching.
as we have described here for the particular case of the Mott
metal–insulator transition.
As for the resistance switching for the sandwich structure,
there have been many theoretical models suggested so far [7],
[8], [46]–[50]. However, those models are not comprehensive
enough to explain all the anomalous behaviours, which accompany the resistance switching. The DT model we have
suggested here is one of a few efforts for applying the physics
of the strongly correlated electron systems to the rather oldfashoned but still mysterious resistance switching systems. We
hope this could be a breakthrough for the future correlated
electron devices.
ACKNOWLEDGMENT
This study is partly supported by NEDO Nanotechnology
Program.
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