2. Atomic-Scale Filament Memristor Microwave Switches
Atomic-scale or atomically thin materials are either van der Waals materials, also known as 2D materials (such as graphene and molybdenum disulphide MoS
2), or hexagonal boron nitride (h-BN) which is made of billions of monolayers bound together by weak van der Waals forces in the vertical plane, while in the horizontal plane there are strong bonds between atoms. Graphene is a semi-metal, MoS
2 is a semiconductor, and h-BN is an insulator, thus offering a large variety of atomic-thin materials, each of them with its own physical properties [
4]. The majority of the atomic-scale switches are vertical devices such as MIM (metal–insulator–metal) or MSM (metal–semiconductor–metal) structures, where the insulator or semiconductor have atomically thin dimensions. If a MIM or MSM have the additional property of being a non-volatile resistive memory, then it is termed memristor. Moreover, the current-voltage must be pinched at 0 V. The known memristors are mostly based on oxides having a large density of oxygen vacancies [
5].
In any memristor, the resistance R is reversibly changed from a high-resistance state (HRS), corresponding to the OFF-state (
ROFF), to a low-resistance state (LRS), associated to the ON-state (
RON). The process of resistance change from HRS to LRS is termed as
Set, while the inverse process (resistance change from LRS to HRS) is termed
Reset. In bipolar memristors, the
Set voltage signal is positive, thus transforming the atomically thin material from an insulation-like state (hence, displaying an HRS) to a metallic-like state (associated with an LRS). The process is controlled by a current compliance; otherwise, the memristor could be destroyed by high current values. The memristor remains in the LRS until a
Reset negative voltage is applied to transform the memristor state from LRS to HRS. Therefore, any memristor behaves as a non-volatile memory. The current-voltage dependence of any memristor is represented in
Figure 1.
Since during the reversible insulator-metal process the conductance of the memristor is modulated in time, i.e., it increases during the transition from HRS to LRS and decreases in the transition from HRS to LRS, any memristor can be seen as an artificial synapse [
6] and, thus, many applications in the new field of neuromorphic computing can be envisaged. The equation of any memristor is given as follows:
where
γ(
t) is a continuous time-dependent function with values in the range [0, 1]. The function
γ(
t) reaches its maximum and minimum values, of 1 and 0, when
R =
RON (LRS) and
R =
ROFF (HRS), respectively.
γ(
t) is considered as a linear function of the flux linkage.
A recent review about memristors and their applications as memories and synapses can be found in [
1,
7]. Furthermore, the majority of memristors are oxide memristors, in which the reversible transformation from HRS to LRS is due to conduction filaments formed inside the oxide; for this reason, they are also termed as filament memristors.
In the
Set process, pairs of oxygen vacancies (anions) are created inside the oxide due to the impact ionization process: O
L → V
O2+ + O
i2−, where O
L are the oxygen atoms in the oxide lattice, V
O2+ are the oxygen vacancies and O
i2− are supplementary oxygen ions produced in the lattice. The O
i2− ions are migrating to the top electrode, while the oxygen vacancies are migrating in the opposite direction to the bottom electrode, and trap the electrons. Thus, at the bottom electrode the population of oxygen vacancies is formed and is propagating to the top electrode, which causes the formation of tiny current filaments, hence providing conduction in the oxide and, as a consequence, the transition from an insulating to a conduction state (i.e., the transition from HRS to LRS). In the
Reset process, the large densities of current filaments are cancelling oxygen vacancies via Joule heating: V
O2+ + O
i2− → O
L. Therefore, we have the inverse transition from LRS to HRS. These processes are depicted schematically in
Figure 2.
Soon after the discovery of the memristor, it was used as a high-frequency switch [
8]. This was a logical step, since memristors have low
RON (in the range of 10–100 Ω), while
ROFF is in order of tens or hundreds of MΩ. The oxide memristor is embedded in a planar waveguide termed coplanar waveguide (CPW), consisting in three metallic electrodes separated by two gaps, with the central conductor being the signal line and the outer electrodes being the ground planes; all the three electrodes are deposited on an insulator substrate. The CPW line has both input and output impedances of 50 Ω (standard reference impedance for microwave circuits). In the case of the microwave memristor switch described in [
8], the substrate is a 525 μm-thick high-resistivity (HR, with resistivity of 1000 Ω·cm) silicon (Si) wafer having a 200 nm-thick silicon dioxide (SiO
2) layer grown over it, such that the memristor is isolated from the substrate containing surface charges. The memristor is a MIM-like device, having two dissimilar metallic electrodes: the bottom electrode is Ti (5 nm)/Pt (20 nm), while the top electrode is Ta (30 nm)/Pt (200 nm). The oxide is amorphous Ta
2O
5 having the thickness of 7 nm, with a high density of oxygen vacancies. This memristor is integrated in the central electrode of the CPW as it is shown in
Figure 3. The
Set pulse has an amplitude of +2 V and a duration of 105 ps, while the
Reset pulse has an amplitude of +3.3 V and a duration of 120 ps. The ON- and OFF-state are evidenced by the sub-ns time response, meaning that the memristor works as a switch up to 20 GHz.
Further developed memristors based on monolayers, such as MoS
2 or h-BN, rely upon the concepts described above, i.e., the monolayer is embedded in the central conductor, the ON resistance is kept low (at 10–20 Ω), and the results show that the monolayer memristors are very good microwave switches, having low insertion loss (<2 dB) and high isolation (between −25 and −30 dB); moreover, they are able of high-power handling [
9,
10]. The first experimental results show that these memristors are filament memristors, even if they are monolayers.
3. Atomic-Scale Nano-Ionic Memristor Microwave Switches
There exist other types of memristors which are good microwave switches, such as nano-ionic memristors [
11]. Cations, anions or a combination of both can be used for the implementation of such memristors. The implementation via cations is simple and effective, as it is based on electrochemical metallization. Two separate metallic contacts, deposited on a dielectric such as SiO
2, are needed. The two metals are dissimilar, one of them must be electrochemically active (such as Ag or Cu), and the other one is electrochemically inert (such as noble metals, like Pt, Pd, Au). When a positive DC voltage is applied, the Ag electrode produces Ag
+ cations which migrate to the inert electrode. In time, metallic filaments are formed between the active and the inert electrodes, thus obtaining a switch in the ON-state. The distance between the electrodes must be in the range 10–40 nm.
When a negative voltage is applied, the migration direction is reversed and the filament is destroyed; this implies that the switch enters the OFF-state.
Regarding RF applications, it was shown that Ag cations give rise to filaments that are periodically destroyed between two Au electrodes (which are integrated in the central electrode of a CPW line) when a DC voltage is applied [
12]. This way, it was obtained an insertion loss of 0.3 dB and an isolation of 30 dB up to 40 GHz (see
Figure 4). The gap between the Ag filaments is 35 nm wide. The compliance current is used to avoid the destruction of the switch in the ON-state.
Besides this, we showed (based on 3D electromagnetic (EM) design–CST Studio Suite
® 2014, CST AG, Darmstadt, Germany–integrated with microwave measurements) that the beam of an antenna array can be steered with an angle of ±28° at 2 V bias using the experimental data of either oxide or nano-ionic memristors [
13]. A major problem of all these memristor switches is the control of LRS by current compliance, meaning the limitation of current, and this limitation could be different from one memristor to another due to the dynamics of oxygen vacancies and to defects inside the oxide. This could degrade the microwave properties of the memristor switch, as shown in
Figure 5.
We see that as soon as
RON is increased, the degradation of the transmission is clear due to the degradation of the impedance matching. In other words, the switch’s main characteristics degrade visibly if
RON varies with just an order of magnitude. This effect can be seen in the TiO
2-x memristor fabricated and studied by us in [
13]. This filament memristor has a low forming (1.8 V) and switching voltages (−1.5 V for
Reset and 1.2 V for
Set). The minimum ON resistance of the switch is 42 Ω but, due to the current limitations of electrodes, the minimum programmable ON resistance of the switch is 241 Ω, for a current value of 3 mA. However, other memristors referenced above were able to control the ON resistance at the level of 10 Ω or lower.
We will now present in
Table 1 the performances of the above high-frequency memristors extracted from experiments considering the main switch performances in microwaves such as insertion loss, isolation, power handling, but also fabrication performances such as reproducibility denoted as R. We have denoted by V
A the voltage necessary to switch in a reversible manner the two states ON and OFF. In the case of memristors two values are resented in the parentheses corresponding with HRS and LRS, respectively.
These atomic-scale microwave switches are compared with RF-MEMS switches which are standard microwave switches today and commercially available. We see that in terms of insertion loss and isolation all the high frequencies switches are comparable, showing good performance. However, the switching voltage for microwave atomically thin memristors is at least tens time lower and their switching time is one order of magnitude lower which is a huge advantage in terms of power consumption and cutoff frequency which is in THz region. Power handling reflects the self-switching of the microwave switches due to applied microwave power. The 2D memristors switches consisting in one single monolayer or having thicknesses up to 4–5 nm support a rather high microwave power of 0.1 W without self-switching phenomena.
The main problem of atomic-thin memristors is their reproducibility since they are fabricated on flakes, and not at the wafer level. The growth of 2D materials is still a challenging problem not solved yet. A graphene monolayer is the single 2D material commercially available on 4-inch or 6-inch Si wafers. The MoS2 or h-BN are commercially available on Si substrates not exceeding 1 cm2.
Therefore, we are searching an atomically thin material and a device associated to it which has similar performances with the above atomically-scale switches but is CMOS compatible with high reproducibility. Our answer is ferroelectric tunneling junctions (FTJs) fabricated on HfO2 ferroelectrics which will be described below.
4. Atomic-Scale Ferroelectric Junctions as Microwave Switches
The ferroelectric tunneling junctions [
14] are MIM-like diodes, where a few-nm-thick ferroelectric is sandwiched between two metal electrodes. An FTJ differs significantly from a MIM diode because the DC current at a certain bias can be switched ON and OFF by an external DC voltage that switches the orientation of the ferroelectric domains. Hence, an FTJ can be seen as a resistive memory with two states, expressed by the so-called tunnel electro-resistance (
TER) defined as [(
RON −
ROFF)/
ROFF] × 100% or as
JON/
JOFF, where
RON and
ROFF are the resistances of the ON- and OFF- states, while
JON and
JOFF are the ON and OFF current densities. We have to point out that both definitions are used in the literature, and thus TER is defined either in % or has no units. TER is in the order of 10
2–10
5 depending on the ferroelectric type, reaching a giant TER of 6 × 10
6 in Pt/BaTiO
3/Nb:SrTiO
3, which is a metal/ferroelectric/semiconductor FTJ [
15]. The resistance, and thus the TER of any FTJ, is dependent on the amplitude of the applied voltage, which is a pulse of few volts with a duration of tens of ns. This dependence has a hysteretic behavior and the FTJ behaves like a memristor due to the dynamics of the ferroelectric domains at various electrical fields [
16]. We will consider in the following that the FTJ has attained its maximum TER and we will consider it as a tunneling diode with two states ON and OFF selected by applied DC signals, which are switching the polarity of the built-in field of the ferroelectric material.
FTJ experimental results are reported for many ferroelectrics such as Pt/BTO/NSTO [
15], BaTiO
3/La
0.67Sr
0.33MnO
3 (BTO/LSMO) [
17], Sm
0.1Bi
0.9FeO
3/Nb:SrTiO
3 (SBFO/NSTO) [
18]. In this work, we will focus on the FTJ-based on HfZrO ferroelectric, since it is the single CMOS-compatible ferroelectric; furthermore, devices based on such ferroelectrics can be grown at the Si wafer level [
19]. The TER effect in HfZrO has been evidenced so far in many experimental research works. A structure made of Pt/Hf
0.5Zr
0.5O
2/Pt has a TER of 20 [
20]. A TER higher than 30 was obtained growing HfZrO directly on Si, and using various processes on top TiN electrode [
21]. We successfully designed, fabricated and tested a HfZrO-based tunneling diode where the HfZrO having a thickness of 6 nm was grown directly on doped Si [
22], showing ON currents higher than 1 mA; after that, we used it in the context of electromagnetic energy harvesting with a TER >10
3. Decreasing the FTJ thickness down to 1 nm, very recently a TER of 1900% was obtained growing HfZrO directly on Si [
23]. In all these examples, the growth technique is atomic layer deposition (ALD).
Furthermore, the FTJ is an ultrafast switch, since the polarization of the HfZrO thin film makes the ferroelectric domains change their orientation within few ns [
24], or even below 1 ns [
25], when positive and negative voltages are applied.
We used FTJs reported in [
22] based on HfZrO (
Figure 6a) to demonstrate that an FTJ is acting as a microwave switch. The structural tests, fabrication and measurements are reported in [
22]. The FTJ considered henceforth is made up of a 6 nm-thick HfZrO ferroelectric layer grown directly on doped Si substrate, on whose back side an Al bottom electrode with a thickness of 100 nm is deposited. The top electrode is a metal layer of Cr (5 nm)/Au (100 nm), with a contact area of 150 μm × 150 μm. Tens of such FTJ were grown on the same chip and the electrical measurements showed a good yield. The current density is displayed in
Figure 6b: here, we can observe two distinct curves in ON- (
JON) and OFF- (
JOFF) state, as a function of the applied voltage. The dependence is rather symmetric and ambipolar. The ON-state is characterized by a current density of 9 A/cm
2 at +5 V, while at the same polarization value we have an OFF-current of 1 mA/cm
2. This high ON-OFF ratio is typical for HfZrO grown directly on Si and is similar with that from [
23], where 1 nm-thick HfZrO was grown by ALD directly on Si.
The TER for positive voltages is displayed in
Figure 7 and shows a value of 9 × 10
3 at +5 V. The ON-state current was obtained by applying a poling ramp signal of +10 V for 20 s, and the OFF-state current was then achieved by using the same poling signal with reversed polarization of −10 V. Repetitive measurements were performed to switch on and off the polarization dipoles and, thus, the ON- and OFF-states of the current, revealing that no significant changes could be observed. Note that when the above FTJs are used in microwaves at the wafer scale, the doped Si (which is the bottom electrode of the FTJs) can be obtained by ion diffusion in selected areas of an HR Si substrate. This is necessary, since doped Si is a lossy substrate for microwaves, while HR Si with a resistivity higher than 10,000 Ω·cm behaves as an insulator.
The equivalent circuit of the considered FTJ at microwaves is represented in
Figure 8. The FTJ is modeled as a parallel resistance-capacitance circuit, where the capacitance
CD is estimated from measurement to be around 200 pF, and the resistance
RD =
∂V/
∂I is the differential resistance of the FTJ (since its current-voltage dependence is strongly nonlinear);
RC and
LC are the resistance and inductance of the metal contacts, respectively. We consider that
RC = 0.1 Ω and
LC = 1 nH, as resulted from measurements. We stress here that
CD is the junction capacitance, which plays an effective role only when the diode is in reverse bias (OFF-state, no DC current flowing), while
RD is equal to some tens of MΩ in reverse bias (OFF-state) and to about 2 kΩ in forward bias (ON-state). Keeping this in mind, the microwave behavior of the FTJ-based switch (which is different from its DC behavior) is as follows: in
Figure 8a, a negative DC polarity is applied (reverse bias) and the FTJ is in OFF-state in DC and in ON-state at microwaves; vice versa, in
Figure 8b, a positive DC polarity is applied (forward bias) and the FTJ is in the OFF-state in DC and in the ON-state in microwaves. In the case of reverse bias, the big capacitance is a short-circuit for microwave signals (since it is equal to an impedance of just 0.08 Ω at 10 GHz), whereas in the case of forward bias, the 2 kΩ resistor behaves as an attenuator, thus blocking the microwaves passing through the FTJ. In other words, the ON-state in microwaves corresponds to the OFF-state in DC and vice versa. In the following, we will avoid any confusion by indicating clearly in the text to whom the ON- and OFF-state are assigned, i.e., to DC or microwave switch. This decoupling between the DC behavior of the FTJ and the functioning of the switch in microwaves has an important advantage regarding the noise. More specifically, as will be shown later on, the FTJ is a low-noise microwave switch.
The dependence of
RD on the applied DC voltage is represented in
Figure 9 for the DC OFF-state (
Figure 9a) and ON-state (
Figure 9b) (ON- and OFF-state of the microwave switch, respectively, as explained above). In
Figure 9a, the differential resistance takes values of some MΩ up to about 50 MΩ (as expected), while in
Figure 9b it goes down to about 2 kΩ at +5 V.
The noise equivalent power (
NEP) is defined as
NEP = (4
kBTRD)
1/2/[(
RD2/2)(
∂2I/
∂V2)] [
26] and is represented in
Figure 10 in the two states of the DC switch. In the OFF-state, the NEP takes values of some
fW/√Hz, whereas in the ON-state it reaches about 1 nW/√Hz at +5 V. This means that the microwave switch is a very low-noise device in its ON-state, which represents a major advantage for high-frequency components.
In
Figure 11 we have depicted the geometry of the FTJ-based microwave switch made on HfZrO/high-resistivity silicon (HR Si) substrate, with the ferroelectric layer having the same thickness as in the previously reported experiments [
22]. The simulation results of this FTJ-based microwave switch are displayed in
Figure 12. Here we show the scattering parameters, in terms of modulus of the reflection coefficient (|S
11|) and of the transmission coefficient (|S
21|), in the ON- and OFF-state of the microwave switch in the band 0.1–32 GHz. In the OFF-state of the microwave switch, |S
11| is about −0.98 dB over the whole frequency range, whereas |S
21| is about −19.4 dB. In the ON-state of the microwave switch, in the X band |S
11| is between −10.22 dB and −13.8 dB (and it remains better than −6 dB up to 22.14 GHz), whereas |S
21| is between −0.2 dB and −0.44 dB. These results confirm that the FTJ-based microwave switch ensures good performance in a large band in terms of both isolation (|S
21| in OFF-state) and insertion loss (|S
21| in ON-state).
Thus, we see that FTJ is a good microwave switch that could have less than 1 ns switching times, low applied DC voltages allowing reversible switching between ON and OFF states, and is highly reproducible using existing clean-room technologies and ALD deposition methods.
Finally, in
Figure 13 we present a transmitter/receiver (T/R) module based on the FTJ-based microwave switch under study. The T/R module consists of a 2-element patch antenna array with operating frequency in the X band. Each antenna is made of a 110-nm-thick graphene multilayer, with overall dimensions of 5.5 mm × 4 mm (width × length), grown on a SiO
2/HR Si substrate (300 nm/525 μm). The conductivity of the two graphene patches can be ideally tuned by a top-gate configuration using a 30 nm-thick HfO
2 layer, two decoupling capacitors (
Cdec) and a polarization network. This way, we can tune the gain and the operating frequency of each antenna [
27,
28] thus conferring “smart” characteristics to the T/R module. We simulated the single graphene patch and the array made of two elements using the 3D EM simulator CST Studio Suite
®, then we used the resulting 1-port (or 2-port) scattering matrix to simulate at the circuit level the entire T/R module (by NI AWR Design Environment
®, AWR Inc., El Segundo, CA, USA). In detail, each antenna is connected to an FTJ-based microwave switch, and each switch can be biased independently in order to achieve a greater degree of freedom in the control of the two FTJs.
From the circuit simulations, we found that in the X band, when both microwave switches are in their OFF-state, the isolation between them is more than 50 dB. Otherwise, when one of the switches is ON and the other one is OFF, the isolation between them is at least 30 dB. If we consider the T/R module in either transmitting or receiving mode (hence, with a single microwave switch in its ON-state), we observed that the reflection coefficient of the active antenna (as seen from the “RF IN/OUT” port in
Figure 13) is better than −10 dB all over the X band, hence the matching to the input impedance of 50 Ω is very good. On the other hand, the power transmission from the “RF IN/OUT” port towards the other antenna is less than −27 dB on the entire X band, hence the antenna connected to the microwave switch in its OFF-state is completed isolated from the excitation port. Furthermore, the isolation between the two antennas is at least 33 dB, hence there is no transmission of microwave power between the two patches, meaning that they are basically decoupled. The results of the simulation are presented in
Figure 14. In this figure we study the T/R module in TX mode. In this case, we will consider the following: port 1 is the “RF IN” port where the RF excitation signal is injected, port 2 is connected to the RX antenna (after the switch “off”), and port 3 is connected to the TX antenna (after the switch “on”).
Figure 14 shows the scattering parameters which relate these three ports.
The 110 nm-thick graphene multilayer has been already fabricated (Plasma Enhanced Chemical Vapor Deposition (PECVD) NANOFAB 1000, Oxford Instruments, Abingdon, Oxfordshire, UK) and fully characterized (4-point probe, Raman spectroscopy, Atomic Force Microscopy (AFM)), exhibiting a conductivity of about 16,150 S/m and a Root Mean Square (RMS) roughness of 3.6 nm (these data were used to properly simulate the patch antennas). The further processing of the graphene/SiO2/HR Si wafer is still on-going for the optimization of the HfO2 layer in the top-gate configuration. After that, a complete set of graphene patches and 2-element arrays will be fabricated and tested.