An RF Model and Memristive Single-Pole Double-Throw

Nicolas´ Wainstein and Shahar Kvatinsky Andrew & Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa, Israel 3200003 Email: [email protected], [email protected]

Abstract—In this paper, we present a scalable physics-based and simulation tools, and is necessary for the expansion of model that accurately predicts the steady-state high-frequency memristive technologies into RF applications. behavior of memristive RF switches. This model is, to the best of our knowledge, the first lumped RF memristor model that In this paper, we present a scalable lumped model that pre- includes device parasitics obtained from physical measurements dicts to a great extent RFMS physical behavior. The proposed reported in the literature. Furthermore, we propose two topolo- model relies on the VTEAM model for the transient analysis gies (series and shunt) for non-volatile single-voltage-controlled (i.e., describes the programming sweep) and introduces a Single-Pole Double-Throw switches using the proposed lumped structure-inspired lumped RLC circuit to describe its behavior RF memristor model. These topologies exhibit low insertion loss at high frequency. We demonstrate the use of the lumped model and high isolation. Adding non-volatility to RF switches will result by designing and evaluating two topologies of non-volatile in reduced power consumption. Single-Pole Double-Throw (SPDT) RF switches with a single bias voltage. SPDT switches [7] play a vital role as control I.INTRODUCTION devices in several RF and applications such as Memristive devices are two terminal passive circuit ele- phase shifters, attenuators, and shared system resource access. ments whose resistance is determined by the history of the applied voltage or current and retained whenever the voltage II.RFMEMRISTIVE SWITCHES i.e. or current is no longer applied ( , non-volatility) [1]. These A. Previously Proposed RFMS devices can be used as switches with discrete states, as they exhibit nonlinear behavior with a High Resistive State (HRS) Previously proposed RFMS can be characterized as elec- and a Low Resistive State (LRS). trochemical metallization (ECM) [2], consisting The switching mechanism varies with the technology, of a pair of electrochemically asymmetric metal electrodes though it is typically determined by the formation or rupture separated by a small-scale gap or an insulator. At LRS, a of conductive filaments between two electrodes owing to thin metal filament shortens the electrodes, while at HRS the electrochemical reactions, ion migration and Joule heating [2]. filament disappears. For instance, Fig. 1a shows the device Switching from HRS to LRS is called SET, while the opposite structure presented in [3], where Ag and Ti/Au/Ag electrodes switching is called RESET. These devices have proven to be an (active and inert, respectively) are separated by a 35 nm attractive feature for several applications (e.g., memory, logic air gap. The device is fabricated over a SiO2 surface in a and neuromorphic) due to their non-volatility, low switching high resistivity silicon substrate, in a Coplanar Waveguide time and energy, scalability, small footprint, and CMOS inte- (CPW) transmission line. The reported device presents an gration compatibility. IL of ∼0.3 dB and an IS of ∼30 dB at 40 GHz, and a typical cut-off frequency of 35 THz. The LRS and HRS are Recently, the use of memristive devices as RF switches achieved by applying, respectively, 3 V and −0.4 V across the has been proposed [3], [4], [5], exploiting their achievable electrodes. The authors claim that frequencies above 40 GHz low insertion loss (IL), high isolation (IS) and high cutoff could be achieved by canceling undesired substrate moding frequency, which are desired characteristics in RF switches. effects that perturb the performance of the , for example The non-volatility of memristors implies that no bias voltage by integrating the device in a grounded CPW structure. or current is required to maintain a particular state, hence reducing the energy consumption. Moreover, the small size Another RFMS, presented in [4] is a 10 µm gapless-type of memristors could improve the density of transceiver chains ECM RFMS with Ag and Ni electrodes (active and inert, in multiple-input multiple-output (MIMO) systems. respectively). Measurements from 1 to 6 GHz demonstrate an IL of less than 0.5 dB and an IS better than 30 dB. The While several physical and mathematical models have been voltage/current required to change the state of the device is developed for memristors (e.g., VTEAM [6]), the literature nominally 1 V/10 mA (SET) and −1 V/10 mA (RESET). still lacks a precise and scalable lumped physical model that In [5], a Cu/SiO2/Al ECM RFMS is presented. This switch describes the behavior of the device at high frequencies, such has been characterized at 0.15 GHz, achieving an IL of 1.6 as those in radio-frequency applications (RF). Such a model dB and an IS of 20 dB. Regardless of its lower performance, would be a fundamental asset for RF Memristive Switches when compared to the aforementioned RFMS, it stands out (RFMS) with different structures and materials over a wide for its simple structure, and therefore its simpler fabrication range of frequencies. This model could be used in RFIC design process. RF lumped device modeling [13]. Particularly, the device is considered as a gap discontinuity in the CPW at HRS and as a high impedance short-line section at LRS. The assumptions made in this model are (a) lossless substrate (i.e., high resistiv- ity silicon), and (b) identical and perfect conductor electrodes (i.e., equal Lw and zero resistance in both electrodes). B. Physical Parameters The lumped elements in the proposed model can be deter- mined directly from the dimensional parameters of the RFMS. The ON-state resistance of the filament (at LRS) accounts for the skin depth of a conductor with finite thickness and is ρ l R = fil gap , Fig. 1. (a) Memristive switch physical structure, as proposed in [3] (Reprinted ON −t /δ (1) by permission from Macmillan Publishers Ltd: Nat. Comm., copyright 2015), wfilδ(1 − e fil ) and (b) our proposed device model. The model is divided into three ABCD where ρfil, lgap, wfil, tfil are, respectively, the filament’s matrices (pointed rectangles), and ABCDY is modeled as a Y-Parameter Π equivalent. The equivalent capacitors, Cp, are highlighted in yellow. resistivity, length, width and height. The skin depth is δ, and wfil depends on the compliance current. The between- B. Previously Proposed Device Models electrodes (gap) capacitance is modeled as Models are indispensable tools in circuit design and simu- ε0εeff ABE lation, as they simplify the understanding of the device and COFF = k, k ∈ [1.3, 1.6], (2) l predict its behavior. Precise models for RFMS will allow gap accurate circuit designs and device optimization. In both [3] where εeff is the effective relative permittivity in the CPW, and [5], the RFMS is modeled as a simple parallel RC circuit. ABE is the electrodes’ lateral section and k is a dimensionless A first order analysis of the physical parameters is described in constant that accounts for the fringe capacitance, which is [3], where the LRS resistance and the gap capacitance (RON between 30% to 60% of the parallel plate capacitance [14]. and COFF , respectively) are theoretically determined. Though The SiO2 parasitic capacitor is determined by the SiO2 height the models are sufficiently accurate to describe the IL and tox, the electrode’s width wE and the SiO2 relative permittivity IS of the device, they do not fully describe its S-parameters εox, and is ε0εox (i.e., their steady-state high-frequency electrical behavior). Cox = (wE + 1.5 tox). (3) Furthermore, neither the skin effect of the conductors nor the tox fringe capacitance [8] at the electrodes are considered in these The silicon substrate capacitance Cs and the fringe capacitance models. These effects will be dominant at high frequencies, C0 are and will determinate the RFMS performance and influence the matching network design. Cs = 2(εSi − 1)ε0FSi ,C0 = 4ε0F0, (4) An RF memristor model that predicts the maximum where εSi is the silicon relative permittivity, FSi is the silicon switching frequency in which a memristive memory cell can geometry factor, and F0 is the air geometry factor at the be operated is proposed in [9]. While this model consi- electrodes. The filament and electrode inducances are ders further high-frequency phenomena, it is still a transient µ µ (time-dependent) model, thus not intended to describe the L = 0 ,L = 0 , (5) 4F w 4F S-parameters of the memristor. In [10], a finite-difference 0fil 0 time-domain implementation of the memristor using the non- where F0fil and F0 are, respectively, the air geometry factor linear ion drift model [11] is proposed. This model allows an at the filament and the electrodes. electromagnetic-wave analysis of the memristor, yet it lacks the capacitive and inductive parasitics present in real devices. C. Fitting the Model to Experimental Data To extract the lumped parameters from experimental data III.PROPOSED RFMSLUMPED MODEL [3], we perform a fitting procedure. As shown in Fig. 1b, the A. Proposed Model Description proposed model can be described as three cascaded two-port Based on an examination of the memristive device structure network ABCD-transmission matrices. Neglecting Lw, the presented in [3], we propose a novel and more accurate model, circuit can be analyzed as a Y-equivalent Π two-port network, shown in Fig. 1b. The model uses the two basic parameters where   from [3], R and C , where R represents the gap’s resistance 1 OFF Y12 = − + jωCOFF , (6) (i.e., describes the presence or absence of the filament) and R + jωL C is the gap capacitance (i.e., capacitive coupling effect OFF Y + Y = Y + Y = jωC , (7) between the electrodes). Additional capacitors and inductors 11 12 22 12 p are added to represent the SiO2 parasitic capacitance, Cox, where Cp is the equivalent capacitor as shown in Fig. 1b. The the Si substrate capacitance, Cs, and the fringe capacitance Y-equivalent Π is transformed to ABCD-parameters to define between the signal line and ground planes, C0. The inductance ABCDY . The total ABCD matrix is the product of the three of the filament and the electrodes are also considered and matrices and is then transformed to S-parameters. are, respectively, L and Lw. The inductors and capacitors are Initial fitting is done using the Simulated Annealing [15] modeled as in [12]. algorithm to search for the minimum RMS error between The model is consistent with previous work in CPW and the experimental and modeled S-parameters. Seed values for TABLE I. COMPARISON OF DIFFERENT MODELS data. Although the RC model exhibits a good match with Extracted parameters Physical parameters S Parameter 21 magnitude, it can be observed that our proposed model [3] This work This work improves the S-parameters’ accuracy, particularly of the RON 2.8 Ω 2.6 Ω 2.56 Ω phase, which is crucial for phase-sensitive applications and COFF 1.145 fF 1.145 fF 1.168 fF for designing matching networks. This trend becomes even Cp - 3.08 fF 1.15 fF more significant when extrapolating to higher frequencies, L - 77 fH 52 fH where the devices become more capacitive, due to the Lw - 3.7 pH 3.1 pH increasing influence of the electrodes’ impedance. Table I lists the fitting parameters for both models. The overall improvement with respect to [3] in the phase RMS error is 87% and 33% for, respectively, the ON and OFF state. The OFF-phase RMS error is still significant and it is caused by S11 phase, which is lower than 90◦. The overall enhancement of the magnitude RMS error is 25% for the ON state when compared to [3]. The RC model is sufficiently accurate for the OFF-state magnitude so no significant improvement is observed. B. Extracted Parameters vs. Physical Parameters Table I shows that the extracted parameters and the physics- based parameters determined by (1)-(5) are almost identical. This confirms that the physical parameters accurately predict the high-frequency behavior of the RFMS. Additional improve- ments in the model should add an analytical expression of the fringe capacitance at the gap and add to Cp the equivalent capacitance of a step change [16]. To validate this model, further tests should be performed with different data sets and different devices, varying the electrode’s size, the gap’s size and the CPW structure. V. RFMSSPDTTOPOLOGIES RFMS exhibits high-performance characteristics, small size and non-volatility, which makes it an excellent candidate to become a building block in high-performance, low power SPDT switches. These switches fulfill important functions in many RF applications, such as controlling the RF signal flow and providing multiple access to shared resources. With the Fig. 2. S-parameter simulation results as determined by the proposed model proposed model, more accurate simulations can be achieved, (black) and the RC model in [3] (blue dashed line) vs. experimental data (red making it possible to test and design RF SPDT and other RF line). (a) S11ON and (b) S21ON . applications. In this section, we present two different RFMS SPDT R and C can be determined as explained in the sup- OFF topologies, which make use of a single control-voltage (i.e., plementary material of [3]. To achieve even more accurate a single bias signal) to simultaneously toggle between LRS results, the obtained value of L can be used to determine the w and HRS the two branches. The switch design is focused on ABCD and then transformed it to a Y matrix. Parameters Y achieving broadband matching (low return loss), high IS and C , L and R can be extracted by fitting (6) and (7). C p OFF low IL, while utilizing only a single memristor per output port is determined from the OFF-state (HRS) S-parameters, where and only one overall control voltage. The topologies have been Y ' −jωC . The extracted parameters from the fitting 12 OFF simulated in Advanced Design System (ADS) from Keysight procedure are listed in Table I. using the aforementioned model and CPW sections as in [3]. IV. RESULTS We assume that no self-switching occurs at the band of interest The proposed model is evaluated in two different ways. and we also assume cold-switching (i.e., switching occurs First by comparing the proposed model against the model when the RF signal is applied). presented in [3] and then by examing the extracted parameters A. Series Switch from the fitting procedure with respect to the physical param- eters determined by (1)-(5). The first evaluation demonstrates Fig. 3a shows the proposed series topology, where one the improvement in the device model as compared to [3]. memristor per port is used (M1 and M2). The circuit works V = 3V The second provides an estimation of the proximity between as follows: when ctrl , M2 switches to LRS and M1 the physics-based calculated parameters and the extracted to HRS, hence providing a conductive path for the RF signal parameters. from port P1 to port P3, while port P2 is isolated (observe the opposite connection). Reciprocal analysis is done when A. Comparison Between Models Vctrl = −3V . Note that because the RESET mechanism is Fig. 2 shows the results of our model and the RC model faster than the SET, particular care must be taken when de- presented in [3] versus experimental results. To perform a fair signing the controller to provide a defined compliance current comparison, the model in [3] is fitted to this experimental to protect the RFMS. The inductors act as RF chokes and oe hntesre PTsnetelse eie rmthe from derived remarkably losses is performance the dB Its since 1 GHz. SPDT 30 λ/ of series at the IL dB than 26 an lower of provides IS an characteristic and narrow-band The 4b. series between the path than IS RF the lower direct to a counterpart. owing provides a However, and is narrow-band branch. there becomes the a HRS in into at When ports LRS) is branch. desired at memristor the is the isolating memristor thus path, the on high-impedance (whenever ground short-circuit quarter-wavelength to the the path of resistive use ( makes low configuration a This LRS. provide memristors The htdmns osdrbyisI thge rqece.The frequencies. higher at IS its considerably diminish that when topology, series the in As V grounded. terminal one have Switch Shunt as IS B. in the improvement at the dB [3]. dB 6 over to 0.26 expected below performance compared the results, is broadband and IL simulation a spectrum the shows presents desired and 4a It dB Fig. 36 band. over tee. designed is bias they IS a as the ideal, of where floating considered part avoiding are be thus inductors could blocking, and DC Capacitors and nodes. capacitors feeding the while RF memristors, proposed the provide the for of reference dashed) DC a (black provide IL topologies. and SPDT (red) Shunt IS (b) of and results Series Simulation (a) 4. 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