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1 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH A Ferroelectric-Capacitor-Based Approach to Quasistatic Electric Field Sensing Bruno Andò, Member, IEEE, Salvatore Baglio, Senior Member, IEEE, Adi R. Bulsara, and Vincenzo Marletta Abstract A new sensor for quasistatic electric field (E-field) measurements based on a ferroelectric capacitor (which acts as a nonlinear active dynamic element) is discussed in this paper. The device was theoretically modeled and experimentally characterized, and the data that were gathered were used to refine the model parameters. The E-field sensing strategy is based on the exploitation of a mechanism to convert the external target E-field into a perturbation on the polarization state of a ferroelectric material: a detailed analytical description of this process is given together with its experimental validation. Optimal results have been obtained with a driving (i.e., reference) signal of 10 V at 100 Hz, which was used to polarize the device. The noise floor of the device has been evaluated through an analysis of the power spectral density, which yields a value of 0.4 (V/m)/Hz 1/2. The hysteretic capacitor in this paper is the cornerstone of an innovative system for detecting weak E-fields (assumed to be dc throughout this paper, although it can also be applied to detect time-periodic E-fields) through the exploitation of the nonlinear behavior of a coupled oscillator system wherein the active (nonlinear) elements are the ferroelectric capacitors. Our results cover the basic building blocks that were necessary for the optimal realization of this coupled circuit. Index Terms Ferroelectric capacitor, hysteresis, nonlinear devices, quartic double-well potential, quasistatic electric field (E-field) sensors, Sawyer Tower (ST) circuit. I. INTRODUCTION ELECTROSTATIC field sensors are employed in many applications, either as stand-alone devices or as parts of more complex measurement systems [1]. Their common applications include the monitoring of fields that were generated by atmospheric phenomena, particle detectors, mass spectrometers, scanning microscopes, and electrophoresis systems [2], prevention of problems due to static charges either in the processing or the storage of inflammable materials, and the production of electronic devices. The automotive industry makes use of these sensors in active and passive safety systems (e.g., air bags), occupant sensing systems, and touch controls [3]. Other interesting applications occur in the areas of security Manuscript received October 23, 2008; revised April 28, First published September 22, 2009; current version published February 10, This work was supported in part by the Office of Naval Research under Code 30 and the Office of Naval Research Global under a Naval International Cooperative Opportunities in Science and Technology Program Grant. The Associate Editor coordinating the review process for this paper was Dr. Mark Blodgett. B. Andò, S. Baglio, and V. Marletta are with the Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, University of Catania, Catania, Italy ( bruno.ando@diees.unict.it; salvatore.baglio@diees.unict.it). A. R. Bulsara is with the Space and Naval Warfare Systems Center Pacific, San Diego, CA USA ( bulsara@spawar.navy.mil). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TIM and surveillance, where the sensors can be used to remotely detect weak fields that were produced by humans or animals. Traditional electric field (E-field) meters (e.g., body and ground reference meters, electro-optic meters [4], the Kelvin probe [5], [6], and shutter- and cylindrical-type field mills [7]) are generally based on linear transduction mechanisms. However, recently, the idea of innovative E-field sensing solutions based on nonlinear coupled oscillators with hysteretic elements has been presented by the authors [8] [10]. Other applications of ferroelectric transducers have been reported in the literature [11], with applications, among others, to storage element [12], temperature sensors [13], [14], infrared sensors [15], and force, pressure, vibration, and acceleration sensors [16], [17]. In this paper, we exploit the nonlinear dynamics of an (active) ferroelectric material for transduction applications; our approach is based on ferroelectric capacitors that were embedded in a ring oscillator whose polarization state is perturbed by the external target E-field. For such systems, a theoretical (nonlinear dynamics based) model has already been investigated together with some preliminary experimental confirmations [8]. However, to optimize the performance of these systems, it is of primary importance to accurately characterize and model a single ferroelectric capacitor together with the mechanism for perturbing its polarization state. This approach is the specific topic of this paper, which also focuses on the exploitation of the E-field sensing properties of a single ferroelectric capacitor for E-field sensing applications. In Section II, some relevant theories are presented, and the ferroelectric capacitive device (together with the characterization of the hysteretic behavior) and the strategy for gathering the target E-field are described. In Section III, the capacitor response to an external perturbation is discussed, and experimental confirmations of the proposed approach are reported. Some concluding remarks and a perspective on the importance of the results that were presented here for the coupled capacitor device are given in Section IV. II. BASIC THEORETICAL BACKGROUND AND THE SENSING STRATEGY From the time of their discovery, ferroelectric materials have widely been studied and used for the development of a wide range of transducers [11]. A ferroelectric material has a spontaneous reversible polarization due to the displacement of the central ion of the crystal from its symmetric position; due to this structural asymmetry, it is polarized, even in the absence of an external E-field [18], [19]. A typical hysteresis loop that describes the relationship between the resulting polarization P and the applied E-field E is shown in Fig. 1(a). When the /$ IEEE

2 642 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH 2010 Fig. 1. (a) Ferroelectric hysteresis loop and (b) the corresponding potential energy function that underpins the dynamics. E-field is zero, the ferroelectric polarization resides in one of the two stable states Pr and P r + ; these states are the negative and positive remnant polarizations, respectively. If an external field E sat + is applied to the ferroelectric, it is polarized to P sat, + i.e., the positive saturation polarization. After the external field is removed, the polarization settles back to P r +. In the opposite case, with an external field Esat, the ferroelectric is polarized to Psat. After the field is removed, the polarization settles back to Pr. Thus, the polarization of a ferroelectric depends not only on the actual value of E but also on its previous values. The points where P =0are indicated as Ec and E c +, i.e., the negative and positive coercive fields, respectively [20]. The idea that is highlighted throughout this paper is the possibility of exploiting the inherent nonlinearity of ferroelectric materials to sense unknown E-fields. To start with, an appropriate analytical model for the prediction of the device dynamics is addressed. Several models that were aimed at predicting the behavior of hysteretic devices are present in the literature, e.g., the state-space model [21], the viscoelastic model [22], the Tanh model [23], and the Preisach model [24], [25], whereas many other models have been developed to address ferroelectric capacitors [26] [28]. A significant analytical representation of the macroscopic dynamic behavior in a ferroelectric sample can be realized by the Landau Khalatnikov equation [29], i.e., τ dp dt = U(P, t) P where P is the electric polarization, and τ is the system time constant. This model describes the hysteretic behavior through the (bistable) potential energy function U(P, t), which underpins the switching mechanism between the two stable states of the system. An example of the potential is given in the Fig. 1(b), together with its correspondence with the hysteresis loop. The height of the potential barrier represents the energy that was required to switch from one stable state to another under a static applied E-field. We adopt (following the Landau Khalatnikov model [29]) a standard quartic form for the potential, i.e., (1) U(P, t) = a 2 P 2 + b 4 P 4 ce(t)p (2) which yields the dynamic model τ P = ap bp 3 + ce(t) (3) where a, b, c, and τ are quantities that will be estimated. In particular, a and b are material dependent, c is a fitting parameter, and τ is a time constant that rules the dynamic behavior of the system, whereas E(t) represents the driving field. As will be discussed in the next sections, the ideal driving signal E(t) would have an amplitude just above what is necessary to overcome the coercive field of the material. The overdot denotes (throughout this paper) the time derivative. A. Device Under Test The ferroelectric capacitor in this paper is depicted in Fig. 2(a). It consists (from bottom to top) of a common bottom electrode, a thin layer of ferroelectric material, and a pair of driving electrodes (which produce the bias polarization) that host a central sensing electrode. The capacitor polarization is induced through the voltage that was applied to the driving electrodes, with the charges that were accumulated in the sensing electrode producing a perturbation to the polarization state. A view of the actual prototype, which hosts several top electrodes set in the same die, is shown in Fig. 2(b). The electrodes are made of platinum, whereas the ferroelectric layer, with a thickness of 2.17 μm, has a composition of 30/70 PZT with a 20% excess of Pb. The idea is to use a three-electrode configuration, i.e., two medium or large electrodes will be used to polarize a region of the ferroelectric layer ( the sensing region ), and a small electrode, which will be placed in the same region, will be used to convey the perturbation (due to the target field) to the sensing region. The latter electrode is wired to a charge collector that consists of a copper plate. The purpose of the charge collector is to collect the charges that were induced by the target E-field; in turn, the collected charge is immediately transferred to the sensing plate, thus perturbing the polarization of the sensing region. This behavior has been confirmed through the finite-element method analysis [8], and in Fig. 3, a typical polarization state of the cross section is shown without [see Fig. 3(a)] and with [see Fig. 3(b)] a perturbing action that was produced through the sensing electrode. The changes that were induced in the polarization status of this capacitor will manifest themselves in alterations of the output signal from the signal conditioning circuit.

3 ANDÒ et al.: FERROELECTRIC-CAPACITOR-BASED APPROACH TO QUASISTATIC ELECTRIC FIELD SENSING 643 Fig. 2. Ferroelectric capacitor. (a) Device schematic, wherein the dashed line outlines the ferroelectric capacitor in which two large top driving electrodes are used to polarize the ferroelectric sensing region. The small electrode in the middle is wired to a charge collector that collects the charges that were induced by the target E-field. (b) Real view of the prototypes that were used in this paper, together with a detailed view of the material layers. (c) Schematic of the charge collection strategy. Fig. 3. Qualitative FEM analysis of the ferroelectric capacitor (a) without and (b) with a perturbing action that was produced through the sensing electrode. B. Signal-Conditioning Circuit The readout strategy utilizes a Sawyer Tower (ST) circuit [30], as shown in Fig. 4(a), where C FE and C f represent the ferroelectric capacitor (with the sensing electrode to induce a perturbation ΔP in the ferroelectric polarization status, as schematically shown) and the feedback capacitor, respectively, whereas R f was introduced to avoid the drift in the circuit output. Effectively, the ST circuit is a charge integrator that, by a charge-to-voltage conversion, permits the measurement of the average polarization in the material. The frequency response of the ST circuit is given by G(s) = V out(s) V in (s) = C FE sc f R f C f (1 + sc f R f ). (4) Choosing an appropriate value (in the frequency domain, with s denoting the frequency) for R f (R f 1/sC f ) leads to V out = A FE C f P (5) with A FE and P being the areas of the driving electrodes of the ferroelectric capacitor and the material polarization, respectively. The driving voltage V in is related to the applied E-field E and the material thickness d 2 by V in = Ed 2. (6) The ST circuit operates in a high-pass mode. To suitably stimulate the ferroelectric capacitor, the constant target E-field must be modulated into a quasistatic signal, and this condition can be accomplished through a field-mill strategy. In the remainder of this paper, a low-frequency external E-field will be used for experimental characterization purposes. An example of a typical ST output is shown in Fig. 4(b), where the amplitude modulation of the reference driving signal (applied to overcome the coercive field and induce hopping events between the stable steady states of the potential) due to a (low-frequency) target E-field is clearly visible. C. Charge Collection Strategy The methodology for sensing a quasistatic E-field can be synthesized through the following relationship: ΔE ext ΔP ΔV out. (7)

4 644 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH 2010 Fig. 4. (a) Schematic of the ST conditioning circuit, where the sensing electrode in the C FE capacitor for inducing the perturbation ΔP as in the ferroelectric polarization status is highlighted. (b) Typical output voltage signal, where the amplitude modulation of the reference signal is a result of the applied (target) low-frequency signal. Simply put, a variation of the target E-field produces a concomitant variation in the polarization state of the ferroelectric layer in the sensing region ; in turn, this change in polarization is transduced into a voltage variation by the conditioning circuit, as indicated in (5). Naturally, the first part (ΔE ext ΔP ) of (7) must be modeled and validated. An analytic model that describes the relation between the target E-field and the polarization in the ferroelectric related to the dimensions of the charge collector is now presented. Let us consider a model system that consists of two large electrodes for generating the target E-field (the exact experimental setup will be described in Section III): 1) the charge collector and 2) the ferroelectric capacitor. This system can be represented by two parallel plate capacitors that were connected in a series configuration, as indicated in Fig. 2(c), where C 1 represents the capacitors that were formed by the large electrode and the charge collector, and C 2 represents the ferroelectric capacitor under the sensing electrode. Denoting S 1 as the area of the charge collector and assuming a symmetrical distribution of the charge Q on the plates of capacitors, we obtain, as a natural result of Gauss law σ 1 = Q S 1 = ε 0 E ext (8) where σ 1 is the charge density on the surface of an electrode of C 1. This configuration readily leads to σ 2 = Q = S 1 ε 0 E ext (9) S 2 S 2 where S 2 and σ 2 represent the surface area of the sensing electrode of capacitor C 2 and its charge density, respectively. Now, considering that, for weak perturbations, the relationship between polarization and the dielectric displacement vector is given by D = P + ε 0 Epol (10) and assuming that the polarization field is close to zero in the vicinity of the sensing electrode (E pol = 0) for C2,itfollows that P = D = σ 2 u n, with u n representing the normal vector to the surface S 2. As a direct consequence, we obtain ΔP =Δσ 2 = ε 0 S 1 S 2 ΔE ext. (11) Hence, the perturbation in the polarization state of the ferroelectric material is directly related to the external target field, and this effect is amplified by the ratio between the two plate areas. These theoretical results will experimentally be verified in the final part of this paper, and some corrections to parameters that account for the particular prototype that was considered in this paper will be derived. D. Experimental Characterization in the P E Domain The ferroelectric capacitor follows the dynamics (3) in the P E domain. Before proceeding to the main point of this paper, i.e., the detection of target E-fields, the material parameters (a, b, c, τ) must be determined. This approach has been performed by driving the device with an AC E-field at various frequencies and amplitudes and acquiring the output voltage V out of the ST circuit. No (other) external E-field is present. The driving AC E-field must be suprathreshold, i.e., of sufficient amplitude, to cause the system to sweep through its hysteresis loop or, equivalently, switch between the two stable states in the potential of Fig. 1 on a timescale that was controlled by the driving period. Clearly, the driving field must be of sufficient amplitude and frequency to overcome the coercive field of the material in a real system. Here, it is important to note that, from a theoretical standpoint, one can compute the deterministic switching threshold of the dynamics (13) by a simple calculation of the inflexion points of the potential energy function (2). For a static driving field, one obtains a value of (4a 3 /27b) 1/2. With a time-sinusoidal driving field, the corresponding threshold value of the driving amplitude scales as the 2/3 power of the driving frequency [31]. The evaluation of the model parameters starts by identifying a, b, c, and τ at the highest frequency and amplitude of the

5 ANDÒ et al.: FERROELECTRIC-CAPACITOR-BASED APPROACH TO QUASISTATIC ELECTRIC FIELD SENSING 645 Fig. 5. Experimental and theoretical (dashed line) hysteresis loops for driving voltages with amplitudes of (a) 10 V pp and (b) 50 V pp with a frequency of 100 Hz. TABLE I MODEL PARAMETERS THAT WERE DERIVED BY THE NELDER MEAD OPTIMIZATION ALGORITHM driving. The Nelder Mead optimization algorithm [32] for minimizing the squared difference between the experimental and theoretical polarizations is then applied; at its core is the rootmean-square-type functional J that computes (as a percentage) the residuals between the predicted (through the model) and the observed values of the polarization that we seek to minimize, i.e., J% = ( ˆP Pexp ) 2 (Pexp ) (12) Here, ˆP represents the estimated polarization that was obtained through the evaluated parameters, and P exp represents the experimental polarization that was obtained by inverting (5). To prevent convergence of the minimization algorithm to a local minimum point in any iteration, the constraint P r = (a/b) is imposed on parameters a and b; this relationship derives from the potential (2), which represents the two stable states in Fig. 1(b), when no forcing field is present. Another convenience that was adopted for the same purpose has been to consider the parameters that were identified for a given frequency and amplitude of the driving voltage as the initial conditions for the identification of parameters that were related to the driving with the same frequency but smaller amplitude, and vice versa. Fig. 5 shows two examples of the experimental and theoretical hysteresis loops for driving voltages with amplitudes of 10 and 50 V pp and a frequency of 100 Hz, with 10 V pp being the smallest value that can induce switching (between the two stable minima of the potential energy function) in the polarization. Table I summarizes the values of the parameters that were obtained through the minimization procedure for the case shown in Fig. 5. First, all the model parameters have been estimated with 50 V pp at 1-kHz driving to take into account the system dynamics. Then, the time constant τ has been fixed to this value, whereas the other parameters have been used as the initial values for the estimations that were performed in the other working conditions in Table I. It can be observed that different values of parameters a, b, and c are obtained for different driving signal amplitudes, which is in line with earlier predictions [31] of delayed transitions in bistable systems under time-periodic external signals. The aim of the previous analysis has been to understand the nonlinear behavior of the device. This aim is necessary for simulation purposes and for the estimation of the material parameters, which allow us to quantify the potential barrier height that constrains the device response to external perturbations.

6 646 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH 2010 Fig. 6. (a) Example of the polarization signal that was obtained by simulating (13) for a driving voltage of 10 V pp and considering a target E-field with an amplitude of V/m at 10 Hz. The E-field produces a modulation (whose depth depends on the intensity of the target field) of the output signal. (b) Linear interpolation of the peak-to-peak modulation amplitude for three values of the target E-field with three different charge collectors (CC1,CC2,and CC3). The model predicts increasing device sensitivity with an increasing size of the charge collector. The solid lines denote a driving voltage of 10 V pp, whereas the dashed-lines denote a driving voltage of 50 V pp. III. RESPONSE TO AN EXTERNAL E-FIELD Equation (11) relates the polarization of the ferroelectric material with the target E-field through the ratio of the surface areas of the charge collector and the sensing electrode. It asserts that a variation in the target E-field yields a proportional variation in the polarization state of the ferroelectric region under the sensing electrode [see Fig. 2(c)] and, hence, a variation of the output voltage of the conditioning circuit. This behavior can be modeled by modifying (3) as follows: τ P = a(p +ΔP ) b(p +ΔP ) 3 + ce(t). (13) Fig. 6(a) shows an example of a polarization signal that was obtained by simulating (13) and (11) in Matlab for a driving (i.e., reference) voltage of 10 V pp at 100 Hz and a target E-field of V/m at 10 Hz. The target E-field produces a modulation of the output signal, whose depth depends on the intensity of the target field itself [see Fig. 6(a)]: this information is needed to estimate the target field. The modulation depth also depends on the area of the charge collector (considering that the area of the sensing electrode is constant), as stated by (11). Fig. 6(b) shows the results that were obtained for three different values of the target E-field and with three different charge collectors (i.e., 30 cm 39.5 cm for CC1, 25.5 cm 25.5 cm for CC2, and 9 cm 9 cm for CC3). The values that were estimated by simulation have been interpolated by a solid line (10 V pp ) and a dashed line (50 V pp ). It can be observed that the two sets of lines in Fig. 6(b) are almost superimposed; therefore, no significant improvements are obtained with an increase in the driving voltage. The relevant information that can be derived from this result is that the model predicts an increase in the device sensitivity with an increase in the size of the charge collector, without a significant contribution from the larger driving voltage amplitude. One further confirmation of the expected behavior can be obtained through a PSpice model. The simulated model circuit with the ferroelectric capacitor is shown in Fig. 7(a), whereas an example of the output voltage signal is shown in Fig. 7(b). For the purpose of investigating the effect of the polarization ΔP, which was induced in the capacitance by the target E-field on the system output voltage, several simulations for different driving voltages and frequencies have been performed. In each case, we vary the amplitude and the frequency of the perturbation on the third electrode of the ferroelectric capacitance. The results confirm the expected behavior, including the linear relationship between ΔP and the amplitude of the output voltage modulation, as shown in Fig. 8 for two amplitudes of the driving voltage. A. Experimental Results The experimental setup (see Fig. 9) consists of two large sheet electrodes of 2 m 2 m and a guard chamber to shield the sensor to avoid a direct (i.e., bypassing the charge collector) polarization of the ferroelectric. The two electrodes, which were separated at 1.40 m, are used to generate a uniform E-field. An AC voltage is applied to these parallel plates, thus producing the target E-field, which, in turn, produces a modulation (see Fig. 10) of the output signal. As already shown, the modulation amplitude is proportional to the target field intensity. To evaluate this modulation amplitude, the waveforms from the ST circuit have been low-pass filtered. The experiments involve subjecting the capacitor to a target E-field with different intensities and frequencies while also varying the dimensions of the charge collector. In particular, the voltage (which produces the target E-field across the capacitor) that was applied to the electrodes has been varied in amplitude from 5 V pp to 20 V pp in steps of 5 V pp, and its frequency was varied from 5 Hz to 100 Hz. Treating the two large electrodes as a parallel plate capacitor, the target E-field amplitudes were 3.57, 7.14, 10.7, and V/m. The driving voltage, which was directly applied to the capacitor plates, has amplitudes that range from 10 V pp to 50 V pp and frequencies of 100 Hz, 500 Hz, and 1 khz. All the experiments have been repeated

7 ANDÒ et al.: FERROELECTRIC-CAPACITOR-BASED APPROACH TO QUASISTATIC ELECTRIC FIELD SENSING 647 Fig. 7. (a) PSpice model and (b) an example of the output voltage signal, which show the effect of the perturbation on the third electrode of the ferroelectric capacitance. Fig. 9. Experimental setup. (a) Two large electrodes (2 m 2 m each) and the guard chamber. (b) Charge collector. Fig. 8. Linearity feature that relates the V out amplitude modulation with different ΔP. with the three charge collectors CC1, CC2, and CC3. Table II summarizes the settings that were used for the experiments. Then, as already described, the (external) target E-field induces a modulation of the output signal. Fig. 10(a) and (c) show ex- amples of the output signal after the removal of the mean value (this step is necessary to make the low-frequency components visible) that was obtained by a driving signal of 10 V pp at 100 Hz and a target E-field of V/m at 5 and 10 Hz. For an in-depth understanding of the effect of the target E-field on the device polarization, a spectral analysis of the ST output signals (correlated to the device polarization) has been carried out. Fig. 11(a) and (b) show the power spectral density (PSD) in the range (0 110 Hz) of the signals in Fig. 10(b) and (d). It is easy to detect the main peak at the frequency (100 Hz) of the driving signal, and a smaller peak at the frequency of the target field [5Hz in Fig. 11(a) and 10 Hz in Fig. 11(b) (d)]

8 648 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH 2010 Fig. 10. (a) ST circuit output signals for driving voltages amplitude of 10 V pp at 100 Hz and a target E-field of V/m at 5 Hz. (b) Voltage signals from the ST circuit after low-pass filtering. (c) ST circuit output signals for driving voltages amplitude of 10 V pp at 100 Hz and a target E-field of V/m at 10 Hz. (d) Voltage signals from the ST circuit after the removal of the mean value. TABLE II SETTINGS THAT WERE USED IN THE CHARACTERIZATION OF THE DEVICE WITH A TARGET E-FIELD shows a magnification (i.e., a zoom ) of the PSDs in the range (0 30 Hz). It is clear that a stronger target signal enhances the height of these peaks in the PSD. The intensity of the target E-field is then estimated by lowpass filtering the output voltage signal of the ST circuit, and examples of such signals are reported in Fig. 10(b) and (d). Taking (5) and (11) into account, a relationship between the low-pass-filtered ST output signal and the external target field E ext can be considered to have the following form: ΔV pp out = αδe ext + β. (14) Considering the peak-to-peak values of the filtered signals in Fig. 10(b), and repeating the experiments with three charge collectors, the results in Fig. 12 have been obtained for target E-fields, with frequencies of 5 and 10 Hz. A linear interpolation of the experimental observations leads to the parameters (α, β) in Table III. It is immediately apparent that there might exist an ideal dimension (between CC1 and CC2) for the collector, which is probably due to a saturated operation of the device after a certain value of the charge collector area. Fig. 12 has two different y-axes scales: the peak-to-peak output voltage is shown on the

9 ANDÒ et al.: FERROELECTRIC-CAPACITOR-BASED APPROACH TO QUASISTATIC ELECTRIC FIELD SENSING 649 Fig. 11. PSD plots of the ST output signals for the cases of a driving (i.e., reference) signal of 10 V pp at 100 Hz and a target E-field at (a) 5 Hz and (b) 10 Hz. Zooms are given in (c) and (d). The legend on each graph shows the amplitudes of the target E-field. Fig. 12. Linear interpolation of the peak-to-peak values of the output signals that were obtained through the various charge collectors and a target E-field having frequency of (a) 5 Hz and (b) 10 Hz The energy barrier is U 0 =5.3812e 6 C/m 2. left axis, whereas the normalized (to the energy barrier height U 0 = a 2 /4b) filtered polarization is shown on the right axis. Note that the ratio P/U 1/2 0 is dimensionless. Although the experimental results demonstrate the ability of the ferroelectric device to sense quasistatic E-fields, an actual characterization (through a measure that can be used for

10 650 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH 2010 TABLE III PARAMETERS THAT WERE RELATED TO THE LINEAR INTERPOLATION INDICATED IN (14) TABLE IV EVALUATION OF NOISE FLOOR FOR TWO FREQUENCIES OF THE E-FIELD (5 AND 10 Hz) AND TWO AMPLITUDES OF THE DRIVING VOLTAGE (10 AND 50 V pp) comparison purposes) of the performance remains to be done. One important performance parameter is the resolution that defines the smallest variation of the measurand that the device can resolve. To obtain this figure of merit, it is necessary to evaluate the noise floor through an analysis of the PSD. The results, for the cases of driving voltages of 10 and 50 V pp and two frequencies (5 and 10 Hz) of the E-field and for the three charge collectors are reported in Table IV. We note that the best results in terms of low noise (noise floor) have been obtained with a driving voltage of 10 V pp and a target field frequency of 10 Hz. Finally, to conclude this section, the pending problem of demonstrating the validity of the model (11) is addressed. To this end, starting from the results in Fig. 12, the ratio between the variation of the polarization P and the variation of the target E-field (this ratio provides a measure of the device efficiency) as a function of the ratio between the two areas S 1 and S 2 [recall that these functions are the areas of the surface of electrodes of the two capacitors in Fig. 2(c)] has been evaluated for the three charge collectors. The results for the two driving signals of 10 V pp at 100 Hz and 50 V pp at 100 Hz are shown in Fig. 13 and have been interpolated by the following relationship: ΔP S 1 = θ 1 ε 0 + θ 2 (15) ΔE ext S 2 where, taking the theoretical expressions (11) into account, the coefficients θ 1 and θ 2 must assume values of 1 and 0, respectively. Referring to the experimental data in Fig. 13, the values for θ 1 and θ 2 have been derived through a linear interpolation of the two first points (before then are the saturation effects observed for larger plates). The slopes of the two lines are identical, thus demonstrating the effectiveness of the charge collection strategy, although the efficiency is lower than what is theoretically predicted (this result is probably related to the nonidealities in the experimental prototype). In addition, the Fig. 13. Ratio between the variation of the polarization P and the variation of the target E-field (this ratio provides a measure of the device efficiency) as a function of the ratio between the two areas S1 and S2. Square and star symbols are used for a driving signal of 10 V pp at 100 Hz and 50 V pp at 100 Hz, respectively. A linear interpolation was used to estimate parameters θ 1 and θ 2 ; only the data that were not affected by saturation have been considered. effect of the driving signal amplitude is apparent: as expected, the external target E-field can produce a stronger perturbation effect over a lower polarized device, and therefore, the 10 V pp working condition appears to be the most suitable setup for the capacitors considered here. Put differently, the target signal is quantified through its modulation of the output waveform, and this modulation will be more visible if the driving signal is lower; hence, the ideal driving signal would have amplitude that is just above what is necessary to overcome the coercive field of the material.

11 ANDÒ et al.: FERROELECTRIC-CAPACITOR-BASED APPROACH TO QUASISTATIC ELECTRIC FIELD SENSING 651 IV. CONCLUSION Recently, a novel approach for E-field sensing has been proposed by the authors [8] [10]. It is based on nonlinear coupled oscillators with hysteretic capacitive elements. Ferroelectric capacitors are embedded in a ring oscillator, their polarization status is perturbed by the external target E-field, and this result reflects into changes in the oscillatory behavior; the sensitivity to the external field is greatly increased by the nonlinear dynamics of the system. Extensive theoretical investigations have been made on this approach. However, the ferroelectric capacitor and the charge collection mechanism (the thrust of this paper) are central to the coupled oscillator system. Hence, their characterization and modeling are of primary importance, which has been the subject of this paper. REFERENCES [1] IEEE Recommended Practice for Instrumentation: Specifications for Magnetic Flux Density and Electric Field Strength Meters 10 Hz to 3kHz, IEEE Std. 1308, [2] P. S. Riehl, K. L. Scott, R. S. Muller, R. T. Howe, and J. A. Yasaitis, Electrostatic charge and field sensors based on micromechanical resonators, J. Microelectromech. Syst., vol. 12, no. 5, pp , Oct [3] Motorola s MC33794 Electric Field Imaging and System IC. [4] IEEE Guide for the Measurement of Quasistatic Magnetic and Electric Fields, IEEE Std. 1460, [5] M. A. Noras, AC-feedback electrostatic voltmeter operation, Trek, Inc., Medina, NY, Trek Application Note, No. 3006, /MAN Rev. 0b. [6] M. A. Noras, Noncontact surface charge/voltage measurements Capacitive probe: Principle of operation, Trek, Inc., Medina, NY, Trek Application Note, No. 3001, /MAN Rev.2. [7] IEEE Guide for the Measurement of DC Electric-Field Strength and Ion Related Quantities, IEEE Std. 1227, [8] B. Andò, S. Baglio, F. Di Grande, F. Passaniti, N. Savalli, V. In, and A. R. Bulsara, Electric field detectors in a coupled ring configuration: Preliminary results, in Proc. SPIE: Complexity Nonlinear Dyn., 2006, vol. 6417, p (Invited Paper). [9] B. Andò, S. Baglio, A. Bulsara, V. Marletta, and N. Savalli, E-field ferroelectric sensors: Modeling and simulation, IEEE Instrum. Meas. Mag., vol. 12, no. 2, pp , Apr [10] V. In, A. Palacios, A. R. Bulsara, P. Longhini, A. Kho, J. D. Neff, S. Baglio, and B. Andò, Complex behavior in driven unidirectionally coupled overdamped duffing elements, Phys. Rev. E: Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 73, no. 6, p , Jun [11] D. Damjanovic, P. Muralt, and N. Setter, Ferroelectric sensors, IEEE Sensors J., vol. 1, no. 6, pp , Oct [12] H. Kimura, T. Hanyu, M. Kameyama, Y. Fujimori, T. Nakamura, and H. Takasu, Complementary ferroelectric-capacitor logic for low-power logic-in-memory VLSI, IEEE J. Solid-State Circuits, vol. 39, no. 6, pp , Jun [13] S. Kohei, T. Hiroshi, R. Wang, P. Bambang, M. Noboru, and I. Mitsuru, Capacitance temperature sensor using ferroelectric (Sr 0.95 Ca 0.95 )TiO 3 perovskite, Ferroelectrics, vol. 331, no. 1, pp , Mar [14] J. A. Lynch and J. Jordan, Ferroelectric temperature sensors for thermometric titrations and enthalpimetric analysis, Anal. Chim. Acta, vol. 251, no. 1/2, pp , Oct [15] B. Willing, M. Kohli, P. Muralt, N. Setter, and O. Oehler, Gas spectrometry based on pyroelectric thin-film arrays integrated on silicon, Sens. Actuators A: Phys., vol. 66, no. 1 3, pp , Apr [16] J. M. Herbert, Ferroelectric Transducers and Sensors, vol. 3. NewYork: Gordon and Breach, [17] J. W. Waanders, Piezoelectric Ceramics: Properties and Applications. Eindhoven, The Netherlands: Philips Components, [18] B. Andò and S. Graziani, Basic measurements for the characterization of ferroelectric devices, IEEE Trans. Instrum. Meas., vol. 54, no. 3, pp , Jun [19] B. Andò, P. Giannone, and S. Graziani, A new platform for modeling ferroelectric devices, IEEE Trans. Instrum. Meas., vol. 55, no. 6, pp , Dec [20] J. T. Rickes, Advanced circuit design of gigabit-density ferroelectric random-access memories, Philosophy Doctorate dissertation, Institut für Werkstoffe der Elektro-technik (RWTH Aachen), Aachen, Germany, Dec [21] R. Banning, W. L. de Koning, H. J. M. T. A. Adriaens, and R. K. Koops, State-space analysis and identification for a class of hysteretic systems, Automatica, vol. 37, no. 12, pp , Dec [22] H. Richter, E. A. Misawa, D. A. Lucca, and H. Lu, Modeling nonlinear behavior in a piezoelectric actuator, Precis. Eng., vol. 25, no. 2, pp , [23] B. Jiang, P. Zurcher, R. E. Jones, S. J. Gillespie, and J. C. Lee, Computationally efficient ferroelectric capacitor model for circuit simulation, in Proc. Symp. VLSI Technol. Dig. Tech. Papers, 1997, pp [24] Y. Yu, N. Naganathan, and R. Dukkipati, Preisach modelling of hysteresis for piezoceramic actuator system, Mech. Mach. Theory,vol.37,no.1, pp , Jan [25] P. Ge and M. Jouaneh, Generalized Preisach model for hysteresis nonlinearity of piezoceramic actuators, Precis. Eng.,vol.20,no.2,pp , Apr [26] A. Sheikholeslami and P. G. Gulak, A survey of behavioral modeling of ferroelectric capacitors, IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 44, no. 4, pp , Jul [27] S. W. Wood, Ferroelectric memory design, M.S. thesis, Univ. Toronto, Toronto, ON, Canada, [28] R. C. Smith and C. L. Hom, A domain wall theory for ferroelectric hysteresis, J. Intell. Mater. Syst. Struct.,vol.10,no.2,pp ,1999. [29] S. Sivasubramanian, A. Widom, and Y. Srivastava, Equivalent circuit and simulations for the Landau Khalatnikov model of ferroelectric hysteresis, IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 50, no. 8, pp , Aug [30] B. Andò, Notes on the dynamic behavior of hysteretic devices, IEEE Instrum. Meas. Mag., vol. 7, no. 4, pp , Dec [31] P. Jung, G. Gray, and R. Roy, Scaling law for dynamical hysteresis, Phys. Rev. Lett., vol. 65, no. 15, pp , Oct [32] J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, Convergence properties of the Nelder Mead simplex method in low dimensions, SIAM J. Optim., vol. 9, no. 1, pp , Bruno Andò (S 97 M 98) received the M.S. degree in electronic engineering and the Ph.D. degree in electrical engineering from the Università di Catania, Catania, Italy, in 1994 and 1999, respectively. From 1999 to 2001, he was a Researcher with the Electrical and Electronic Measurement Group, Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, University of Catania, where he has been an Assistant Professor since His research interests include sensors design and optimization, in particular advanced multisensors architecture for visually impaired people, characterization of new materials for sensors, nonlinear techniques for signal processing (with emphasis on stochastic resonance and dithering applications), characterization and conditioning, and distributed measurement systems. He is a coauthor of several scientific papers, which were presented in international conferences and published in international journals and books. Salvatore Baglio (S 93 M 95 SM 03) received the Laurea in electronic engineering and the Ph.D. in electrical engineering from the University of Catania, Catania, Italy, in 1900 and 1994, respectively. He is currently an Associate Professor of electronic instrumentation and measurements with the Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, University of Catania. He teaches courses in Electronic measurements systems and Integrated sensors and transducers and is also a member of the Board of Ph.D. course in electronic and automation engineering of the University of Catania. He is the Principal Investigator in several scientific research projects regarding the development of innovative sensor systems, which are granted by private companies and different national and international institutions. He has authored more than 250 scientific publications, including international journals, books, conference proceedings, and patents. He has worked on nonlinear and chaotic dynamical systems, soft computing methodologies for identification and modeling, and smart measurement systems. His research interests are integrated microsensors, design methodologies for microsensors and microsystems, integrated transducers and nonlinear dynamics, and exploitation of material properties toward integrated transducers. Prof. Baglio has served as an Associated Editor for the IEEE TRANSAC- TIONS ON CIRCUITS AND SYSTEMS I and a Distinguished Lecturer of the IEEE Circuit and Systems Society. He is currently an Associate Editor for the IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENTS.

12 652 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 3, MARCH 2010 Society. Adi R. Bulsara received the Ph.D. degree in physics from the University of Texas, Austin, in He is currently a Senior Researcher with the Space and Naval Warfare Systems Center Pacific, San Diego, CA, where he heads a group that specializes in applications of nonlinear dynamics. He is the author of more than 150 articles in physics. His research interests include the physics of noisy nonlinear dynamic systems, with a preference for applications. Dr. Bulsara is a Fellow of the American Physical Vincenzo Marletta received the M.S. degree from the University of Catania, Catania, Italy, in He is currently working toward the Ph.D. degree in the Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, University of Catania. His research interests include sensors design and characterization, in particular aids for visually impaired people, characterization of new materials for sensors, soft computing methodologies for instrumentation and measuring systems, smart sensors, and exploitation of nonlinear dynamics in sensors, microsensors, and microsystems in standard and dedicated technologies.