Electric field detectors in a coupled ring configuration: preliminary results
Sensors for static electric fields (E-fields) based on unidirectionally coupled nonlinear dynamical systems1 are currently under development. They will exploit the synergic use of bistable ferroelectric materials, micromachining technologies, and novel sensing strategies. Considerable practical interest in such devices stems from the variety of uses to which they might be adapted. These range from biomedical tools to detection and characterization of E-fields in vehicles and other moving machinery, including specialized and sundry military applications.
Operating the E-field sensor as a single device—using a reference applied signal to induce switching between stable polarization states—is problematic due to the high coercive fields typical of ferroelectric materials. However, recent work2,3 has demonstrated that coupling an odd number of overdamped bistable elements in a ring, with unidirectional coupling and application of cyclic boundary conditions, can lead to oscillatory behavior when the coupling strength exceeds a critical value.
Here we consider in preliminary fashion the effects of inserting a small dc ‘target’ E-field signal into the (coupled) sensor system via an appropriate charge collection mechanism that perturbs the polarization status of the capacitors. The resulting oscillatory behavior is characterized by a network oscillating frequency that is a function of the field to be measured.
From a technological standpoint, the solutions we are exploring aim to create integrated ferroelectric capacitors in which the electrode configuration allows a part of the device to be polarized and to convey the effect of the electric target field into the sensing part of the same device (e.g., by altering the polarization).
From models to experimental setupThe entire system has been modeled to estimate overall performance. The following differential equation represents the nonlinear ferroelectric devices under consideration:
The overdot denotes the time derivative, P represents the material polarization, and a, b, and τ denote material-dependent system parameters governing its bistable behavior. Finally, c is a coefficient that relates the action of the external electric fields applied to the dielectric sample.
The ferroelectric capacitors investigated here were fabricated at Penn State University Laboratories. A microscopic view of a sample is shown in Figure 1. Their hysteretic behavior has been experimentally confirmed (see Figure 2) and a suitable model extrapolated.
In the case of three unidirectional ring-coupled circuits, the coupled dynamics have the following form: 
where λ is the coupling coefficient and Δ P represents the effect of the external electric field on the ferroelectric device polarization.
A simulation program with integrated circuit emphasis (SPICE) dynamic model has been developed in order to duplicate the behavior of the readout electronics for the single cell and the whole coupled system. The model for the ferroelectric device schematizes the capacitor as a `displacement current’ generator, shown in Figure 3. Excellent agreement was achieved between our measurements and the corresponding circuit simulations.
The electronics implementing the coupled system, composed of three elementary cells with a ferroelectric capacitor as a basic element, are shown in Figure 4.4 We also estimated, for a given coupling gain value, the effect of the polarization perturbation on the position of the main peaks of the output signal power spectrum. The results of this analysis are shown in Figure 5.
We observed that, as oscillation frequency decreases, perturbation in the polarization induced by the external target electric field increases. The second harmonic (i.e., twice the original oscillation frequency) behavior shows slightly greater sensitivity and emerges only in the presence of the target field. In fact, the system symmetry gives a spectrum with only odd harmonics, while even harmonics appear in the case of unbalanced potential.
Work currently in progress aims to develop suitable sensing architecture and optimization of the readout electronics.
Bruno Andö received his MS and PhD in electrical engineering in 1994 and 1999, respectively, from the University of Catania, Italy, where he became assistant professor in 2002. His main research interests are sensor design and optimization, advanced sensing architectures for the impaired and disabled, smart materials, and nonlinear techniques for signal processing with particular interest in stochastic resonance and dithering applications.
Salvatore Baglio received his laurea in 1990 and his PhD in 1994, both from the University of Catania, where he has been with the Department of Electronic and Electrical Engineering since 1996. He is currently associate professor of electronic instrumentation and measurements. His main research interests are measurement methodologies, smart sensors, microsensors, and microsystems.
Alberto Ascia received his MS in information engineering in 2005 from the University of Catania, where he is also pursuing a PhD in electronic and automation engineering. His research interests concern the development of novel transducers based on smart materials and advanced signal processing.
Visarath In is a researcher at the Space and Naval Warfare Systems Center in San Diego. His main fields of interest are nonlinear dynamics and its applications. He has authored numerous articles.
Adi R. Bulsara received his PhD in physics from the University of Texas at Austin in 1978. He is currently a senior researcher at the Space and Naval Warfare Systems Center, where he heads a group that specializes in applications of nonlinear dynamics. He is the author of over 100 articles and was recently elected a fellow of the American Physical Society. His primary research interests concern the physics of noisy nonlinear dynamic systems.
