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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Series-connected thin film piezoelectric elements can generate large output voltages. The output voltage ideally is proportional to the number of connections. However, parasitic capacitances formed by the insulation layers and derived from peripheral circuitry degrade the output voltage. Conventional circuit models are not suitable for predicting the influence of the parasitic capacitance. Therefore we proposed the simplest model of piezoelectric elements to perform simulation program with integrated circuit emphasis (SPICE) circuit simulations). The effects of the parasitic capacitances on the thin-film Pb(Zr, Ti)O_{3}, (PZT) elements connected in series on a SiO_{2} insulator are demonstrated. The results reveal the negative effect on the output voltage caused by the parasitic capacitances of the insulation layers. The design guidelines for the devices using series-connected piezoelectric elements are explained.

For several decades, there has been increasing interest in the healthcare industry for human healthcare monitoring systems. This has led to an increase in research on this topic. The medical and welfare costs to governments worldwide have now reached critical levels. Various human-activity monitoring systems have been developed and are commercially available. To realize such monitoring systems, miniaturization and integration of sensors are essential. A small, robust, integrated, wireless, and low-power-consumption sensor system would have a significant impact on patient monitoring in the human-healthcare and wellness industries. Various healthcare monitoring systems using micro-electro-mechanical-systems (MEMS) sensors have been reported [

Previously, we have reported fine-resolution processing techniques for piezoelectric Pb[Zr,Ti]O_{3} (PZT) thin films [

Output-voltage multiplication has significant potential in the development of energy harvesters with high output voltages, which are greater than the built-in voltage of the p-n junction, and sensors with high signal-to-noise ratios. Ideally, the output voltage would increase to infinity with the increasing number of elements. However, the parasitic components in the measurement system prevent this from happening. In the design of devices that employ output-voltage multiplication, estimation of the optimum number of series connections and the effect of parasitic capacitances are important. However, the system becomes very complicated when the number of connections increases, and therefore the estimation of the parasitic capacitance becomes complicated. This study proposes a simple procedure using simulation program with integrated circuit emphasis (SPICE) to estimate the effect of parasitic capacitances and specifies a design guideline for series-connected piezoelectric elements.

For the thin-film piezoelectric elements, the mechanical behavior, including the stress in the piezoelectric film, is determined by the substrate deformation. This is because the film has negligible thickness compared to that of the substrate structure. For piezoelectric bulk transducers, some equivalent circuits have been proposed. Mason’s models, which are derived from the constituent equation of piezoelectric materials, are generally used as equivalent circuits for piezoelectric transducers [

In this paper, we investigate the influence of parasitic capacitances on the output voltage generated from series-connected piezoelectric elements. To understand the charges obtained from the output pads of the device with taking account of the influence of the parasitic capacitance, a model with a charge source, a capacitance of the piezoelectric elements, and parasitic capacitances is sufficient. The model is based on assuming ideal piezoelectric elements without leakage, and does not take dynamic phenomena into account.

The charge source is not included in the standard SPICE library. Therefore, a charge source with piezoelectric capacitance should be produced from basic SPICE elements. The models in _{0} is shown in _{0} connected in series with a capacitor is shown in

A charge source model is shown in _{0}. The Vccs, which supplies electrical current proportional to the input voltage, is a standard element in SPICE. The constant scale factor can be set arbitrarily. The application of input voltage, _{i}(_{i}(_{i}(_{i}(_{i}(

The simplest basic model proposed in this paper is a capacitor with initial voltages.

The influence of parasitic capacitances on the output signal can also be estimated analytically without using SPICE. The piezoelectric film is segmented into _{i}, has an initial voltage _{i} with an electric charge _{i} = _{i}_{i}, and the _{pi}, has no initial voltage. After charge distribution, piezoelectric elements and parasitic capacitances have electric charges, _{i}’, and _{pi}’, respectively. The electrical potentials at the right-side node of each piezoelectric element and at the substrate are _{i} and _{s}, respectively. The nodal potentials are calculated from the law of charge conservation. The relationship between the initial and equilibrium charges is expressed by the following simultaneous matrix equation:
_{p}_{jk} is −1 for _{jk} is 1/_{i} for _{jk} is 0 for _{pjk} is 1/C_{pi} for _{pi} + 1 for _{1}’, _{2}’ … _{n}’}, _{p}_{p1}’, _{p2}’ … _{pn}’}, _{1}, _{2} … _{n}}, and _{n}, is the summation of (_{i}’/_{i}). The influence of the parasitic capacitance is evaluated as a multiplication factor, which is defined as the ratio between the obtained output voltage, _{n} and the initial voltage from the thin film before segmentation. When the thin film is segmented into elements with equal areas (each element has capacitance, _{p}), the equation can be expressed as a ratio of the parasitic capacitance to piezoelectric capacitances, _{p}/_{p}/_{p}. Although the analytical solution can be obtained from the matrix formula, it becomes too complex when the segmented number is large.

The use of the circuit simulation tool, SPICE, for the estimation is much easier than the analytical procedure. SPICE transient analysis of the circuit model of capacitors with initial voltages can demonstrate the charge distribution after reaching an equilibrium state. Although the charge source is not prepared in SPICE, the previously mentioned model of the capacitor with an initial voltage makes it possible to use SPICE to easily estimate the influence of the parasitic capacitances. The transient analysis in the SPICE software has the option of providing initial voltages to capacitors. The equilibrium solution of the transient analysis provides nodal potentials after charge distribution. The influence of the parasitic capacitance is evaluated as the multiplication factor.

To evaluate the influence of the parasitic capacitances, the output voltage from series-connected piezoelectric elements is calculated using SPICE. The capacitance of the piezoelectric thin film is given by _{0}·_{piezo}·_{piezo}, where _{0} is the dielectric constant of a vacuum, _{piezo} is the relative dielectric constant of the piezoelectric material, _{piezo} is the thickness of the piezoelectric thin film. The parasitic capacitance is given by _{p} = _{0}· _{ins}·_{ins}, where _{ins} is the relative dielectric constant of the insulation layer and _{ins} is the thickness of that layer. The areas

First, we evaluated influential factors that affect the piezoelectric thin film segmented into equal areas, _{n}, is equal to the multiplication factor, _{p}^{−1}^{−1}.

As an example, series-connected PZT elements (with a relative dielectric constant of 1,000 and an area of 1 mm^{2}) placed on a SiO_{2} insulation layer (with a relative dielectric constant of 4 and a thickness of 1 μm) are evaluated for various numbers of segments. The initial area does not affect the relationship between the number of connections and the multiplication factor because the solution of

For actual systems, other parasitic capacitances are also present. For example, the insulation layer under bonding pads forms a parasitic capacitance, and measurement instruments also have parasitic elements. ^{2} and assuming a 10 pF probe capacitance.

For MEMS devices, cantilever-type sensors are commonly used (e.g., accelerometers have proof mass with a supporting cantilever). We evaluated the influence of the parasitic capacitance for series-connected piezoelectric elements on a cantilever. When a horizontal cantilever with length _{s}, and piezoelectric element _{p}, the mean stress across the piezoelectric element σ(

Therefore, the output voltage generated from the element is proportional to the distance from the free end of the cantilever. The calculation is performed using SPICE with the piezoelectric thin film (with dimensions of _{p} = 3 μm) segmented into _{0} (set to 1 V for simplification) is the apparent voltage, which is estimated from the stress on the fixed end. _{1}, _{2}, . . . _{n}} in

In case of a tri-axis accelerometer, both-ends-fixed beams are often employed. For beams fixed at both ends, the sign of the stress (

The beam center (

While using output-voltage multiplication using a series connection of piezoelectric elements is a promising technique for piezoelectric MEMS sensors, it is important to estimate the influence of parasitic capacitances in the design stage. To investigate the influence of the parasitic capacitance, piezoelectric elements are modeled as a charge source with a capacitor. The influence of the parasitic capacitance is analytically expressed in Section 2.2. Although the analytical equations are useful to predict the influence of the parasitic capacitances, the model should be incorporated in SPICE for the extensibility, e.g., consideration of leakage and load resistance for energy harvesters. Since the charge source is not included in the standard SPICE library, the simplest model of a piezoelectric capacitance with initial voltage is proposed. In addition, the calculation using the SPICE model has been consistent with the experimental output voltage for the series-connected 8 piezoelectric elements in the previous work [

The demonstrated calculations indicate severe limitations on the output voltage because of the influence of parasitic capacitances. This effect depends on the ratio of the capacitance of the piezoelectric element to the parasitic capacitance. To reduce this influence, reduction of the ratio is one solution,

The proposed technique using SPICE calculations can easily predict the influence of parasitic capacitance without the need for experiments. The areas and locations of the segmented elements for more complicated devices should be designed to maximize the output voltage based on the stress characteristics. In the design of actual devices, the piezoelectric elements should be connected in series by processing the electrodes and depositing the insulation layers. In addition, the fill factor of piezoelectric elements occupying the structure area, locations, and shapes used to load the stress are important. SPICE calculation in the design stage is a powerful tool for such piezoelectric devices.

The influence of the parasitic capacitance on series-connected piezoelectric elements is evaluated using the proposed SPICE calculations. We propose a simple-circuit model for piezoelectric elements to make it applicable to SPICE calculations. SPICE calculation easily estimates the influence of the parasitic capacitance on the output voltage of series-connected piezoelectric elements. The calculation results for series-connected PZT elements subjected to a uniform stress demonstrated the limitation of the output voltage based on the thickness of PZT. It was found that other parasitic capacitances derived from bonding pads and measurement instruments were also influential. By applying the technique to PZT elements located on beams, the design guidelines for series-connected piezoelectric devices have been explained.

The authors thank Junya Matsuoka of Yamaha Co. for the fruitful discussions. We also thank Travis Bartlay for proofreading of the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Japan, and Grant-in-Aid for Young Scientists (B), 23760233, 2011.

_{3}Thin Films for MEMS: Integration, Deposition and Properties

Diagram of output-voltage operation using series-connected piezoelectric elements. (

Insulation layers below bottom electrodes form parasitic capacitances.

Circuit models for a charge source with a piezoelectric capacitor. (

Equivalent circuit model of the series-connected piezoelectric elements. The piezoelectric elements are modeled as simple capacitors with initial voltages.

Calculated results using SPICE for series-connected PZT elements.

Equivalent-circuit model of series-connected piezoelectric elements. The piezoelectric elements are modeled as simple capacitors with initial voltages.

Influence of the parasitic capacitance. (

Influence of the parasitic capacitance for piezoelectric elements on a cantilever.

Tri-axis accelerometer using series-connected piezoelectric elements. The stress directions applied to the elements differ from each other.