A study of circular piezoelectric micro speakers is presented for applications in the audio frequency range, including values for impedance, admittance, noise figures, transducer gain, and acoustic frequency responses. The micro speakers were modelled based on piezoelectric micro ultrasonic transducer (pMUT) design techniques and principles. In order to reach the audio frequency range, transducer radii were increased to the order of one centimetre, whilst piezoelectric layer thicknesses ranged the order of several

Multimedia systems and components such as micro speakers are elements of great interest for the research community, driven by the needs of mobile phone, entertainment, laptop, tablets, and computer industries. It has been long time since “full range” multimedia micro speakers are trying to be developed, often finding design conflicts limited by fundamental physics. For example, the concept of miniaturization is in conflict with the idea of full-range: the smaller the radiating source, the higher the operating frequency range. Low frequencies and therefore large wavelengths require big source sizes which mean large loudspeaker diaphragms and piston excursion.

There are usually many more conflicting requirements and tradeoffs found in the design of high sound pressure level output, low noise and distortion, full audio range, omnidirectional, and minimum size transducers.

Some studies concerning micro speakers of the moving coil type have been reported in [

A different approach to micro speaker development is the piezoelectric type, as reported amongst others in [^{2}s) is considerably smaller than that of piezoelectric materials commonly used in ultrasound imaging (30 × 10^{6} kg/m^{2}s), for which matching techniques have to be employed.

In this paper, the techniques used for pMUT design and modelling which comprise some of radio-frequency (RF) system analysis are extended to the audio acoustic frequency range for the numerical analysis and characterization of a piezoelectric unimorph micro speaker. A design is presented by which the actuating membrane is made only of isolating SiO_{2} and a layer of nearly 100 micron of ZnO film, electroded on both sides. The resulting transducer, operating in the thickness mode, may be used for a variety of sound and vibration applications including active noise control, parametric arrays, beamforming arrays, and vibration sensors. Results are presented showing the most important design tradeoffs and their consequences on performance.

The transducer presented is a piezoelectric unimorph with a Si-SiO_{2}-Al-ZnO-Al layer stack, as shown in Figure

Schematic view of simulated actuator. Layers, from top to bottom: top electrode, piezoelectric layer(s), bottom electrode, oxide layer, and Si-structural layer.

The described devices are intended to be fabricated in a post-CMOS technology by stacking layers of piezoelectric material on a mechanical silicon substrate. A schematic view of the layer stack and geometric variables is shown in Figure

Transducer design variables.

Meaning | Symbol | Units | Min. value | Max. value |
---|---|---|---|---|

Sustrate thickness | mm | 1 | 10 | |

Si thickness | mm | 1 | 10 | |

SiO_{2} thickness | 1 | 100 | ||

Electrode thickness | 1 | 100 | ||

ZnO thickness | 1 | 500 | ||

Radius | mm | 0.75 | 12.5 | |

Top electrode radius | (% of | 1 | 100 | |

Bottom hole radius | (% of | 1 | 100 |

Following the IEEE Standard on Piezoelectricity [

The dielectric polarization ^{2}) representing the 3 × 3 permittivity matrix and electric displacement vector, respectively, and

For the electromechanical analysis of our interest, a piezoelectric actuator can be described as a linear two-port network (Figure

The electromechanical transducer represented schematically as a two-port network.

In order to relate the acoustics of the device to the intrinsic material properties of the membrane, the problem has to be tackled from an electromechanoacoustical perspective. In the mechanical domain considering vibrating plates, Euler’s flexural equation of motion for a forced circular plate with clamped edges would apply. According to our results and following previous work on vibrating piezoelectric circular diaphragms [

Solving (

In our case, the vibration of the membrane was computed numerically by means of the commercial design and visualization software MEMS+.

The acoustic pressure field

When integrated over a circumference of radius

Therefore the acoustic output of the transducer can be modelled by a directivity function corresponding to a flat circular piston multiplying the current frequency response characteristic of the transducer, together with a complex exponential in time and distance and a

The commercial software MEMS+ from Coventor Inc. was used for transducer design and visualization in conjunction with Cadence Virtuoso as a numerical calculation engine. An AC analysis was performed to calculate the frequency response voltages and currents. An

As it can be seen in Figure

Transducer impedance magnitudes (a) and admittance magnitudes (b) calculated for three different radii, all of them for a piezoelectric layer thickness of 80

(a) First resonance frequency versus radius calculated for a piezoelectric layer thickness of 80 um. (b) First resonance frequency versus piezoelectric thickness calculated for a radius of 1 cm.

Plotting the data of Figure

Diaphragm first resonance frequency versus inverse radius.

Three sample transducer frequency responses for radii of 8.3, 9.7, and 12.5 mm and piezoelectric thicknesses of 0.08, 220, and 500 micron are shown in Figure

(a) Transducer electromechanical frequency response magnitudes for different radii. (b) Transducer electromechanical frequency response magnitudes for different piezoelectric layer thicknesses.

Depending on the values of transducer radii or piezoelectric thicknesses, the resonance peaks in transducer FRF magnitude might increase more or less with respect to each other. To have a complete picture of how radii and thicknesses affect the impedance or transducer frequency response peaks, 3D plots are presented in Figures

Peaks of impedance versus radius and piezoelectric layer thickness at four fixed frequencies.

First resonance in FRF magnitude versus radius and piezoelectric layer thickness at four fixed frequencies.

Noise figure and transducer gain are characterized in a similar manner: in the case of noise figure (NF), for a fixed radius of 1 cm, the values of NF versus frequency were obtained from the Cadence design environment for each piezoelectric layer thickness and are shown as a 3D plot in Figure

Noise figure versus frequency and piezoelectric thickness at fixed radius = 1 cm.

Maximum stable power gain versus frequency and piezoelectric thickness at fixed radius = 1 cm.

The results presented characterise the transducer design space and yield information and details on impedance, resonance frequency, noise figure, and transducer gain as a function of frequency, piezoelectric layer thickness, and transducer radius.

The main variables considered in this study induce to treat the problem as a 4-variable problem: frequency

Therefore, 3D plots can be made of any of the

Main parameters calculated after

This approach introduces a complete way of characterizing the piezoelectric transducer in terms of impedance, frequency response, admittance, transducer gain, and noise figure. Any two independent variable values might be set and the relation with the two others might be obtained numerically. After the design space is characterised the next logical step would be to introduce a multiobjective optimization of the transducer design variables. This approach will hopefully help improve the process steps involved in micromachining and manufacturing this kind of piezoelectric micro speakers.

The design and analysis of a piezoelectric micro speaker based on pMUT operation modelling and characterization is presented. The analysis is based on s-parameter analysis for a two-port network, after which values for impedance, admittance, frequency response, noise figure, and transducer gain have been presented. Relations for transducer radius, piezoelectric thickness, and operating frequency were obtained which yield diaphragm displacement and therefore sound pressure level and noise figure values. Results represent useful tradeoffs for piezoelectric micro speaker design.

This work has been partially supported by the ESA project COSMIC VISION and by the Spanish Department of Science and Technology Project TEC2008-04920. J. Mendoza-López is grateful to partial funding by the postdoctoral program JAE-DOC granted by the Spanish National Research Council (Consejo Superior de Investigaciones Científicas, CSIC).