In our previous two blog posts, How Ultrasonic Fingerprint Sensing Works and Why it is Important and Which transducer type is best for ultrasonic fingerprint sensing: CMUT, PMUT or PZT?, we explained the fingerprint sensing principles and the different ultrasound transducers. Micromachined ultrasound transducers (MUTs) can be fabricated in a small size in an array suitable for relatively large frequency applications compared to bulk piezoelectric transducers, and are then suitable to perform beamforming to generate ultrasound images. Piezoelectric micromachined ultrasonic transducers (PMUTs) are a better candidate for fingerprint sensing compared to CMUTs, though there is no need for DC bias voltage for both Tx and Rx operation. In fact, PMUTs AC only working regime reduces the charging effect in the dielectric/piezo improving the reliability of the device.
Structure of a PMUT
A PMUT is a transducer operating in flexural mode using a thin membrane made of silicon, silicon nitride or silicon oxide, coupled with a thin piezoelectric film made of lead zirconate titanate (PZT), aluminium nitride (AlN), or polyvinylidene fluoride (PVDF) -. An electric field is applied over the piezoelectric layer that is sandwiched between the top electrode (TE) and bottom electrode (BE), creating a transverse stress and a bending moment resulting in the deflection of the membrane, see figure 1. The membrane vibration generates an acoustic wave into the surrounding medium (for example air, water, or blood). At this point, the PMUT operates in transmit (Tx) mode. The transmitted wave hits a target object, the wave reflects and deflects the PMUT membrane, which now operates in receive (Rx) mode. In Rx mode, this deflection creates small stress and electric charge that requires further amplification and is detected by an application specific integrated circuit (ASIC), to be analyzed.
Figure 1. PMUT general structure. The piezoelectric layer is sandwiched between top and bottom electrodes.
Despite the electrostatic nature of a CMUT membrane, where the electric field is applied over a gap height and a thin dielectric layer, which usually causes reliability issues, the role of the gap in a PMUT membrane is only to have enough space for the membrane to oscillate. One conventional approach for PMUT fabrication is using cavity silicon-on-isolator (CSOI) wafer with a defined foundry gap .
Mathematical Modeling and Optimization of a PMUT
In the small signal regime, PMUTs can be modeled through an equivalent electrical circuit as shown in figure 2. The equivalent circuit models and links electrical, mechanical, and acoustical parts of the transducer. The electrical part is driven by voltage (Vin) and current, while the mechanical part is described by force and velocity. These phenomena are coupled through a positive quantity called transformer ratio (η). The acoustical part is modeled using pressure and volume velocity, which are coupled to the mechanical part via a quantity named effective area (Aeff). The acoustical domain output (Pout) is calculated by multiplying the volume velocity by the radiation impedance, which results in the transmitted pressure. Radiation impedance is the integration of the reaction force of the medium over the entire transducer moving surface. In fact, radiation impedance is a measure of the transferred energy into the surrounding medium that can be water, air or blood. The surface integration of the radiation force contains both real and imaginary terms therefore, the radiation impedance is modeled as a series resistor and inductor. The transferred energy is associated with the resistor thus the goal is to optimize the real part of the radiation impedance to maximize the converted energy into the medium.
Figure 2. PMUT modeling in the small signal regime .
There are several design parameters to consider in order to optimize a PMUT array for optimal performance in a specific application. After defining a suitable working frequency range (frequency (fr) and wavelength (λ)) for the device operation, the PMUT lateral size can be chosen around (λ/2) to satisfy the Nyquist sampling criteria which is required to avoid unwanted grating lobe artifacts and also to have large directivity . By considering the relationship of the membrane resonance frequency (fr) with the membrane lateral size, the initial thickness value can be derived from the following equation:
The next step using a small signal analysis is to extract the values of the parameters shown in figure 2. Capacitance of the PMUT membrane (C0), mass (mm), stiffness (1/km), transformer ratio (µ), natural axis length and flexural rigidity calculations are explained in detail in  . Pout is the radiated pressure into the medium that is proportional to radiation impedance. In general, the behavior of the radiation impedance for a clamped radiator is demonstrated in figure 3.
Figure 3. Radiation impedance of a PMUT membrane
The goal is to maximize the real part of the radiation impedance to optimize the transferred energy into the medium. Since the radiation impedance is a function of wave number (k) and PMUT lateral size (a), for a given frequency, the lateral size of the transducer is designed to operate in the region that maximizes the real part of the radiation impedance.
PMUT Fabrication Process
Both CMUTs and PMUTs fabrication processes are categorized based on the cavity definition. Sacrificial release is the common approach to define the cavity: the gap height is defined by depositing a sacrificial layer followed by an etching step at the end of the process. The benefit of this method is that both cavity and membrane are defined on a single wafer and: if all the processes are designed in low temperature, the entire manufacturing process can be complementary metal–oxide–semiconductor (CMOS) compatible, thus suitable for monolithic integration. The disadvantage of this technique is the stress due to thermal mismatch within different layers, adhesion, bucking, and accumulative topography of final surface due to various deposition-etching processes. The cavity can be also defined with a wafer back-side or front-side etching. The back-side etching is done by KOH wet etching that is time consuming, not CMOS compatible, and limits the pitch of PMUT individual membranes due to sloped etching walls. Front-side etching is done by XeF2 through the hole/via in the middle of the PMUT membrane, hence the membrane must be sealed with extra material, e.g. polymer, following by an additional photolithography-etch step. The extra layer changes the stiffness and mechanical behavior of the membrane . Another approach is to define cavity and membrane on different wafers following by a wafer bonding step, which is a reliable fabrication process. The disadvantage of this method is the cost of the SOI wafer used for membrane, accuracy of the photolithography/back-side aligning, and surface preparation steps in wafer bonding process .
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