Giga-hertz ultrasonic reflectometry for fingerprint imaging using epitaxial PbTiO₃ transducers

Fingerprint readers based on piezoelectric transducer (PZT) and ScAlN as piezoelectric micromachined ultrasonic transducers (pMUTs) in the MHz range have been extensively studied.^1–3 The pMUTs enable efficient radiation of sound waves to a low acoustic impedance medium such as air and water by lowering the spring constant owing to its flexure mode of self-standing structure. However, because of the flexure mode, operating frequency of pMUTs is limited to several tens of MHz at most.

On the other hand, it is difficult to match a thickness extensional mode piezoelectric thin-film transducer to a medium with low acoustic impedance. However, fingerprint imaging is possible by evaluating the acoustic reflectance of the medium/transducer interface. Above all, spatial resolution can dramatically improve by using GHz ultrasonic waves in the thickness extensional mode. There has been a report on fingerprint imaging by the acoustic reflectance of the backside of the thickness extensional mode AlN transducer substrate.⁴ Table I shows the comparison of acoustic fingerprint sensors.

In order to efficiently input power to a transducer, it is crucial to match the electrical impedance of the transducer and a measurement system. The capacitive impedance of a piezoelectric transducer is expressed by the following equation:

where ω is thickness extensional mode resonant frequency, ε is dielectric constant of piezoelectric material, S is area of top electrode, and d is thickness of piezoelectric film.

Large electrode area of the transducer is required to match the electrical impedance of a piezoelectric material, for example, with 50 Ω measurement system. However, to achieve high spatial resolution, the area of electrode should be minimized. In fact, the relative dielectric constant ε_r33 of AlN is approximately 10, while that of PbTiO₃ is as high as 82. In the theoretical simulation, when the insertion loss of PbTiO₃ and AlN transducers are adjusted to be the same, the electrode size of PTO transducer of 0.17 mm² is 4.4 times smaller than that of AlN transducer of 0.039 mm². Therefore, by employing PbTiO₃, further improvement of spatial resolution is expected.^5,6

In this study, fingerprint imaging using a device with nine arrayed PbTiO₃ transducers was conducted. To investigate the improvement of spatial resolution by GHz range transducer, piezostage that allow mechanical movement in the 100 nm order was introduced. Fingerprint was imaged by acoustic characteristics measured using a network analyzer. The voltage sensitivity of a network analyzer reaches about 1 μV, which is 1000 times as higher than the voltage sensitivity of an oscilloscope of 1 mV. We here propose fingerprint images with high signal-to-noise ratio (S/N ratio) using a network analyzer.

PbTiO₃ epitaxial films were grown on a conductive La-SrTiO₃ single crystal substrate with 0.3 mm thickness by RF magnetron sputtering. When conducting the measurement, the 0.6 mm round trip distance in the substrate may degrade the resolution of the image due to the diffraction effect. However, the 0.3-mm-thick substrate was employed to certainly avoid mechanical cracking of the substrate when the transducer is pressed on the phantom. The crystal orientation of La-SrTiO₃ was (100), and La concentration of the conductive La-SrTiO₃ single crystal was 3.73 wt. %. Conductive La-SrTiO₃ was adopted as a substrate because of its close lattice parameter to PbTiO₃. The crystalline orientation of the PbTiO₃ film was examined by x-ray diffraction (PANalytical, X'pert pro). PbTiO₃ (002) peaks were observed in 2θ-ω XRD patterns, and the typical FWHM of ω scan PbTiO₃ (002) rocking curves were 0.2°.

Electromechanical coupling coefficient k_t² of PbTiO₃ epitaxial transducers was estimated from longitudinal wave conversion loss curves. Conversion loss of the transducer was obtained by inverse Fourier transform of the detected ultrasonic echo signals in the time domain analysis using a network analyzer (Keysight Technologies, E5071C). Electromechanical coupling coefficient k_t² was determined by comparing experimental conversion loss curves and theoretical conversion loss curves by the Mason's equivalent circuit model^7–9 (see Fig. 1). The constants used in the model are as indicated in Table II. Minimum conversion loss was 2.5 dB at 0.8 GHz. The theoretical curves agreed well with the experimental curves. Electromechanical coupling coefficient k_t² of PbTiO₃ transducer was estimated to be 28.9%.

The thermoelastic elastomer was adopted as a substitute for fingerprint. The acoustic impedance of elastomer is assumed to be approximately 1.67 Mrayl, where that of air is approximately 0. Thus, the difference between the acoustic impedance difference at the substrate/elastomer interface is smaller than that at the substate/air interface. The reflectance R at the interface can be calculated using the following equation:

where Z₁ is acoustic impedance of incident medium, and Z₂ is acoustic impedance of reflecting medium. The reflectance of the substrate/elastomer interface was approximately 0.83, whereas that of the substrate/air interface was 1. Transducer insertion loss of PbTiO₃/La-SrTiO₃ with and without elastomer on the bottom side of La-SrTiO₃ substrate were measured as shown in Fig. 2(a). Mason's equivalent circuit model for transducer contacting elastomer is shown in Fig. 2(b). Figure 3 shows the comparison of first echo amplitude of impulse response with and without the elastomer. Additionally, Fig. 4 shows the maximum insertion loss with and without elastomer was 60% and 55%, respectively. Figures 3 and 4 indicate degradation of insertion loss by contacting elastomer owing to the change of reflection coefficient of the substrate/elastomer interface. Consequently, the difference of the reflection coefficient with and without elastomer was confirmed.

A schematic diagram of 3 × 3 array transducer imaging device is shown in Fig. 5. The measurement system configuration for fingerprint imaging is shown in Fig. 6. Ni top electrode was deposited on the fabricated PbTiO₃ epitaxial thin film so that each PbTiO₃ transducer is spaced 1.3 mm apart, as shown in Fig. 5. A stepping motor stage was used to mechanically scan a 3.9 × 3.9 mm² area of the fingerprint phantom while pressing the fingerprint phantom onto the backside of the PbTiO₃ transducer substrate. The number of mapping data points was 9801 (99 × 99 points in a 3.9 × 3.9 mm² area). Each of the nine PbTiO₃ transducer acquired an image of 1.3 × 1.3 mm² area, and the nine images were connected to form a single fingerprint image of 3.9 × 3.9 mm². Three network analyzers were used to perform measurement with an array of 3 × 3 transducers. However, rather than using three network analyzers, using an RF switch is more reasonable if available. The stepping motor stage and network analyzer were controlled using LabVIEW (National Instruments).

The longitudinal insertion loss of each transducer was measured while the fingerprint image was pressed against the backside of the transducer substrate. An impulse response was obtained by performing inverse Fourier transform on the S₁₁ parameter. Fingerprint images were obtained by mapping the maximum value of the insertion loss of longitudinal wave and the maximum amplitude of the first echo.

Figure 7(a) shows an optical micrograph of fingerprint phantom. When mapping is conducted with raw measured values, the images obtained by the nine transducers have different darkness due to the different ultrasonic excitation efficiency of each nine transducers. Therefore, the maximum amplitude of insertion loss and impulse response of the first longitudinal wave echo when nothing is pressed on each nine transducers were measured as a reference. Figures 7(b) and 7(c) were obtained by subtracting the reference values from the raw measured values of maximum amplitude of insertion loss and impulse response of the first longitudinal wave echo, respectively. Fingerprint image was obtained by using the two methods. The image obtained using insertion loss has a wider area of light and shade. Therefore, we adopted the insertion loss method in the following investigation.

To quantitatively examine the resolution of the proposed fingerprint reading method, the image obtained by the stepping motor stage was compared with that obtained by a piezostage. For simplicity, fingerprint image was acquired by mechanical scanning of a single PbTiO₃ transducer. An elastomer phantom molded with 100 μm width ridges and 200 μm valleys was prepared as imaging object.

First, the stepping motor stage was used to mechanically scan a 180 × 180 μm² area of the phantom. The distance between each measurement point was set to the minimum value of 2 μm. The acoustic image of phantom was obtained by mapping the maximum value of insertion loss, as shown in Fig. 8(b) at each measurement points. The number of data points for mapping was 8100 (90 × 90 points in a 180 × 180 μm² area) for this measurement.

Next, the same imaging process was performed with the piezostage, as shown in Fig. 9. to mechanically scan a 500 × 500 μm² area of the phantom. Figure 10(b) was acquired to confirm that the piezostage performed the same function as the stepping motor stage. Therefore, we measured a larger area to certainly observe valleys and ridges with the piezostage measurement. The distance between each measurement point was set to 10 μm. The acoustic image of phantom was obtained by mapping the maximum value of insertion loss as shown in Fig. 10(b).

We then observed an enlarged image to evaluate the resolution. The same imaging process was performed with the piezostage. This time, the imaging area focused on the edge of the previously scanned 100 μm ridge of the phantom. A 12 × 12 μm² area of the phantom was scanned using the piezostage. The acoustic mapping result of the maximum value of insertion loss is shown in Fig. 11(b).

A comparison of the acoustic image of 12 × 12 μm² area obtained by the two methods, as shown in Figs. 11(b) and 11(c), implies that resolution was improved by using the piezostage measurement system. Table III shows the imaging conditions for each measurement system. In the imaging with stepping motor stage, the interval between each measurement points is 2 μm, whereas in the imaging with the piezostage, the interval between measurement points can be 200 nm. This would allow the number of data points to increase, therefore improving the resolution.

In conclusion, the GHz range nine thickness extensional mode PbTiO₃ transducer array was fabricated for fingerprint imaging. Fingerprint imaging was performed by mapping the difference of acoustic reflectance at the ridges and valleys of elastomer fingerprint phantom when pressed at the backside of the transducer substrate. The resolution of the two measurement systems was compared. The number of data points with stepping motor stage was 6 × 6 points (total 36 points) in a 12 × 12 μm² area, while the number with the piezostage was 60 × 60 points (total 3600 points), indicating improvement of imaging resolution. As a future prospect, further imaging of small objects by the GHz range ultrasound transducers will be considered.

This work was supported by JST CREST (No. JPMJCR20Q1), JST FOREST, and KAKENHI (Grant-in-Aid for Scientific Research B, Nos. 19H02202 and 21K18734).