Effects of Elastic Coupling between BaTiO₃ Ferroelectric Film and a Substrate with Finite Thickness on Piezoelectric Coefficients

Abstract

The effective piezoelectric coefficients of BaTiO3 ferroelectric films epitaxially grown on different single crystal substrates with finite thickness have been theoretically analyzed. The effective longitudinal converse piezoelectric coefficients d33 of film and "film-substrate" heterostructure all monotonously increased with increase of the film thickness fraction k, and the latter is always larger than the former at the range of 0 < k < 1. Meanwhile, we also found that the effective piezoelectric coefficients d33 were affected by the substrates due to different elastic constants. These results show that the elastic deformation and clamping effect of substrate have significant impacts on the piezoelectric behavior of bilayer heterostructure.

Extraction of Electromechanical Coefficients from Capacitance–Voltage Measurements of Unannealed Solution‐Processed KNN Thin Films: Effects of Frequency and Electrostatic and Mechanical Deformation

“…As mentioned earlier, the analysis relies on the assumption that the thin piezoactive film is unclamped, and that the fractional change in capacitance (≈/) is due to the change in physical dimensions of the device ( & ) and is independent of the dielectric constant (), as suggested by Equation (). [ 26,39 ] The in‐plane dimensions of the actual device are much larger than the total stack thickness (), which avoids edge effects [ 5,40 ] visible in simulations on small scale ( Figure b inset). Further, in the case of submicrometer dimensions, the thin film is always clamped to the substrate via van der Waals forces [ 41 ] ; thus, the assumption is invalid.…”

“…[4] A precise measurement of these matrix elements in thin-film form is thus expected to be instrumental in developing advanced, cost-effective, and high-performing material systems and harvester designs. [5] Methods such as Berlincourt, [6] laser Doppler vibrometry (LDV), [7] double-beam interferometry, [8] and piezoresponse force microscopy (PFM) [9] have been standard methods of piezoelectric coefficient characterization. Issues such as substrate bending, [10,11] elastic coupling, [5] electrostatic artifacts between cantilever and substrate, [11,12] top electrode size effects, [13,14] large leakage currents, [15] concentrated inhomogeneous electric fields, [16] and local poling [17] complicate precise measurements.…”

“…[5] Methods such as Berlincourt, [6] laser Doppler vibrometry (LDV), [7] double-beam interferometry, [8] and piezoresponse force microscopy (PFM) [9] have been standard methods of piezoelectric coefficient characterization. Issues such as substrate bending, [10,11] elastic coupling, [5] electrostatic artifacts between cantilever and substrate, [11,12] top electrode size effects, [13,14] large leakage currents, [15] concentrated inhomogeneous electric fields, [16] and local poling [17] complicate precise measurements. Further, thin-film based measurements (except PFM) usually are known to underestimate parameters like d 33 due to substrate clamping effects; when compared with the bulk material, [5,18] PFM, on the other hand, has been found to overestimate electromechanical coefficients d 33 .…”

“…Issues such as substrate bending, [10,11] elastic coupling, [5] electrostatic artifacts between cantilever and substrate, [11,12] top electrode size effects, [13,14] large leakage currents, [15] concentrated inhomogeneous electric fields, [16] and local poling [17] complicate precise measurements. Further, thin-film based measurements (except PFM) usually are known to underestimate parameters like d 33 due to substrate clamping effects; when compared with the bulk material, [5,18] PFM, on the other hand, has been found to overestimate electromechanical coefficients d 33 . [11,12] To develop new materials and device designs for the thin-film-based MEMS industry, uncomplicated, competent, and robust methods of characterization are essential.…”

Piezoresponse in Ferroelectric Materials under Uniform Electric Field of Electrodes

“…Lefki and Dormans derived the solution [ 38 ] for the case of the tetragonal (001) oriented ferroelectric materials bonded to the rigid substrate, as it is imperative to the interpretation of the Doppler vibrometer and laser interferometry data [ 39 , 40 , 41 ]. More complicated cases considering the flexible substrate contribution, top electrode lateral size, and multilayered structure were studied using sophisticated analytical models and finite element simulations [ 41 , 42 , 43 , 44 , 45 , 46 , 47 ].…”