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Flexoelectricity offers an energy harvesting alternative to piezoelectric materials. Although flexoelectricity is generally weak in most materials, recent findings show that bending a semiconductor with insulating barrier layers could induce a significantly enhanced flexoelectric response. We call this effect the Space Charge Induced Flexoelectric (SCIF) effect. This study explores the induced polarization resulting from free charge redistribution in a doped silicon beam. To understand the underlying physics, a 3D numerical model combining flexoelectric principles and the drift-diffusion theory of semiconduction was developed. The effective flexoelectric coefficient was computed by comparing the differential charge accumulation at the top and bottom of the beam and compared that with the experimental observations. 

In undoped lead zirconate titanate films of 1–2  μm thick, domain walls move in clusters with a correlation length of approximately 0.5–2  μm. Band excitation piezoresponse force microscopy mapping of the piezoelectric nonlinearity revealed that niobium (Nb) doping increases the average concentration or mobility of domain walls without changing the cluster area of correlated domain wall motion. In contrast, manganese (Mn) doping reduces the contribution of mobile domain walls to the dielectric and piezoelectric responses without changing the cluster area for correlated motion. In both Nb and Mn doped films, the cluster area increases and the cluster density drops as the film thickness increases from 250 to 1250 nm. This is evident in spatial maps generated from the analysis of irreversible to reversible ratios of the Rayleigh coefficients. 

Lead zirconate titanate (PZT) is widely used in energy harvesting because of its excellent material properties. However, as the material contains lead, there are significant environmental concerns with its production and use. Flexoelectricity refers to the coupling between strain gradient and electric polarization that exists, in principle, in all dielectric materials and would allow for energy harvesting without using piezoelectric materials. However, the effect is very weak in most materials. Promisingly, it has recently been shown that space charge polarized materials (i.e., semiconducting materials with insulating barrier layers) can exhibit enhanced flexoelectricity. This space charge induced flexoelectric effect opens up the possibility of a non-toxic replacement for PZT in energy harvesting applications. In this paper we investigate the use of doped silicon with hafnium oxide insulating layers as flexoelectric transducers that could replace PZT in many applications including energy harvesting. Specifically, we experimentally demonstrate flexoelectricity in a bending beam and show an effective flexoelectric coefficient of 4.9 uC/F. Finally, we develop and demonstrate a finite element model for flexoelectricity. 

Crack initiation stresses for different lead zirconate titanate (PZT) film compositions were investigated. PZT/Pt/TiO2/SiO2/Si stacks with 2.0 μm thick {100} oriented PZT films at the morphotropic phase boundary (MPB) showed a characteristic strength of 1137 MPa, and the film thickness served as the limiting flaw size for failure of the film/substrate stack. In contrast, for Zr/Ti ratios of 40/60 and 30/70, the characteristic stack strength increased while the Weibull modulus decreased to values typical for that of Si. This difference is believed to be due to toughening from ferroelasticity or phase switching. X-ray diffraction showed that the volume fraction of c-domains increased in Ti-rich compositions. This would allow for more switching from c to a-domains under biaxial tensile stress. Zr/Ti concentration gradients were present for all compositions, which contributed to the observation of a rhombohedral phase off the MPB. Due to the reduced tendency toward cracking, off-MPB compositions are potentially of interest in actuators, albeit with the trade-off of needing a high actuation voltage. 

The receive sensitivity of lead zirconate titanate (PZT) piezoelectric micromachined ultrasound transducers (PMUTs) was improved by applying a DC bias during operation. The PMUT receive sensitivity is governed by the voltage piezoelectric coefficient, h31,f. With applied DC biases (up to 15 V) on a 2 μm PbZr0.52Ti0.48O3 film, e31,f increased 1.6 times, permittivity decreased by a factor of 0.6, and the voltage coefficient increased by ~2.5 times. For released PMUT devices, the ultrasound receive sensitivity improved by 2.5 times and the photoacoustic signal improved 1.9 times with 15 V applied DC bias. B-mode photoacoustic imaging experiments showed that with DC bias, the PMUT received clearer photoacoustic signals from pencil leads at 4.3 cm, compared to 3.7 cm without DC bias.