The significance of the piezoelectric coefficient d31,eff determined from cantilever structures

The method used by SolMateS to determine the effective piezoelectric coefficient d31,eff of Pb(Zr,Ti)O3 (PZT) thin films from cantilever displacement measurements is described. An example from a 48 cantilever dataset using different cantilever widths, lengths and crystal alignments is presented. It is shown that for the layer stack of our cantilevers, the multimorph model is more accurate compared to the bimorph model for the d31,eff determination. Corrections to the input parameters of the model are further applied in order to reduce the geometrical error of the cantilever that is caused by its design and processing, as well as correction to the measured tip displacement caused by resonance amplification. It is shown that after these corrections, the obtained d31,eff values are still up to 10% uncertain as the plate behavior and the non-constant radius of curvature of the cantilevers lead to inconsistent results. We conclude that quantitative determination of d31,eff from the cantilevers is highly subjective to misinterpretation of the models used and the measurement data. The true value of d31,eff was determined as −118.9 pm V−1.

[1]  Paul Muralt,et al.  Tensile and compressive stress dependency of the transverse (e31,f) piezoelectric coefficient of PZT thin films for MEMS devices , 2007, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[2]  Laxman Saggere,et al.  PZT thin films for low voltage actuation: Fabrication and characterization of the transverse piezoelectric coefficient , 2007 .

[3]  J.G. Smits,et al.  The constituent equations of piezoelectric heterogeneous bimorphs , 1991, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[4]  L. Abelmann,et al.  Determination of the Young's modulus of pulsed laser deposited epitaxial PZT thin films , 2011 .

[5]  H. Kolsky,et al.  Dynamics of vibrations , 1965 .

[6]  Leon Abelmann,et al.  Characterization of epitaxial Pb(Zr,Ti)O3 thin films deposited by pulsed laser deposition on silicon cantilevers , 2010 .

[7]  Rainer Waser,et al.  Phase diagrams and physical properties of single-domain epitaxialPb(Zr1−xTix)O3thin films , 2003 .

[8]  S. Kaldor,et al.  Differentiating between elastically bent rectangular beams and plates , 2002 .

[9]  M. Dekkers,et al.  Misfit strain dependence of ferroelectric and piezoelectric properties of clamped (001) epitaxial Pb(Zr0.52,Ti0.48)O3 thin films , 2011 .

[10]  W. Brantley.  Calculated elastic constants for stress problems associated with semiconductor devices , 1973 .

[11]  A. Vaz,et al.  Measurement of the elastic modulus of nanostructured gold and platinum thin films , 2003 .

[12]  Jun-Ming Liu,et al.  Piezoelectric coefficient measurement of piezoelectric thin films: an overview , 2002 .

[13]  L. Abelmann,et al.  Influence of silicon orientation and cantilever undercut on the determination of the Young's modulus of thin films , 2011 .

[14]  M. Weinberg.  Working equations for piezoelectric actuators and sensors , 1999 .

[15]  D. A. Berlincourt,et al.  Piezoelectric Properties of Polycrystalline Lead Titanate Zirconate Compositions , 1960, Proceedings of the IRE.