Estimation of the Effective D₃₁ Coefficients of the Piezoelectric Layer in Rainbow Actuators


We have analyzed the performance of Rainbow (reduced and internally biased oxide wafer) actuators by assuming that the key difference between these devices and unimorph actuators is the presence of internal stress that alters the extrinsic (domain switching) contribution to electromechanical response, and thus, the effective d31 coefficient of the piezoelectric layer. Based on this assumption, we calculated the d31 coefficient as a function of device geometry and electric field and found that the coefficients ranged from approximately −300 to −600 pm/V. The highest d31 value was obtained for a Rainbow actuator that was fabricated by reducing 1/3 of the piezoelectric layer; other studies indicated that this device possessed the highest tensile stress in the surface region of the piezoelectric. We observed that geometric effects on calculated d31 coefficients were as significant as voltage effects. The analytical approach utilized also permitted estimation of the relative contributions of mechanical and stress effects to the performance of these devices, which were determined to be dependent on field and geometry. Although the estimated d31 coefficient for certain geometries is twice the typical low field value, it must be remembered that this value represents an "average" value for the entire piezoelectric layer, which is under a stress gradient; i.e., the lower region of the piezoelectric is in lateral compression, while the upper region is in lateral tension. This suggests that the true electromechanical coefficients of the lead zirconate titanate composition utilized in these devices would display an even broader range of d31 values, if d31 was characterized as a function of uniform lateral stress.


Materials Science and Engineering

Keywords and Phrases

Piezoelectric Materials; Piezoelectric Properties; Strain; Stress

International Standard Serial Number (ISSN)

0002-7820; 1551-2916

Document Type

Article - Journal

Document Version


File Type





© 2001 John Wiley & Sons, All rights reserved.

Publication Date

01 Jul 2001