Influence of test capacitor features on piezoelectric and dielectric measurement of ferroelectric films

This paper presents both theoretical and numerical analyses of the piezoelectric and dielectric responses of a highly idealized film-on-substrate system, namely, a polarized ferroelectric film perfectly bonded to an elastic silicon substrate. It shows that both effective dielectric and piezoelectric properties of the films change with the size and configuration of the test capacitor. There exists a critical electrode size that is smaller than the diameter of the commonly used substrate. The effective film properties converge to their respective constrained values as capacitor size increases to the critical size. If capacitor size is smaller than the critical size, the surface displacement at the top electrode deviates from the net thickness change in response to an applied voltage because the film is deformable at the film/substrate interface. The constrained properties of the films depend only on those of bulk ferroelectrics but are independent of film thickness and substrate properties. The finding of the critical capacitor size together with analytical expressions of the constrained properties makes it possible to realize consistent measurement of piezoelectric and dielectric properties of films. A surface scanning technique is recommended to measure the profile of piezoresponses of the film so that the constrained properties of the film can be identified accurately.