Experimental, analytical, and finite element analyses of nanoindentation of multilayer PZT/Pt/SiO u2 thin film systems o
- PDF / 357,983 Bytes
- 11 Pages / 612 x 792 pts (letter) Page_size
- 65 Downloads / 173 Views
R.W. Whatmore and Q. Zhang Cranfield University, Cranfield, Bedfordshire MK43 0AL, United Kingdom (Received 19 July 2005; accepted 21 October 2005)
The mechanical properties of lead zirconate titanate (PZT) multilayer systems are needed to model and design micro-electromechanical systems (MEMS) devices. Nanoindentation is a promising tool for obtaining the elastic properties of thin films. However, no means exist to obtain the elastic modulus of the lead zirconate titanate (PZT) in the multilayer system. The indentation modulus versus a/t behavior of the multilayered PZT/Pt/SiO2 film system on a silicon substrate was investigated and compared with finite element models and a new analytical solution. Six different PZT film thicknesses were indented (100, 140, 400, 700, 1500, and 2000 nm), using 5-, 10-, and 20-m radius indenters. Good agreement was shown between the finite element analysis (FEA) and analytical solutions, and the experimental data. However the behavior of multilayer systems is complex, making deconvolution of properties difficult for films of less than a micron thick.
I. INTRODUCTION
The role of nanoindentation using spherical indenters as a method for obtaining the elastic properties of thin films used in micro-electromechanical systems (MEMS) applications has been described in detail in previous research.1–3 Lead zirconate titanate (PZT) has become increasingly important in MEMS applications because of its high electromechanical coupling factor when compared to conventional piezoelectric materials.4 The elastic-plastic behavior of bulk PZT in compression has been well documented.5–7 In thin film form, however, the elastic properties are largely unknown. In addition, an important difference is that the films tend to be crystallographically oriented, in this case, in the [111] direction, and there are substrate effects that influence the measured modulus as a function of penetration depth. For an isotropic material, the indentation modulus obtained from the force versus penetration data can be related to the Young’s Modulus by the following expression EIY = EIS共1 − 2兲 ,
(1)
where EIY is the indentation Young’s modulus and EIS is
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0047 J. Mater. Res., Vol. 21, No. 2, Feb 2006
http://journals.cambridge.org
Downloaded: 22 Feb 2015
the experimentally measured indentation modulus.8 The significance of the indentation modulus is not clear for the indentation of elastically anisotropic materials. Conway published the solution relating the indentation modulus of a transverse isotropic material to its elastic constants in 1967, and in 2001 Swadener and Pharr published the solution for fully anisotropic materials.9,10 The impact of anisotropy on the measured indentation Young’s modulus of PZT thin films will be the subject of a subsequent paper. In this study, we used the effective Young’s moduli for the Pt electrode and Si substrate in the finite element analysis (FEA) and analytical modeling. These wer
Data Loading...
