Determination of the elastic moduli and residual stresses of freestanding Au-TiW bilayer thin films by nanoindentation

Highlights

• A new method for the assessment of elastic moduli and residual stresses in bi-layer suspended micro-beams is presented

• The method is based on micro-bending experiments performed by nanoindentation testing

• An analytical procedure is adopted to extract the elastic modulus and residual stress of each layer

• Nanoindentation method is validated by Focused Ion Beam - Digital Image Correlation (FIB-DIC) double-slot technique

• The developed procedures can be useful for design of Microelectromechanical devices with improved performance

Abstract

In this paper, we present a detailed mechanical characterization of freestanding bilayer (Au-TiW) micro-cantilevers and double clamped beams, for applications as Radio Frequency (RF)-switches Micro-Electromechanical Systems (MEMS). The testing structures have been characterized by an optical profilometer and Scanning Electron Microscopy (SEM) equipped with Energy Dispersive X-ray Spectroscopy (EDS), in order to acquire information about their geometries, composition, and the gap between the substrate underneath. Then, the micro-beams are deflected by using a specifically designed nanoindentation procedure based dynamic stiffness measurement during bending in order to extract the elastic modulus and the residual stresses of both layers. Firstly, the classic beam theory has been implemented for bilayer cantilevers enabling the extraction of elastic moduli. Then, residual stresses are estimated by deflecting double clamped beams, while implementing new analytical models for a bilayer system. The obtained elastic moduli are consistent with the average ones obtained for a single layer micro-cantilever and with nanoindentation results for TiW and Au homogeneous films. The residual stresses are in agreement with the values obtained from the double slot Focused Ion Beam (FIB) and Digital Image Correlation (DIC) procedure, providing an alternative and portable way for the assessment of residual stresses on composite double clamped micro-beams.

Introduction

Micro Electro-Mechanical Systems (MEMS) have found a growing number of applications involving sensors, actuators to active Radio Frequency (RF) components, optics as well as energy generation devices [1]. The assessment of reliability and life time of MEMS devices is a major concern in the microelectronic industry, requiring a full understanding of the mechanical properties of micrometer-sized materials employed in MEMS fabrication [1]. Among other factors, residual stress has been identified as one of the main parameters affecting both performance and lifetime of double-clamped MEMS structures [1].

Small-scale dimension materials exhibit mechanical properties which are different from their bulk counterpart because of the dominance of surface effects possible microstructural changes [2]. In crystalline materials, the thickness confinement prevents dislocation motion [3] and limits the grain growth favoring strengthening phenomena [2]. The nucleation and propagation of shear bands are also affected by size effects in metallic glasses involving an increase of ductility, yield strength and change in fracture mode [2], [4]. However, a conclusive understanding of mechanical properties and of the associated deformation mechanisms of small-scale materials is still missing. The difficulty arises from the challenge to generate consistent and reproducible data on small-scale specimens, while avoiding artifacts. Mechanical size effects can affect the mechanisms behind the deformation and fracture of thin films, which can have significant impact on MEMS functionality. Therefore, specific testing methodology are needed to characterize the mechanical properties of thin films.

Many techniques have been employed to investigate freestanding MEMS materials' mechanical behavior including micro-tensile [5], bending [6], bulge tests [7] as well as nano-mechanical testing actuated by residual stress films [8]. Although these techniques can provide useful information about mechanical properties of freestanding films, they often relay upon complicated experimental apparatus which require several steps [6], [7], [8] and can only assess specimens with dimensions above few micrometers in length and width and 500 nm in thickness direction [5]. Nanoindentation provides high resolution in load, displacement and x-y positioning and is therefore suitable for characterizing the mechanical response of freestanding thin films [9], [10]. Bending of freestanding cantilever was originally performed by Weihs et al. [11] on Al thin films and has since been applied to other materials such as Ni [12], Ti [13] and metallic glasses [14], [15]. This technique involves the deflection of a freestanding cantilever using a nanoindenter. The stiffness can be extracted as the slope of the load-deflection curve enabling the determination of the material elastic modulus which is a key parameter in the behavior of MEMS devices [11]. Since then, Guo et al. [14] have minimized the error caused by uncertainties in the effective indentation position performing multiple indentations, Tsou et al. [12] have improved the analysis by subtracting the indentation effect during deflection, while Florando and Nix [16] have used triangular cantilever in order to avoid inhomogeneous strain distribution during bending. Bilayer cantilevers have been tested by Boyd et al. [17] and Fang [18] to extract the elastic moduli using nanoindentation and resonant methods. However, in both cases a complicated Finite Element Modeling (FEM) was required.

Residual stresses are usually extracted measuring the change of substrate curvature consecutive to film deposition using the Stoney Equation [19]. Other techniques based on Focused Ion Beams (FIB) milling can be been employed to precisely account for the effect of the local microstructure [20]. Freestanding MEMS structures can be used to capture the magnitude of the residual stress. Double clamped beams with different length can be used as a strain sensor [21]. Once released, compressive stress can induce buckling above a critical length [21]. An array of beams with different lengths enables to capture the magnitude compressive stress. Tensile residual stress can be extracted using a similar structures involving rings fixed to the substrate at two points with a central beam spanning perpendicularly to the anchor points [22]. After releasing, the tensile internal stress puts the central beam in compression, involving buckling above a critical length [22]. Angular variation of residual stresses (both in compression and in tension) can be made using rotating sensors as well [23]. However, most of these techniques are limited to a specific material and are inaccurate for large deflections [23]. Zhang et al. [24] first proposed a new method for extract the elastic modulus and residual stresses using nanoindentation. Specifically, SiN freestanding double clamped beams are deflected in the center by a nanoindenter. Then, FEM is then applied to extract the elastic modulus and residuals stresses, while accounting the support compliances and the bending moment. Zhou et al. [25], [26] extended the procedure for metallic Ni and NiFe double clamped beams, while Herbert et al. [27] improved the procedure to extract the elastic modulus and residual stress. Specifically, they developed an analytical solution that manages to accurately fit nanoindentation data under the assumption that the film deformation is dominated by stretching during indentation experiments [27]. Other assumptions consider the film flat, while the indent location is exactly in the center of the double clamped beam. The deflection is normal and elastic and the effect support posts are and the bending moments are ignored. In this model the residual stress are originated by the constrained beam geometry which prevent a full relaxation of residual stresses after releasing.

Bilayer double clamped beams have also been investigated due to the possibility to reduce the amount of residual stresses. Zhang et al. [28] and Nie et al. [29] used nanoindentation and pull-in methods respectively, to obtain the elastic moduli and residual stresses. However, a complex experimental set-up combined with FEM is required.

In this work, we use nanoindentation to study the mechanical properties of bilayer cantilevers and double clamped beams in order to extract elastic moduli and residual stress. Specifically, (i) we implemented the classic beam theory for a stress-free bilayer cantilever enabling the extraction of the elastic moduli of both layers using the stiffness measurement obtained by nanoindentation on different cantilever lengths. Then, (ii) we determine the residual stress by nanoindentation testing of double clamped beams, which are fabricated on the same Si wafer with the cantilevers, extending the analytical model of Herbert et al. [27] for a bilayer system and taking into account the indentation effect during loading.

We show that: (i) the obtained elastic moduli are in good agreement with TiW and Au films given by nanoindentation and with the average results given by Herbert's model [27]; (ii) the extracted residual stress are agreement with the values obtained from the double slot FIB and Digital Image Correlation (DIC) procedure, providing an alternative way to assess of residual stress estimates for composite double clamped beams.