A Theoretical Examination of Mems Microactuator Responses with an Emphasis on Materials and Fabrication
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Resultant deflection
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Silicon substrate Figure 1 Surface micromachined cantilever structure. The fabrication process for this structure is similar to a process that has been previously used to fabricate microsensors [2,3]. A trench is etched into the silicon substrate, and this trench is either oxidized or filled with a low temperature oxide layer to form an oxide well.
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Mat. Res. Soc. Symp. Proc. Vol. 360 ©1995 Materials Research Society
Building the sacrificial oxide into the substrate helps to preserve planarity for subsequently deposited layers. A 1 gim core material (low stress silicon nitride and undoped polysilicon), RF sputtered bottom platinum/titanium, sol-gel PZT, and RF sputtered top platinum/titanium layers are then successively deposited on the substrate. The polysilicon is used to promote the adhesion of the layers to follow, and the titanium aids in the adhesion of the platinum. Using standard photolithography techniques, the top metal, piezoelectric and bottom metal layers are patterned and ion milled. This structure is then encapsulated with RF sputtered chrome which is patterned and etched to expose the nitride/polysilicon core layer. The core layer is reactively ion etched thereby exposing the sacrificial oxide. The sacrificial oxide can be easily removed in a ten minute hydrofluoric acid vapor etch leaving a freestanding cantilever beam, and the chrome encapsulant is wet etched to complete the processing. THEORY Analytical In modeling the cantilever structure in Figure 1, thicknesses assumed for the core, bottom metal, piezoelectric material, and top metal were 1.0, 0.2, 0.3, and 0.1 microns respectively. Several rigorous theories have been derived for piezoelectric devices [4,5]. A simple beam theory can be applied to the cantilever to determine how it will behave. This theory begins with redefining the thin film cantilever structure using the transformed sections method [6]. Figure 2a shows the actual cross-section of the cantilever structure. Each layer of the cantilever (core material, bottom electrode, piezoelectric material, and top electrode) should be properly accounted in terms of variations in thickness and Young's modulus. The transformed section method allows the width of the beam layers to be proportioned by the ratios of their Young's moduli, thereby defining the entire beam as having one Young's modulus. The moduli for the core, bottom metal, piezoelectric, and top metal are 16, 15, 7, and 15 x 1010 N/m 2 , respectively [7]. The bottom metal transformed width is 15/16 of the core width, the piezoelectric material width is 7/16 of the core width, and the top metal width is 15/16 of the core width as shown in the cross-section of Figure 2b. This transformed structure behaves as though it has a modulus of 16 x 1010 N/m2 . Top metal Piezoelectric Bottom metal
b
a
Figure 2 Cantilever cross-section before and after section transformation. The neutral axis for the transformed cross-section is equal to the moments of th
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