Stress and Deformation of Pzt Thin Film on Silicon Wafer Due to Thermal Expansion
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MODELING A theoretical model is developed to predict the stress and deformation of PZT thin films on silicon wafers due to thermal expansion in the annealing process and analyzed using the 3-D shell model of ANSYS 5.3. For convenience and because of symmetry, a quarter part of the wafer (4inch diameter, p-type, (100)) is considered in this model. Two designs of PZT films on silicon wafers are modeled. The first design is a PZT/Pt/Ti/silicon dioxide/silicon wafer, which is used for making acoustic emission sensors. The second is a PZT/Pt/Ti/silicon dioxide/silicon nitride/silicon dioxide/silicon wafer, commonly used in the fabrication of cantilever beams. In both designs, the thickness of PZT film is 0.411, platinum is 0.1[i, titanium is 0.01fj, silicon dioxide is 0.2ga and 0.5gi, silicon nitride is 1.5gj, and silicon wafer is 500gx. The mechanical properties used for each layer are carefully selected and shown in Table I. Thermal expansion coefficients varying with temperature in the range from 20 to 700 °C are also taken into account, as shown in Table II. SHELL99, a 100-layer structural shell element with isotropic properties, is used to perform structural and thermal analysis under ANSYS 5.3. The Jacobi Cojugate Gradient (JCG) solution is used because it is best suited for 3-D scalar field analyses. The boundary conditions used in the modeling are shown in Figure 1. Displacement is set to zero at the origin of the quarter wafer, symmetric on the rays R, and free on the edge L.
•R Figure 1. Schematic of boundary conditions on a quarter of silicon wafer.
Fixed
,. 0
L Free
R
Symmetric
TABLE I Properties Materials Silicon wafer [101 Silicon nitride[ 111 Silicon dioxide [101 Titanium Platinum PZT
Temperature T( 0C)
Silicon
20 200 300 350 400 500 700
2.616 3.614 3.842 *3.929 4.016 4.151 4.26
[20]
Properties of Materials Young's modulus Poisson's ratio Y (GPa) _ _ _ 169 (110) 0.279 222 0.28 72 0.17 110 [121, [131 0.34 [121 [141 170 [151 0.39 [161 75 [171 0.31 [181 TABLE II Thermal Properties of Materials Thermal ex 3ansion coefficients, aX(10.6) SiO 2 [21] Silicon Titanium Platinum [221, [231 nitride[241 8.74 [251 8.92 [271 9.1 [261 9.5 [24] *9.28 9.7 [241 0.4 2.25 *9.37 *9.96 9.4 [261 10.0 [241 9.7 [261 10.2 [241 9.98 [251 11 [281
(* represents an average value.) 108
Density (k_/m_) 2329 3440 2200 4506.3 [131 21450 [121 7500 [191
PZT-5A [191 2.1 1.5 0.7 -3.0 5 8.2 8.2
PZT-4 [191 1.8 1.0 0.0 6.2 7.8 8.2 8.2
RESULTS AND COMPARISONS By means of color distribution, Figures 2a-f and 3a-h show the thermal stresses and deformation of the layers on the quarter wafer at an annealing temperature of 700 °C. For the design without silicon nitride layer, the thermal stress of the PZT film is 298MPa, Pt 128OMPa, Ti 647MPa, silicon dioxide 228MPa, and silicon wafer 0.41-1.67MPa. In the design with silicon nitride layer, the thermal stresses are PZT 301MPa, Pt 128OMPa, Ti 651MPa, silicon dioxide (second) 226MPa, silicon nitride 416MPa, silicon dioxide (first) 226MPa, and silicon wafer 1.05-4.23MPa.
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