Temperature Dependence of Biaxial Modulus and Thermal Expansion Coefficient of Thin Films Using Wafer Curvature Method
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U11.29.1
Temperature Dependence of Biaxial Modulus and Thermal Expansion Coefficient of Thin Films Using Wafer Curvature Method M. Capanu, A. Cervin-Lawry, A. Patel, I. Koutsaroff, P. Woo, Lynda Wu, J. Oh, J. Obeng, B. McClelland Technology R&D, Gennum Corporation, P.O. Box 489, Station A, Burlington, Ontario, L7R 3Y3, Canada. ABSTRACT The present work uses wafer curvature (disk) method to measure the temperature variation of the biaxial modulus and the thermal expansion coefficient TEC from 25ºC to 205ºC. The following thin films were measured: PolySi, low stress LPCVD SixNy and (Ba0.7, Sr0.3)TiO3 (BST). To improve the precision, perfect circular thin wafers were used: 4 inches circular 280µm thick Si and 450µm thick Fused Silica. The measurements were performed using a commercial Tencor FLX2320 Stress Measurement System. The film thickness was measured with Tencor TF1 thin film optical system. INTRODUCTION Thin film properties such as the thermal expansion coefficient TEC, the biaxial modulus and the temperature coefficient of Young modulus are important in design, manufacturing and testing of micromachined devices, especially for MEMS applications. The wafer curvature (disk) method allows measurements of residual stresses using the Stoney equation. When the stresstemperature dependence of a thin film is measured on two different substrates, this gives thermal expansion coefficient TEC and elastic constants of that film if no irreversible change occurs in the film during heating and cooling. This wafer curvature method is nondestructive and does not require any further processing, any special equipment or any technical skills, making it very attractive, especially in industry. EXPERIMENTAL DETAILS The desired thin films were deposited onto circular 280µm thick 4” Si and 450µm thick 4” Fused Silica (FS) wafers. The films were vacuum-dehydrated at 120ºC for 30min just before the measurements. For each of the two substrates, the residual stresses in the film were calculated by measuring the wafer curvature from 25ºC to 205ºC every 10ºC and using the Stoney equation [1]:
σ R (T ) =
2 Es hs 1 1 − 6(1 − ν s ) T h f R(T ) R0
(1)
Where σR, Es, hs, νs, hf , 1/R, 1/R0 are residual stresses, substrate’s Young modulus, substrate’s thickness, substrate’s Poisson ratio, film thickness, the wafer curvature with film and the wafer curvature without film respectively. R0 is constant with T. The Es/(1-νs) is commonly named the biaxial modulus. The substrate thickness was measured using a micrometer, the film thickness was measured with Tencor TF1 thin film optical system, and the wafer curvature and temperature were measured using Tencor FLX2320 Thin Film Stress measurement system.
U11.29.2
When the temperature is changed, the residual stresses in the film are changed due to the thermal expansion mismatch of the film with respect to the substrate. The stress temperature slope is [2], [3] or [4]: bs =
dσ R (T ) = E dT 1 −ν f
(α (T ) − α (T )), s = 1,2. s
(2)
f
T
Where E/(1-νf), αf, αs are the fi
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