A Method of X-Ray Stress Measurement of Silicon Single Crystal
Keisuke TANAKA, Yoshiaki AKINIWA, Kenichi MIZUNO and Kaori SHIRAKIHARA
Abstract:An X-ray method is proposed to measure the stress in a specimen made of silicon single crystal wafer which has the [001] direction perpendicular to the surface. In an X-ray diffractometer with parallel beam optics, X-ray profiles were recorded by a scintillation counter while the specimen was oscillated. The X-ray measurement conditions were first determined, and then the method was successfully applied to measure the loading stress in a silicon single specimen subjected to four-point bending. The oscillation of the specimen between ±1 to 2 deg during recording is necessary to determine the peak position. The miss-setting of 25 μm does not influence the measured stress value. The uniaxial stress was applied in [110] direction （longitudinal direction with φ=0 deg） of the specimen and three stress components, σ11, σ22 and σ12 were determined from the measurement of strains in three directions, φ=0 deg, 90 deg, and 45 deg. From the diffractions of 115 and 333 for two directions φ=0 deg and 90 deg, the stresses σ11 and σ22 were determined by the 2θ-sin2ψ method. The shear stress component, σ12, was determined from the strain measurements of two directions, φ=26.565 deg and 63.435 deg by using the diffractions of 004 and 133. The measured stress of σ11 is 102% of the applied stress and the two other components, σ22 and σ12, were nearly zero. The uniaxial state of stresses in plate under four point bending was confirmed as predicted by the finite element method. Key Words:Silicon single crystal, X-ray stress measurement, Four-point bending, Plane stress state, Measurement condition