Analytical Die Stress Modeling and Hysteresis Compensation in MEMS Sensors
Analytical die stress modeling isolates mechanical package strain from sensor signals while hysteresis compensation algorithms eliminate viscoelastic offset drift.
Wafer Bow Metrology
Geometry Analysis
Precise measurement of the out-of-plane deformation of semiconductor substrates enables the quantification of the mechanical effects of thin-film deposition and thermal processing. Applying wafer bow metrology allows process engineers to quantify the spherical curvature of the wafer caused by internal stresses in deposited films. This dimensional analysis ensures that the wafer remains flat enough for subsequent photolithography steps, which have strict depth-of-focus limitations.
Stress Calculation
Stoney’s equation relates the measured change in wafer bow to the average stress in the deposited thin film, assuming a homogeneous substrate of known thickness and elastic properties. By measuring the bow before and after film deposition, the tensile or compressive stress state can be determined.
Interferometric Scan
Non-contact optical methods such as multi-beam intensity interferometry or capacitive sensing arrays scan the wafer surface to generate a three-dimensional topography map. These scans capture the height variation across the entire diameter, filtering out any overall tilt of the specimen.
Reference Plane
Establishing a virtual reference plane based on three-point support geometry provides the baseline from which the bow is calculated. The maximum deviation from this plane, measured at the center of the wafer, defines the bow value reported by the metrology system.