Silicon Substrate Thermal Expansion Mechanics in Inertial Sensors
Substrate thermal expansion creates packaging shear stress that warps MEMS proof masses, demanding central single-anchor isolation and polynomial offset calibration.
Out-of-Plane Warping
Geometric Distortion
Departure from a flat profile occurs in planar components due to internal or external stresses. Out-of-plane warping typically happens during the curing of polymers or the cooling of composite materials. This deformation complicates the assembly process and can lead to mechanical failure of the solder joints.
Causal Mechanism
Differential shrinkage between layers with different coefficients of thermal expansion drives the change in shape. In out-of-plane warping, the top surface of a printed circuit board may contract more than the bottom, causing a curved profile.
Measurement Technique
Laser profilometry or shadow moire interferometry provides a topographic map of the surface. Quantifying out-of-plane warping involves comparing the highest and lowest points of the part to a theoretical reference plane.
Control Strategy
Symmetrical design of the layers helps to balance the internal forces and reduce distortion. Managing out-of-plane warping requires optimizing the temperature profiles during reflow and curing. Fixtures or jigs may be used to hold parts flat while they undergo thermal processing.
Verification involves measuring the displacement after the part has reached room temperature. Any part exceeding the flatness tolerance is rejected to prevent issues with automated pick and place machines. The amount of warp is often expressed as a percentage of the diagonal length of the board.