Finite Element Modeling of Polymeric Underfill Creep for Silicon Sensors
Finite element modeling of underfill creep uses Prony viscoelasticity and Anand viscoplasticity to predict and compensate long-term silicon sensor drift.
Element Aspect Ratio
Geometric Proportion
Design specifications for micro-scale features define the relationship between the height and the width of a sensing element or structural component. The element aspect ratio influences the mechanical stiffness and the sensitivity of a transducer to external loads. Designing for a specific ratio allows for the optimization of the signal to noise ratio.
Manufacturing Limit
Fabrication processes such as deep reactive ion etching impose constraints on the achievable dimensions of micro-scale features. A high element aspect ratio can lead to structural instability or collapse during the release phase of manufacturing. Etch lag and scalloping effects become more pronounced as the trench depth increases relative to the width.
Mechanical failure occurs when the internal stresses exceed the material strength.
Measurement Interference
Cross-axis sensitivity often arises from deviations in the planned geometry of the sensing element. When the element aspect ratio is not strictly controlled, the sensor may respond to forces acting perpendicular to the primary measurement axis. This geometric imperfection introduces parasitic signals that require electronic compensation.
Tight tolerances on the etching process minimize these errors.
Stability Analysis
Thermal expansion creates differential stresses in structures with extreme proportions. The element aspect ratio affects how these stresses are distributed across the sensor surface and the resulting drift in the zero point. Long, thin structures exhibit greater deflection for a given temperature change.
Stability is achieved through symmetric design and material matching.