Meaning
Mathematical expression used to calculate the internal stress of a thin film based on the measured change in the radius of curvature of a substrate. Non-destructive monitoring of the mechanical stability of coatings is performed using the stoney formula. This calculation is a standard part of the quality control loop in semiconductor and optical filter manufacturing.
Curvature Relationship
The stress is proportional to the square of the substrate thickness and inversely proportional to the film thickness. Using the stoney formula, an engineer measures the wafer before and after deposition with a laser profiler to determine the change in bow. This value allows for the adjustment of deposition parameters like temperature or bias voltage to keep the stress within safe limits.
Stress maps across the wafer surface help identify uniformity issues in the deposition chamber.
Boundary Condition
Accuracy requires very thin film layers and elastic deformation.
Process Audit
Monitoring these stress levels is necessary to prevent the delamination or cracking of optical coatings during thermal cycling. If a production run shows a shift in curvature that exceeds the baseline, it indicates a drift in the vacuum system or gas flow rates. Applying the stoney formula at the start of every shift ensures that the mechanical properties of the batch match the pilot data.
