| In general, thin films deposited during semiconductor manufacturing exhibit intrinsic stress. If these stresses are not controlled, they can lead to failure of electronic devices by a variety of mechanisms.; To some extent, film stress can be controlled by deposition process variation or annealing. But, in order to accurately control film stress, it must be accurately measured. Most film stress measurements are based on Stoney's equation. However, when in-plane film stress gradients are present, Stones equation is not an accurate stress-curvature relationship.; A method of calculating plane film stress based on out-of-plane wafer displacements has been formulated using an inverse finite element model. The inverse model resolves graded film stresses and also includes the orthotropic elastic properties of single crystal silicon. Using simulation, the model has been tested with several virtual cases. It was also used in a case where an analytical relationship between film stress and wafer displacement was known.; To evaluate the inverse model's ability to resolve a stress gradient experimentally, a gradient was induced into one film by local heating. The wafer shape was measured by a laser-scanning, curvature-based stress mapping tool, before and after deposition, as well as after heating. The inverse model was used to determine film stress from the measured wafer shape. The resulting film stress was then applied to a displacement-based finite element model, which successfully reproduced the measured wafer shape. However, the inverse model has not been verified by a comprehensive experimental testing program. |
