The paper examines the problem of film stress applying a correct three dimensional model. The results are compared with two different forms of Stoney´s equation existing in the Litera-ture and being widely used in the determination of stresses in thin films. It is shown theoretically that only one of the forms is based on an adequate model and yields accurate results whereas the other causes errors of about 30-40 % for typical substrate materi-als. In addition limits for the applicability of the correct Stoney equation are given.

The paper treats the question of feasibility of measuring intrinsic thin film stresses due to nanoindentation. A variety of different methods is proposed and analysed with respect to their applicability. As this accuracy-estimation results in boundary conditions for the measurements which can not be fulfilled yet, the whole topic is considered from a purely academic point of few. With the help of a special software package [25] the following methods are considered: 1. Taking the moment of beginning plastic flow within the substrate as indictor, 2. Taking the moment of beginning plastic flow within the film as indictor, 3. Applying mixed loads (normal and lateral forces), 4. Applying the concept of the effectively shaped indenter. While the methods 2 to 4 appear to be in principle feasible, method 1 can completely be ruled out as being of no practical use. The mentioned software package (FilmDoctor prototype) is part of the supplemental material of this study.

The paper examines the problem of film stress applying a correct three dimensional model. The results are compared with two different forms of Stoney´s equation existing in the Litera-ture and being widely used in the determination of stresses in thin films. It is shown theoretically that only one of the forms is based on an adequate model and yields accurate results whereas the other causes errors of about 30-40 % for typical substrate materi-als. In addition limits for the applicability of the correct Stoney equation are given.

The paper treats the question of feasibility of measuring intrinsic thin film stresses due to nanoindentation. A variety of different methods is proposed and analysed with respect to their applicability. As this accuracy-estimation results in boundary conditions for the measurements which can not be fulfilled yet, the whole topic is considered from a purely academic point of few. With the help of a special software package [25] the following methods are considered: 1. Taking the moment of beginning plastic flow within the substrate as indictor, 2. Taking the moment of beginning plastic flow within the film as indictor, 3. Applying mixed loads (normal and lateral forces), 4. Applying the concept of the effectively shaped indenter. While the methods 2 to 4 appear to be in principle feasible, method 1 can completely be ruled out as being of no practical use. The mentioned software package (FilmDoctor prototype) is part of the supplemental material of this study.

Ce travail a pour objectifs de comprendre et de prédire les gauchissements de plaquettes en silicium durant le procédé de fabrication des composants électroniques de type PTIC. Ces gauchissements sont en partie responsables de plusieurs problèmes de productivité. Cette étude repose sur un couplage entre les calculs analytiques, la modélisation par élément finis et l’expérimentation. La caractérisation mécanique des films minces constituant l’empilement a été effectuée par des techniques spécifiques comme la nanoindentation complétée par des modélisations numériques. Les contraintes intrinsèques dans les films minces ont été déterminées en couplant des mesures de gauchissements des plaquettes et des calculs par éléments finis. Les valeurs du module d’Young et des contraintes intrinsèques obtenues constituent des variables d’entrée pour calculer les gauchissements de la plaquette par des approches analytiques et numériques. La complexité des structures (plaquettes avec des milliers de puces) a nécessité l’utilisation des modèles d’homogénéisation pour estimer numériquement les gauchissements. Les résultats obtenus ont permis de prédire les gauchissements à l’échelle des plaquettes dans le but d’optimiser les conditions de fabrication afin de minimiser les risques d’apparition des problèmes mécaniques. / The aim of this work is to understand and predict the warpage of silicon wafers during the fabrication process of PTIC microelectronic components. The warpages are partially responsible for several productivity problems. This study is done by coupling analytical calculation, finite element modeling and experimentation. The mechanical characterization of thin films constituting the multi-layered stack has been carried out by an experimental method nanoindentation with the help of a finite element model. The intrinsic stress in the thin films has been determined by coupling measurements of the wafer warpage and a finite element model. The obtained Young’s modulus and intrinsic stress are used to feed the database for calculating the wafer warpage by analytical and numerical approaches. The complexity of the structures (thousands of components in the wafer) required the use of homogenized models to calculate the wafer warpage. These results obtained allow the prediction of the wafer-level warpage in order to optimize the fabrication process flow and therefore reduce the risk of the mechanical problem.