THERMAL OXIDATION is one of the most important process steps in semiconductur fabrication, which is used to produce high quality insolation layers. The chemical reaction during oxidation converts silicon into silicon dioxide. The formed oxide material has more than twice of the original volume of silicon. This significant volume increase is the main source for stress and displacements in the oxidized structure. There is a big interest in the simulation of oxidation, because the volume increase and the fact that the oxide growth rate depends on a number of parameters and also on the stress in the material, make it impossible to predict the final shape of the silicon dioxide without simulation in practically used structures. Furthermore, the possible stress distribution and deformation which are caused by the oxidation process in the neighboring structure, can be only evaluated by simulation.
All conventional models are based on the moving boundary concept. Unfortunately moving boundaries are the most restricting factor for three-dimensional oxidation simulation, because they need complicated algorithms and an enormous data update. Therefore, a modern three-dimensional oxidation model should be based on a new concept which avoids the difficulties and drawbacks regarding the mechanics. An up-to-date model should also enable the simulation of even complex structures within an acceptable time period on convential computers. Furthermore, for universal application an oxidation model should be physically based, which means that it takes into account that thermal oxidation is a process where a diffusion, a chemical reaction, and a volume increase occur simultaneously. In the course of this work an advanced three-dimensional oxidation model which is able to fulfill all listed requirements, was developed. This model is based on a diffuse interface concept.
The implementation of the model in a simulation tool is an important task. The numerical solving of the mathematical formulation is performed with the finite element method which is most suitable for the mechanical displacement problem. The discretization of the (differential) equations is an important part of modeling. For the practical application of the simulation tool a simple method for the model calibration is shown. Despite the diffuse interface concept, the simulation results can be presented with a sharp interface between silicon and silicon dioxide for a physical interpretation. It is known that stress has a significant influence on the oxidation growth rate. For obtaining physically meaningful simulation results, the stress dependence of the oxidation process is taken into account in the oxidation model.
Stress in copper interconnects is an important promoting factor for electromigration. The material transport due to electromigration can lead to void formation in the interconnect. These voids can cause an enormous increase of the resistance or even a total failure in the interconnect. Thermal stress arises from the self-heating effect of the current flow in the interconnect, because the copper interconnects are embedded in materials with different thermal expansion coefficients. A stress simulation is the only possible way to determine high-stress areas in the interconnect structure in order to locate critical points with respect to electromigration.
During the fabrication of micro-electro-mechanical systems and aftermath, where thin film deposition is a widely used technique, an intrinsic stress is generated in the layers. In micro-electro-mechanical systems which are mostly used as sensors, the stress can change the electrical and magnetic characteristics and can also cause unwanted deformation in free standing structures. The determination of intrinsic stress in thin films is demanded, but a number of microscopic effects which lead to stress do not allow a straightforward stress calculation. In this work a number of intrinsic stress sources are discussed. For the different intrinsic stress sources, which describe the stress development due to the microscopic effects, macroscopic mechanical formulations are given. Furthermore, a methodology which allows to predict the stress distribution in the deposited thin film, was developed.