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# 1.4 Outline of the Thesis

The topic of this thesis are the three-dimensional modeling and simulation of thermal oxidation, which is the first and main part, and the three-dimensional modeling and simulation of stress and its effects in the second part.

In the beginning of Chapter 2 the characteristics, properties, and structure of the material silicon dioxide and the principle of the oxidation process are described. Next the influence of the different oxidation parameters on the oxidation process are lighted up. Some aspects of nitrided oxide films are also listed. At last the concept of the traditional oxidation modeling, which is still used in state of the art oxidation simulators with more or less extensions, is explained.

In Chapter 3 an advanced oxidation model with an effective and improved modeling concept is presented. The new concept avoids the drawbacks of the traditional oxidation models, especially regarding the mechanics in case of complex three-dimensional structures. This chapter includes mainly the mathematical formulation of the advanced oxidation model, where the mechanics is an essential part. Thermal oxidation of doped silicon material leads to a redistribution of the dopands as described in Chapter 4.

Chapter 5 treats the discretization of the mathematical formulation with the finite element method which starts with some basics. This chapter concentrates on the discretization with tetrahedrons, which is explained at first in general and then in detail for the used differential equations of the advanced oxidation model and the mechanics. The chapter continues with the description of the assembling procedure, also for the needed special cases like mechanical interfaces, in order to built-up the complete equation system. At the end the solving of this equation system with the Newton method is described.

Chapter 6 is focused on the simulation of thermal oxidation with the in-house process simulation tool into which the models were implemented. The architecture and main components of this tool are depicted and the simulation procedure for oxidation is explained. Since not only the accuracy, but also the simulation time and computer resources depend on the number of discrete elements, the used mesh plays a key role for simulation. So in this chapter an effective meshing strategy is discussed. Furthermore, the procedure for the sharp interface interpretation of the displayed simulation results is described. Finally the optimal way found for the model calibration is shown.

In Chapter 7 the developed oxidation model is applied for stress dependent oxidation. A universal stress calculation concept for the oxidation simulation is presented. In order to demonstrate the good performance of the model and the simulation tool, representative examples for oxidation are presented.

Because stress is a promoting factor for electromigration, in Chapter 8 the simulation procedure of thermo-mechanical stress in copper interconnect structures is described. The stress distribution for a demonstrative interconnect layout is simulated.

In Chapter 9 intrinsic stress effects in deposited thin films are discussed. At the beginning a typical effect, the cantilever deflection problem, is shown. Furthermore, some stress sources are listed and a macroscopic stress formulation is given. A strain curve predicted by the methodology is analyzed and calibrated for a multilayer film. The calibrated curve is applied to investigate a fabricated cantilever structure. The thesis is concluded with a summary in Chapter 10.    Next: 2. Physics of Thermal Up: 1. Introduction Previous: 1.3 Overview and History

Ch. Hollauer: Modeling of Thermal Oxidation and Stress Effects