Three Dimensional Modeling of Anisotropic Stress Effects in Thermal Oxidation of Silicon
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Three Dimensional Modeling of Anisotropic Stress Effects in Thermal Oxidation of Silicon Xiaopeng Xu, Norbert Strecker and Victor Moroz Avant! Corporation, 46871 Bayside Parkway, Fremont, CA94538, U.S.A. ABSTRACT Three-dimensional analyses of anisotropic stress effects during thermal oxidation of silicon are performed in this study using finite strain formulation. A reaction rate model that conjugates pressure to a crystalline direction dependent activation volume is employed for the modeling of facet formation in an STI MOSFET device. The numerical results agree well with TEM observations. The 3-D nature of stress evolution in fabrication process is demonstrated and the implication of stress relaxation on device performance in a strained SiGe based device is discussed.
INTRODUCTION In semiconductor devices stress is directly responsible for many reliability issues such as dislocation nucleation, growth and pileup, defect failure, electro-migration, current leakage and malfunction, etc. Stress also plays important roles in semiconductor fabrication process and device physics, e. g. impurity diffusion, thermal oxidation, silicidation, band gap change, carrier mobility, etc. The deep submicron miniaturization of semiconductor devices has imposed even more stress related technical challenges in semiconductor fabrication process. Since silicon dioxide provides a high quality insulation barrier on the surface of the silicon wafer and serves as a barrier during subsequent impurity diffusion process steps, thermal oxidation of silicon has been an essential step in semiconductor fabrication. Thermal oxidation of silicon involves the following phenomena: 1) oxidant diffusion through the existing oxide layer, 2) oxidation reaction at the silicon/oxide interface, and 3) volume expansion of the newly grown oxide. The mechanical stress has impacts in all three events: the diffusivity and the reaction rate are strongly dependent upon stress, and the final oxide geometry is determined by the stress equilibrium. While experimental tracing of the stress during fabrication process remains extremely difficult, numerical modeling of stress in a real semiconductor device provides an attractive alternative. To accurately model thermal oxidation of silicon, stress analysis needs to be performed carefully to capture the three dimensional effects and various anisotropic material responses that are common in a modern semiconductor fabrication process. In our 3-D process simulator finite strain kinematics is invoked to account for large deformation associated with oxide growth. Crystal elasticity is used to model anisotropic mechanical properties of silicon. The oxide is modeled as a visco-elastic material and the history dependent stress relaxation is governed by the Maxwellian laws. At the silicon/oxide interface, the reaction activation barrier is taken as the product of hydrostatic pressure with activation volume that incorporates crystalline anisotropy. The reactive boundary movement is tracked by solving a level set equation. To valida
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