Modelling and Validation of Contribions to Stress in the Shallow Trench Isolation Process Sequence
K. Garikipati, V.S. Rao, M.Y. Hao, E. Ibok, I. de Wolf, R. W. Dutton

doi:10.3970/cmes.2000.001.065
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 1, No. 1, pp. 65-84, 2000
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Keywords mechanics, diffusion, reaction, coupled, finite elements
Abstract This work is based upon a careful rendering of mechanics and mathematics to describe the phenomena that influence the stress engendered by the Shallow Trench Isolation process. The diffusion-reaction problem is posed in terms of fundamental mass balance laws. Finite strain kinematics is invoked to model the large expansion of \sio2, dielectrics are modelled as viscoelastic solids and annealing-induced density relaxation of \sio2 is incorporated as a history-dependent process. A levelset framework is used to describe the moving Si/\sio2 interface. Sophisticated finite element methods are employed to solve the mathematical equations posed for each phenomenon. These include the incorporation of discontinuity-resolving shape functions to describe jumps in concentration of \o2, methods to prevent oscillations of numerical solutions and techniques that allow highly inhomogeneous deformation of a single element. The use of experimental data to rigorously obtain material properties is emphasized. Mechanical properties of viscoelastic solids are extracted directly from stress-strain data, following which, parameters for the diffusion-reaction problem are obtained. Qualitative and quantitative validation of the models is presented; the latter by comparison with micro-Raman spectroscopy measurements.
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