Robert W. Dutton, dutton@gloworm.Stanford.EDU, (650) 723-4138

Kincho H. Law, law@cive.Stanford.EDU, (650) 725-3154

Krishna Saraswat, saraswat@ee.Stanford.EDU, (650) 725-3610

Peter Pinsky, pinsky@ce.Stanford.EDU

of special interest are CVD and plasma assisted processes that result in high aspect ratio structures such as trenches and filling/planarization of structures for metal interconnects. Algorithmic work focuses on geometric manipulations and surface evolution.*deposition/etching module---*that can solve nonlinear constitutive models for key process steps involving growth of dielectric layers and impurity redistribution as well as the resulting stress fields. Advanced formulations for finite elements are being developed that support: parallel computation, adaptive gridding and domain decomposition.*thermal/stress analysis module---*

The numerical undershoot near sharp concentration gradients in the transient simulation of diffusion equation may be shunned through time step selection, mass lumping schemes and geometrical element constraints, all of which need to satisfy the maximum principle in the finite element analyses with the solutions in all time steps bounded by the initial solution. The maximum principle may put lower bounds for the magnitude of time steps, but this approach is usually unacceptable since time steps need to be controlled by accuracy and stability. In 1-D, mass lumping is most effective with arbitrary spatial discretization. However, in 2D and 3D, mass lumping is not very useful without constraints on geometrical elements. For various element types including triangles, quads, bricks, prisms and tetrahedra, a formal analysis is performed to give geometrical constraints for satisfying the maximum principle. Influence from the reactive term is still under study.

Time domain error estimation for general trapezoidal schemes including local and global discretization errors has been formulated. The local truncation error is based on the divided difference approximation and the global error is calculated using the mass and Jacobian matrices in the nonlinear iteration. The formulation is tested against the standard van der Pol equation for nonlinear systems. The conventional constant-step backward Euler method, although stable and convergent, is not only less efficient owing to unnecessary fine steps in slow transient regions, but also heavily polluted by global errors and hence very inaccurate after a fast transient region. Adaptation criteria in consideration with the spatial error estimation and acceleration methods are still under investigation.

Lack of universally appropriate gridding schemes in 3D in view of boundary conformability and movement, a hybrid set of gridding tools has been collected under the SprintCAD project. For supporting a wide range of 3D TCAD tools, gridders based on unstructured tetrahedra (EUCLID), ct-tree (CAMINO) and the nonconformal Eulerian scheme (level-set) have their respective advantages in different applications and are included in the specification of the minimalistic geometry/field service interface. The geometry is maintained consistent in all spatial discretization, which has greatly simplified the interface design and communication between gridders.

- Physical modeling of conformal and flow-like behaviors in APCVD processes are derived from surface reaction kinetics. A widely applicable parameter set, which accounts for the 0th (planar), 1st (shape) and 2nd (curvature) geometrical effects, is obtained from the surface-site theory and the level-set method.
- Geometrical and mass lumping criteria for satisfying maximum principles in the 1-2-3D diffusive systems are derived for various element types including triangles, quads, bricks, prisms and tetrahedra.
- Time domain error estimation including local and global discretization errors has been formulated and tested against the standard van der Pol equation for nonlinear systems.
- Geometry/Field services combining CAMINO, EUCLID and the level-set method have been provided through a unified geometry class and a minimalistic procedural interface.

- Parallelization of ALAMODE and the geometry/field server functions through the static domain decomposition techniques.
- 3D conformal gridding tools to provide 3D elements that satisfy the maximum principle in various mass lumping schemes for the diffusive-reactive systems.
- Validation of the 1-2-3D geometry/field server using fully adaptive schemes for semi-discrete finite-element based TCAD tools.
- Benchmark the overall SPRINT-CAD modules in terms of a deep submicron MOS technology. The thermal module will demonstrate 3D analysis of locally oxidized isolation and shallow junction diffusion steps. The deposition/etching module will demonstrate first-time functionality of a 3D server-based architecture and implementation.

Edwin C. Kan

kan@gloworm.stanford.edu

CIS-X 334, Stanford University, Stanford, CA 94305

Office: (415)723-9796

Fax: (415)725-7731

Date prepared: 7/31/96