Apr. 1 - June 30, 1996


Stanford University




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


Edwin C. Kan, kan@gloworm.Stanford.EDU, (415) 723-9796


"SPRINT-CAD"---Industry -Networked TCAD using Shared Parallel Computers


The URL for Stanford TCAD projects is: http://www-tcad.stanford.edu


First-time capabilities to bridge solid modeling, FEM-based parallel computation of fabrication processes and electrical analysis of the resulting IC structures will be developed. Models needed to represent diffusion, etching, deposition, oxidation and stress analysis resulting from a sequence of process steps necessary in the creation of electrical devices will be developed. This effort will provide a radically new HPC framework for technology-based 3D process/device modeling as well as realistic benchmarks to test HPC architectures and software.


We will build, integrate and test TCAD modules based on an object-oriented approach that both develops and uses information models in support of CFI-based standards. The modules and software engineering methodology will be designed specifically to exploit parallel computers and library components. The 3D process simulation modules will utilize HPC platforms and provide new functional capabilities for "computational prototyping" of the following key technology fabrication steps:
  1. deposition/etching module---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.
  2. thermal/stress analysis 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.


APCVD has become very important for intermetal dielectric deposition processes in the deep submicron technology owing to its excellent capabilities in void-free filling of narrow and deep trenches. Physical modeling of conformal and flow-like behaviors in APCVD processes are rigorously derived from a generic surface reaction kinetics. Surface reaction follows adsorption of gas-phase precursors on surface sites. When the surface sites are saturated, the deposition rate approaches zero-order reaction and the nonuniform surface site density effects become more apparent. A widely applicable parameter set, which accounts for the 0th (planar), 1st (shape) and 2nd (curvature) geometrical effects, can be extracted from the experimental deposition rates and detailed boundary profiles on test structures. The level-set method is especially appropriate for this formalism owing to its accurate curvature estimation and boundary movement according to the entropy condition. Very good agreement with experimental measurements are obtained for various grove sizes and elbow-shaped 3D structures with the same parameter set.

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.




ALAMODE has been selected as the benchmark platform for the bulk diffusion models developed under the SRC/National Labs CRADA projects. A common 1D field interface is defined by Dr. Martin Giles of Intel to facilitate easy calibration process. Extension to 2D and 3D with various element technology is readily available in ALAMODE. Due to the dial-an-operator design and many finite-element numerical control in ALAMODE, new models and their numerical algorithms will be entirely encapsulated in the extension language level without touching the source code, and hence eliminate problematic comparisons of physical models implemented on different platforms. The binary code is scheduled for release in early August of 1996.

Edwin C. Kan
CIS-X 334, Stanford University, Stanford, CA 94305
Office: (415)723-9796
Fax: (415)725-7731

Date prepared: 7/31/96