SPRINTCAD QUARTERLY SUMMARY

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OBJECTIVE:

APPROACH:

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.

PROGRESS:

The level-set boundary movement method has been calibrated in the etching/deposition simulator SPEEDIE 3.0 for a wide range of processes including Low Pressure Chemical Vapor Deposition (LPCVD), Plasma Enhanced Chemical Vapor Deposition (PECVD), Physical Vapor Deposition (PVD), and Self-Aligned Contacts (SAC) by matching with the 2D cross section of the SEM pictures, and stringer formation by qualitatively comparing the 3D SEM pictures. Elimination of non-physical, rule-base boundary movement has made calibration much easier since numerical errors can be better controlled. Important physical features, such as polymer accumulation in high density plasma oxide etching (HDPOE) and facet formation in the sputtering etchback, are successfully demonstrated within the new SPEEDIE.

The finite element discretization for the diffusion equation may encounter numerical undershoot problems, where concentration becomes negative, if the mass matrix, even though positive-definite, contains negative elements operating on very large concentration gradients. Since negative concentration is not only unphysical, but also may cause numerical problems in reaction and recombination terms. To guarantee that concentration remains positive for all time steps, the discretization has to satisfy the maximum principle. We have analytically derived the criteria for the maximum principle in the diffusion equation in 1D, which can be extended to 2D and 3D. Also, to accelerate convergence rate in the initial phase of nonlinear Newton iterations, damped Newton methods with different line search schemes are implemented to avoid numerical overshoot. For the new physical models defined in ALAMODE, the Jacobian matrix may be very stiff, such as in the case of the five-species model where dopants and dopant-defect pairs have very different scales of transport coefficients, and the damped Newton scheme can help the overall convergence of the numerical system.

The functions to transfer data representations between SUPREM-ALAMODE and CAMINO are implemented. 3D multi-region test structures have been validated with the fermi diffusion model. The Oct-tree based tetrahedral mesh contains anisotropic refinement capabilities and can take general boundary-representation geometry. A hierarchy of error estimators, including implicit/explicit and inter-/intra-element methods, are formulated and partially connected to ALAMODE. Error fields for explicit inter-/intra-element contributions are verified for the diffusion equation. Along with the error estimator implementation, access to strong forms of operators are built, which will later be extended to Galerkin-Least-Square (GLS) implementation.

In collaboration with Dr. B. Froehlich of the Center for Integrated Systems of Stanford University, a prototype of interactive visualization of 3D geometry objects generated by VIP-3D has been implemented on the SGI virtual reality systems. Computer-tracked stereo glasses and gloves can allow users to view objects from different angles and distances, move objects around and investigate flow lines by injecting particles.

RECENT ACCOMPLISHMENTS:

• The 3D geometry/field server based on the minimal SWR specification provides both the Huygens' principle and mass conservation for boundary movement schemes. Parameters and flags for function calls will be passed through attributes in the base class.
• The level set method has been calibrated in the etching/deposition simulator SPEEDIE for a wide range of processes including LPCVD, PECVD, PVD, SAC and stringer formation. The simulation results successfully show important physical features such as sidewall polymer accumulation and facet formation.
• Numerical undershoot at sharp gradients which may cause nonphysical field values such as negative concentration has been identified with the maximum principles in the finite-element method. Damped Newton methods have been added in SUPREM-ALAMODE to accelerate convergence.
• SUPREM-ALAMODE is connected with CAMINO for multi-region 3D simulation. Explicit error estimators with inter- and intra-element contributions are implemented in ALAMODE.
• Interactive visualization of 3D geometry objects generated by VIP-3D has been implemented on the SGI virtual reality systems.

FY-`96 PLANS:

• Test 3D Thermal Module and integration of parallel solver technology.
• Implementation of 3D Oxidation within Thermal Module and transition into unified capabilities (both diffusion and oxidation).
• Implementation of complete server for 3D Deposition/Etching Module, including 3D parallel solver to support flux calculations.
• 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.

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Date prepared: 1/27/96