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Comparison between a posteriori Error Indicators for Adaptive Mesh Generation in Semiconductor Device Simulation
Katsuhiko TANAKA Paolo CIAMPOLINI Anna PIERANTONI Giorgio BACCARANI
IEICE TRANSACTIONS on Electronics
Publication Date: 1994/02/25
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on 1993 VLSI Process and Device Modeling Workshop (VPAD 93))
device simulation, mesh generation, error indicators,
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In order to achieve an efficient and reliable prediction of device performance by numerical device simulation, a discretization mesh must be generated with an adequate, but not redundant, density of mesh points. However, manual mesh optimization requires user's trial and error. This task annoys the user considerably, especially when the device operation is not well known, or the required mesh-point density strongly depends on the bias condition, or else the manipulation of the mesh is difficult as is expected in 3D. Since these situations often happen in designing advanced VLSI devices, it is highly desirable to automatically optimize the mesh. Adaptive meshing techniques realize automatic optimization by refining the mesh according to the discretization error estimated from the solution. The performance of mesh optimization depends on a posteriori error indicators adopted to evaluate the discretization error. In particular, to obtain a precise terminal-current value, a reliable error indicator for the current continuity equation is necessary. In this paper, adaptive meshing based on the current continuity equation is investigated. A heuristic error indicator is proposed, and a methodology to extend a theoretical error indicator proposed for the finite element method to the requirements of device simulation is presented. The theoretical indicator is based on the energy norm of the flux-density error and is applicable to both Poisson and current continuity equations regardless of the mesh-element shape. These error indicators have been incorporated into the adaptive-mesh device-simulator HFIELDS, and their practicality is examined by MOSFET simulation. Both indicators can produce a mesh with sufficient node density in the channel region, and precise drain current values are obtained on the optimized meshes. The theoretical indicator is superior because it provides a better optimization performance, and is applicable to general mesh elements.