COMPARISON BETWEEN A-POSTERIORI ERROR INDICATORS FOR ADAPTIVE MESH GENERATION IN SEMICONDUCTOR-DEVICE SIMULATION

In order to achieve an efficient and reliable prediction of device per formance 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. T his task annoys the user considerably, especially when the device oper ation is not well known, or the required mesh-point density strongly d epends 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 automatica lly optimize the mesh. Adaptive meshing techniques realize automatic o ptimization by refining the mesh according to the discretization error estimated from the solution. The performance of mesh optimization dep ends on a posteriori error indicators adopted to evaluate the discreti zation error. In particular, to obtain a precise terminal-current valu e, a reliable error indicator for the cuffent continuity equation is n ecessary. In this paper, adaptive meshing based on the cuffent continu ity equation is investigated. A heuristic error indicator is proposed, and a methodology to extend a theoretical error indicator proposed fo r the finite element method to the requirements of device simulation i s presented. The theoretical indicator is based on the energy norm of the flux-density error and is applicable to both Poisson and cuffent c ontinuity equations regardless of the mesh-element shape. These error indicators have been incorporated into the adaptive-mesh device-simula tor 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 cuffent values are obtained on the optimized meshes. The theoretical indicator is superior because it pro vides a better optimization performance, and is applicable to general mesh elements.