Extending multiresolution time-domain (MRTD) technique to the simulation of high-frequency active devices

We present a new time-domain simulation approach for large-signal physical modeling of high-frequency semiconductor devices using wavelets. The proposed approach solves the complete hydrodynamic model, which describes the transport physics, on nonuniform self-adaptive grids. The nonuniform grids are obtained by applying wavelet transforms followed by hard thresholding. This allows forming fine and coarse grids in locations where variable solutions change rapidly and slowly, respectively. A general criterion is mathematically defined for grid updating within the simulation. In addition, an efficient thresholding formula is proposed and verified. The developed technique is validated by simulating a submicrometer FET. Different numerical examples are presented along with illustrative comparison graphs, showing over 75% reduction in CPU time, while maintaining the same degree of accuracy achieved using a uniform grid case. Tradeoffs between threshold values, CPU time, and accuracy are discussed. To our knowledge, this is the first time in the literature to implement and report a wavelet-based hydrodynamic model simulator. This study also represents a fundamental step toward applying wavelets to Maxwell's equations in conjunction with the hydrodynamic model for accurate modeling of high-frequency active devices aiming to reduce the simulation time, while maintaining the same degree of accuracy.