| The finite difference method (FDM) and spectral element method (SEM) are implemented for simulation of high electron mobility transistors (HEMT) through self-consistent solution of the Schrodinger-Poisson equations. The two simulation methods are described and discussed in detail. Two iteration techniques are evaluated as part of the solution procedure: the fixed-convergence-factor method and the Newton-Raphson method, applied to both FEM and SEM simulations. The electron conduction band profile and electron density distribution are calculated and plotted, and a comparison of the FDM- and SEM-based results is presented, along with a comparison against results from the literature. Relative L2 errors are calculated and analyzed for the developed simulation algorithms. It is shown that the spectral element method is superior to the finite difference method in accuracy and computing efficiency, when applied to the simulation of HEMT devices.;The Schrodinger-Poisson HEMT solver is further extended to the solution of more advanced problems. The DC current-voltage characteristics of a HEMT device are computed, based on the calculated electron density distribution predicted using the simulation tools, using the assumption of a quasi-2D current model for the HEMT structure. It is shown that the simulated results conform very well to experimental results from the literature, illustrating the validity of the HEMT solver and current model under certain operating conditions. Finally, a surface plasmonic sensor designed with a similar heterostructure as that of a HEMT device is proposed, modeled, and simulated using the simulation tools developed for HEMT analysis. Such a structure has potential application for chemical and biological sensing. |
