2-D Simulation of Quantum Effects in Small Semiconductor Devices Using Quantum Hydrodynamic Equations

We discuss the basis of a set of quantum hydrodynamic equations and the use of this set of equations in thetwo-dimensional simulation of quantum effects in deep submicron semiconductor devices. The equations areobtained from the Wigner function equation-of-motion. Explicit quantum correction is built into these equationsby using the quantum mechanical expression of the moments of the Wigner function, and its physical implicationis clearly explained. These equations are then applied to numerical simulation of various small semiconductordevices, which demonstrate expected quantum effects, such as barrier penetration and repulsion. These effectsmodify the electron density distribution and current density distribution, and consequently cause a change of thetotal current flow by 10-15 per cent for the simulated HEMT devices. Our work suggests that the inclusion ofquantum effects into the simulation of deep submicron and ultra-submicron semiconductor devices is necessary