Full quantum mechanical simulation of ultra-small silicon devices in three-dimensions: physics and issues

The results of a full three-dimensional, ballistic quantum transport model for a quantum wire silicon MOSFET are presented. We use the recursive scattering matrix approach for simulation of the ballistic transport through the device (Gilbert and Ferry). An efficient, three-dimensional, self-consistent quantum simulation technique (Gilbert and Ferry) was utilized with the inclusion of an adaptable non-uniform mesh to optimize the discretization of the solution space. One of the key issues surrounding the use of quantum simulations is the discretization of the solution space, as it is necessary that proper grid selection keep the corresponding energies within the artificially-created bandstructure, even when applying large bias across the device. Should the energies exceed the numerical bandstructure, then errors will result in the output. However, in addition to keeping the solutions physical, the grid must be optimized to reduce the number of grid points in order to hold the computational time, particularly at high bias (/spl sim/ 0.5 V) to acceptable levels. These constraints stipulate the use of a non-uniform mesh with finer grid spacing in the high potential regions. We apply this methodology to the simulation of a quantum wire SOI MOSFET with a narrow channel (8 nm).