Macroscopic Quantum Carrier Transport Modeling

It has been established [1]-[4] that the density gradient (DG) model is the lowest order, in terms of ħ, approximation of the Wigner function approach to including quantum mechanical (QM) effects in carrier transport. In this paper, we report a five-equation PDE system (reduced to three-equation at thermal equilibrium) which preserves the numerical stability of classical drift-diffusion (DD) model, yet faithfully manifests QM corrections. Tunneling through the gate oxide (or barrier region) is modeled by ballistic transport with each type of carrier (electrons or holes) further split into forward and backward moving species and solved for separately. The entire device, including semiconductor and barrier regions, is solved self-consistently. Terminal characteristics, either dc or small signal ac for realistic, multi-dimensional device structures can be simulated using this model. An SOI device example is simulated and the comparison with microscopic (Schrödinger/Poisson) results is excellent. A DG prediction of a dipole in the poly gate near the poly/gate-oxide interface is also confirmed by microscopic simulation. Both I-V and C-V for MOS devices including SOI are shown.