Incorporation of quantum corrections to semiclassical two-dimensional device modeling with the Wigner-Boltzmann equation

A new method for accounting for quantum effects in semiclassical device simulation is presented. The approach is based on the solution to the Wigner-Boltzmann equation, which is derived from the Schrodinger equation. The Wigner-Boltzmann equation is truncated to order ℏ2, and then formulated using spherical harmonics. This facilitates analytical evaluation of the collision integral, and allows for reduction of dimensionality. The Wigner-Boltzmann equation is solved self-consistently with the Poisson and hole-current continuity equations for a BJT and a MOSFET. The results show that the carrier concentrations predicted by the Wigner-Boltzmann equation near the base-emitter junction and the MOSFET channel are less than that predicted by the semiclassical Boltzmann model. Calculations show terminal currents to be 2% and 7% lower for the quantum simulations than the semiclassical results for the BJT and MOSFET, respectively.