Inclusion of the Pauli principle in a deterministic Boltzmann equation solver based on a spherical harmonics expansion

Abstract

The Pauli principle is included in a deterministic Boltzmann solver based on a spherical harmonics expansion of the distribution function. The Newton-Raphson scheme is applied to solve the nonlinear Boltzmann equation, and it is found that the inclusion of the Pauli principle introduces no numerical problems, even for multi-dimensional semiconductor devices. As a numerical example, the impact of the Pauli principle is numerically investigated for a double-gate MOSFET.

A deterministic method study of the impact of the Pauli principle in double-gate MOSFETs

“…[6] The deterministic Boltzmann solver provides such a complete distribution function that it does not inherently suffer from that difficulty. [7] Simulations including the Pauli principle based on a spherical harmonics expansion (SHE) method [8] for both bulk systems [6] and two-dimensional (2D) devices [9] have been reported. However, the impact of the Pauli principle was not obvious in those cases, since the quantum confinement effect was not considered, and a much larger three-dimensional DOS was employed.…”