The solution of the nonlinear Schrödinger-Poisson system of equations for one-dimensional states in a quantum structure (e.g. quantum wire) requires an efficient evaluation of the Fermi-Dirac integral ℱ-3/2(x) at each iteration step if a Newton approach is used. A computationally efficient rational Chebyshev approximation is given here for the complete Fermi-Dirac integral of order -3/2, which limits the maximum relative error well below 10-13. Accurate approximations of different order Fermi-Dirac integrals are achievable with the same algorithm.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Electrical and Electronic Engineering
- Materials Chemistry