Numerical method for the calculation of self-consistent charge densities of reservoir-coupled quantum dots

The calculation of self-consistent charge densities is not a straightforward task in structures with zero-dimensional confinement. In contrast to the semi-classical case the density of states in a quantum dot depends on the potential. However, this dependence is not explicitly given and Newton-Raphson methods are therefore difficult to employ. In this paper we present a numerical method for the calculation of self-consistent electron densities in a quantum dot weakly coupled to a macroscopic reservoir using a multidimensional secant approach that partially overcomes the numerical limitations intrinsic to single-electron transistor device simulations.