A non-linear variational principle for the self-consistent solution of Poisson´s equation and a transport equation in the local density approximation

In order to simplify the numerical investigation of carrier transport in nanodevices without jeopardizing the rigor of a full quantum mechanical treatment, we have exploited an existing variational principle to solve self-consistently Poisson´s equation and Schrödinger´s equation as well as an appropriate transport equation within the scope of the generalized local density approximation (GLDA). In this work, as a benchmark, we have applied our approach to compute the ballistic current density and electron concentration in a Si nanowire.