  In order to quickly study quantum devices in transient problems, this work
demonstrates an analytical algorithm to solve the Hartree potential associated
with charge fluctuations in the time-dependent non-equilibrium green function
(TDNEGF) method. We implement the calculations in the heterojunction system of
gold metals and silicon quantum dots for applications of photoelectric
semiconductors in the future. Numerical results for the transient solutions are
shown to be valid by comparing with the steady solutions calculated by the
standard time-independent density functional method.
