Theory of charge transport in a quantum dot tunnel junction with multiple energy levels

Transport properties of nanoscale quantum dots embedded in a matrix connected with metallic electrodes are investigated theoretically. The Green's function method is used to calculate the tunneling current of an Anderson model with multiple energy levels, which is employed to model the nanoscale tunnel junction of concern. A closed form spectral function of a quantum dot or coupled dots (with arbitrary number of energy levels) embedded in a tunnel junction is derived and rigorously proved via the principle of induction. Such an expression can give an efficient and reliable way for analyzing the complicated current spectra of a quantum dot tunnel junction. Besides, it can also be applied to the coupled dots case, where the negative differential conductance due to the proximity effect is found. Finally, we investigate the case of bipolar tunneling, in which both electrons and holes are allowed to tunnel into the quantum dot, while optical emission occurs. We find dramatic changes in the emission spectra as the applied bias is varied.