The objective of this work is to shed light on electron transport through sub-micron semi-conductor structures, where electronic state quantization, electron-electron interactions and electron-phonon interactions are important. We concentrate here on the most developed vertical quantum device, the double barrier resonant tunneling diode. In this work we analyze particle interactions in two structural limits: 1) large, and 2) small cross-sections, in which the treatments are fundamentally different. Large cross-section structures involve particle-interactions with many electrons and these effects can be described in the Keldysh formalism in a single-particle picture by effective potentials. We present model calculations treating the phonon-peak and electrical bistability in this limit. Small cross-section structures involve only a few particles, whose interactions cannot be described by effective potentials, due to strong particle correlations. The single-particle picture breaks down and a full many-body description has to be used. We present high bias calculations for electron transport through single quantum dots (artificial atoms) and an analysis of the linear response conductance spectrum of two coupled quantum dots (artificial molecules).
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