A Model for Steady-state, Ballistic Charge Transport through Quantum Dot Layer Superlattices

We derive a model for one-dimensional charge-transport through two-terminal semiconducture heterostructure nano-devices comprising stacked layers of quantum dots with transverse Bravais lattice layout. All dots in a layer are assumed to be identical. The stacked layers are assumed to be perfectly vertically-aligned so that the entire device has a well-defined transverse unit-cell. We allow for an arbitrary sequence of quantum dot layers and intervening spacer and wetting layers between two heavily-doped, ohmic contacts. The model naturally accounts for longrange, inter-dot correlations. We rigorously prove that the device behaves as a diffraction grating which distributes incident wavefunction-phases into specific patterns of transmitted phases. This establishes several mathematical properties that allow efficient decomposition of the problem and permit feasible strategies for computational implementation. We motivate the study of this family of devices citing experimental developments.