The future research on simulations using the Wigner formalism can be pursued along three avenues, which all go hand in hand: Theoretical aspects of the Wigner formalism and their implementation with the signed-particle method, algorithmic and computational issues, and the application of the simulator to investigate quantum processes in nanostructures.
The extension of the Wigner Monte Carlo simulator to three spatial dimensions and the capability to calculate a self-consistent solution with the Poisson equation presents the most straight-forward continuation the work presented in this thesis. The challenge is of a computational nature since the existing algorithms must be extended for this purpose.
To garner a wider interest in Wigner Monte Carlo simulation within the semiconductor device research community, the development of features which would enable real device geometries to be simulated with common current-voltage curves as an output would be very beneficial. For this the treatment of boundaries and especially contacts should be further investigated; the consideration of non-uniform meshes will become a necessity to treat complex geometries.
The transient behaviour of quantum point contacts, which essentially form a nanocircuit with quantum resistance and capacitance, is not correctly explained by existing circuit theory. This is a problem which could be investigated with two-dimensional Wigner Monte Carlo simulations, using time-dependent boundary conditions. Moreover, the typical size of these structures could make phonon scattering important.
The inclusion of the vector potential (magnetic field) in the Wigner formalism, and specifically the signed-particle method, is very desirable, since an increasing number of devices is utilizing magnetic fields to operate, e.g. magnetic tunnel junctions. Furthermore, the consideration of magnetic fields will give the capability to investigate the quantum mechanical behaviour demonstrated in many experiments, e.g. Aharanov-Bohm rings, to improve our understanding and interpretation.
The capability to simulate time-resolved quantum transport with phonon scattering, magnetic fields and electrostatics taken into account, will provide the possibility to research a wide range of problems in nanoelectronics. Topics of immediate interest are an investigation of structures like nanowires and how discrete dopants and scattering affect the dynamics of single electrons. More novel concepts, like qubits, where entanglement and decoherence are of primary interest, can also be readily investigated, since phonon scattering can be accounted for.
It is an exciting time to be involved in research of nanoelectronics and in light of the above, simulations based in the Wigner formalism can make a valuable contribution to this undertaking.