Fig.1: Illustration of the current degradation in double-gate MOSFETs resulting from electron-phonon interactions. In this case the one-shot LOA+AC method perfectly reproduces the SCBA results .
We describe a lowest-order approximation (LOA) to the nonequilibrium Green’s function in the presence of interactions, and generally address how one can build Phi-derivable one-shot approximations that satisfy the continuity equation. These approximations produce conserved electronic currents in one shot, requiring only one self-energy evaluation and, when applicable, they are as accurate as but much faster than the corresponding self-consistent approximation. This challenges the currently adopted view that heavy self-consistent calculations are necessary to get a satisfactory prediction of transport in nanoscale structures. We illustrate this with the case of electron-phonon scattering expressed within the self-consistent Born approximation (SCBA). In the LOA, the SCBA is further approximated by accounting only for one-phonon processes. LOA and SCBA are compared in one-dimensional wire where electrons interact with one optical phonon mode at room temperature. The LOA is found to provide a considerable reduction in computational time. Its limitations and extensions to include two-phonon processes are discussed . When LOA fails it is possible to perform its simplest analytic continuation (LOA+AC). By means of scaling argument we show how both LOA and LOA+AC can be easily obtained from the first iteration of the usual self-consistent Born approximation (SCBA) algorithm. LOA and LOA+AC have been then applied to the modeling of n-type silicon i) double-gate  and ii) nanowire  field effect-transistors and have been compared to SCBA current characteristics. In particular we found that LOA fails to describe electron-phonon scattering in nanowires, mainly because of the interactions with acoustic phonons at the band edges. In contrast the LOA+AC still well approximates the SCBA current characteristics, thus demonstrating the power of analytic continuation techniques. The limits of validity of LOA+AC are also discussed, and more sophisticated and general analytic continuation techniques are put forward for more demanding cases .
1) H. Mera, M. Lannoo, C. Li, N. Cavassilas, M. Bescond,
“Inelastic scattering in nanoscale devices one-shot current-conserving lowest order approximation,”
Phys. Rev. B (rapid communications) 86, 161404 (2012).
2) N. Cavassilas, M. Bescond, H. Mera, and M. Lannoo,
“One-shot current conserving quantum transport modeling of phonon scattering in n-type double-gate field-effect-transistors,”
Appl. Phys. Lett. 102, 013508 (2013).
3) M. Bescond, C. Li, H. Mera, C. Cavassilas and M. Lannoo
“Inelastic scattering in n-type nanowire field-effect-transistors: One-shot current conserving approach”, to be submitted (2013).
4) H. Mera, M. Lannoo, N. Cavassilas and M. Bescond.
“Nanoscale device modelling using a conserving analytic continuation technique”, submitted (2013).