Improvement of accuracy in the wave-function-matching method for transport calculations

Abstract

The wave-function-matching (WFM) technique for first-principles transport-property calculations was modified by Sørensen et al. so as to exclude rapidly decreasing evanescent waves [Sørensen et al., Phys. Rev. B 77, 155301 (2008)]. However, this method lacks translational invariance of the transmission probability with respect to insertion of matching planes and consistency between the sum of the transmission and reflection probabilities and the number of channels in the transition region. We reformulate the WFM

Electrical Matching at Metal/Molecule Contacts for Efficient Heterogeneous Charge Transfer

“…We suspended the PDI between two facing Au electrodes by attaching the opposite electrode to the PDI on the Au surface used to compute the LDOS so that the system was symmetric along the z -direction. The semi-infinite Au electrode was treated by the fully energy dependent self-energy, which enables us to minimize the number of the extra buffer layers in the scattering region . The scattering wave functions continuing from one electrode to the other were computed by the overbridging boundary-matching method .…”

RSDFT-NEGF transport simulations in realistic nanoscale transistors

“…Even in the simplest cases, such as the one in Fig. 1, solving this problem in the original real-space grid representation is extremely difficult due to the large size of the supercell [55]. On the contrary, there is no difficulty in computing the 2N b possible scattering states in the EM representation.…”

Complex band structure calculations based on the overbridging boundary matching method without using Green's functions

“…As mentioned in Introduction, we generally do not need all the eigenpair of the generalized eigenvalue problem (8) but only some of the eigenpairs, whose eigenvalues lie in a specific domain of the complex λ plane. For instance, in electron transport calculations, in addition to propagating Bloch waves, one needs evanescent Bloch waves decaying slowly depth-wise in the semi-infinite electrodes, because it is proved that the self-energy matrices of semi-infinite electrodes are correctly calculated only from the propagating waves and slowly decaying evanescent waves [19]. In other words, we need only the eigenvalues just around the unit circle on the complex λ plane, i.e., |λ| ∼ 1, and the eigenvectors belonging to the eigenvalues.…”

“…On the other hand, the generalized eigenvalue problems to be solved with the previously proposed methods, i.e., Eq. (19) in Ref. [12] and Eq.…”

“…1, is transformed into a smaller quadratic eigenvalue problem with the dimension equal to the number of necessary generalized Bloch wave functions. Recently, we proved that only from propagating waves and slowly decaying/growing evanescent waves one can obtain the correct self-energy matrices of semi-infinite systems [19].…”