Phonon effect in quantum electronic transport

Abstract

The non-equilibrium Green’s function (NEGF) method has been combined with the density functional tight-binding method (DFTB) to study the effect of phonons in quantum electronic transport in various cases. The normal modes of the movable atoms in the device regions and the electron–phonon coupling matrices for them are calculated. After that, the contribution from different modes are summed up in the expression of electron–phonon interaction self-energy. The study is done both in real time and for steady state. In the steady state study, the self-consistent Born approximation (SCBA) is implemented with different approximations on the Green’s function in the expression of electron–phonon self-energy. The influence of different approximations are examined and the results are compared. In these implementations the EPI self-energy is not assumed to be local within atoms. The different SCBA implementations have been applied to atom chains that are metallic in terms of conductance to examine the transition from the quantum description of resistance to the classical description. In the real-time study, the method extends the current time-dependent density functional tight-binding theory for open system (TDDFTB–OS) method by including the scattering self-energy and extends the previous work of Yu Zhang by using DFTB for the Hamiltonian. The non-orthogonality of the atomic basis is taken into consideration when deriving the Liouville–von Neumann equation. The method is applied to a typical structure of quantum interference effect transistor (QuIET) containing a meta-linkage benzene ring to study the effectiveness of such device under nuclear vibrations. Together with the statistical result from Ehrenfest dynamics, it has been shown that the QuIET under study remains a valid transistor after nuclear vibration is considered. Finally, as a demonstration of the method applied to medium-sized systems, the steady state property of a carbon nanotube transistor with all-around gates is studied. The SCBA implementation is parallelized to accelerate the computation. It is shown that under the elastic approximation, inclusion of phonons increases the off-state current and decreases the on-state current. There is no clear evidence that the saturation voltage is changed by inclusion of phonons. The validity of usage of tri-block diagonal data structure is also examined in full SCBA calculations with selected modes.