Nonlinear dynamics of transport in mesoscopic systems

Abstract

This thesis adopted two different theoretical frameworks to investigate nonlinear transport phenomenon in mesoscopic systems from first principles. By combining the non-equilibrium Green’s function (NEGF) formulism and the density functional theory (DFT), a quantum transport theory of dc shot noise in the negative differential resistance (NDR) region was proposed and studied. Numerically, the model was tested on a carbon wire made of four atoms connecting with two semi-infinite Al leads. Due to the effective band bottom of leads, our calculation showed a clear NDR region at a relatively high bias. More importantly, a large Fano factor which was around 3 was also discovered in this region, consistent with the super-Poissonion phenomenon in experiments. Furthermore, first principles calculation within NEGF-DFT formalism was also carried out to study the response of electric pulse in molecular devices. A current model induced by rectangular pulse was developed. Furthermore, the time-averaged currents of two popular devices, namely Al-C60-Al and Al-Benzene-Al, were investigated from first principles as well. The result indicated that owing to the existence of sharp resonant levels, the current of Al-C60-Al structure oscillated with the magnitude of pulse. However, the continuous energy levels in Al-Benzene-Al system gave out a nonlinear incremental current with increasing pulse.

For the second framework, kinetic Monte Carlo (kMC) method coupled with DFT was adopted to study the evolutionary configurations of TiO2 in 3-dimension by taking the interactions between vacancies and the non-uniform electric field into account. The simulation confirmed that the localized electric field induced by vacancy hopping was the main driver of the filament formation at the electroforming stage. In addition, density of states calculation was implemented according to the configurations extracted from the kMC’s output. It showed that a transition from an insulator to a conductor was resulted from the vacancy-induced gap states.