Gauge-invariant and current-continuous microscopic ac quantum transport theory

Abstract

Advances in the development of semiconductor technology has completely changed our lives, driven by the miniaturization of microelectronics, as well as the progres- sively high operation frequency of the electronic devices and integrated circuits. As the feature sizes of transistors approach physical limits, there is an acute demand for processing electric signals at an ever increasing high operation frequency. It is thus important to understand the dynamic response of emerging electronics devices, and this leads to the growing interests to understand the frequency dependent processes in these devices, and thus an urgent need for accurate quantum mechanical methods to calculate their dynamic admittances. There have been attempts to develop an ac quantum transport theory for meso- scopic electronic devices since the 1990s. Based on an earlier work, in 1999, a phe- nomenological ac quantum transport theory was proposed to mathematically ensure the gauge-invariance and current-conservation. This phenomenological theory had been well received by the community until some recent works that questioned its validity. For instance, our research showed that there is a discrepancy between the i results from this phenomenological theory and those from the time-domain simu- lation of the transient currents, and thus casts some doubts on the theory. The field was all of a sudden thrown into a situation where there is no shared under- standing on what the correct ac quantum transport theory is. It is my objective to redeem this. In this research, I have established a correct ac quantum trans- port theory, and implemented it with time-dependent density-functional theory. As physics dictates, gauge-invariance and current-continuation should be satisfied. To ensure current conservation, the displacement current in Maxwell’s Equations has to be introduced. It is important to properly distribute the displacement current onto each of the electrodes or terminals. To confirm the validity of the new theory, I will compare its results with the results of time-domain simulation of the correspond- ing transient current, as the time-dependent density-functional theory for quantum transport is now well established. To better prove the gauge-invariant and current-continuous ac quantum trans- port theory, I have also studied and simulated the potential distributions for emerg- ing electronics devices of di↵erent scales. As predicted by my theory, as well as the understanding of Maxwell’s Equations, the steady-state potential distributions of relative larger-scale devices tend to be more constant, which in turn directly con- tradict to the previous phenomenological ac quantum transport theory developed in 1999.