The Tight-binding Model Of Quantum Charge Transport In Molecular Chain

This thesis develops a simple quantum charge transport theory in molecule chains based on the tight-binding model of electrons and electron-phonon interaction. In some molecular or atomic chains with application potential (such as DNA molecular chain, and atomic chains of carbon and gold, each valence electron (such as the π electrons in DNA) is mainly confined in one unit of the chains (atom or atomic cluster). On the other hand, the electrons can migrate from one unit to another through the molecular chain via electronic coupling between units. When the size of the chains (in the scale of nanometer, for example) is smaller than the electronic coherence length (in the scale of micrometer, for example), the electrons in the molecular or atomic chains are in quantum coherent state. In this case, the electron transport or migration have mainly characteristics of quantum transport and can be well described by tight-binding model. Usually, many vibration modes or phonon modes exist in the molecular or atomic chains due to the coupling between atoms. Experiments have shown that the atomic vibrations can play important role in the electronic quantum transport via the electron-phonon interaction in the molecular chains.Some of the phonon modes extend over several units or throughout the whole chain and the corresponding electron-phonon coupling can be described by Su-Schrieffer-Heeger (SSH) mode.Some phonon modes are confined in one unit and mainly interact with the electrons in that unit. Their effects on the electrons can be described by Holstein model Based on these simple models we derive the expressions for quantum transport properties using the Green’s function theory. We then apply the expressions to some simple systems and compare the influences of the extended phonon modes and confined phonon modes on the electronic quantum transport by numerical calculation.The thesis is organized in the following sequence. At first, the development of the mesoscopic physics and the quantum transport theory is outlined. Then we review some recent advances in molecular electronics, including some interesting topics and possible development directions. Here we can see that quantum transport might be an important working mechanism of future electronic devices [15] including molecular devices. Currently, the Green’s function theory combined with the tight-binding model has been widely used in the study and simulation of quantum transport semiconductor nano-devices and molecular devices.Later on, for the sake of simplicity and generality, we assume a device of one-dimensional molecular chain and introduce the tight-binding model and the Green’s function theory to describe the electronics properties in the device before obtaining the expression for the corresponding electronic quantum charge transport. Furthermore, we study and discuss the possible effect of electron-phonon interaction on quantum transport. Finally, with the help of MATLAB for the numerical calculation, we obtain the current voltage(I-V) curve and its first(dI、dV)-V curve) and second ((dI2/dV2)-V curve) derivatives in systems of assumed parameters.