Electronic Transport In Graphene-based Nano-device

As the development of modern microelectronic techniques and fabrication process, the feature size of electronic device is minimizing year by year and working at nanoscale nowadays. At this scale range, the classical circuit theory is no longer applicable due to the quantum effects. A series of experiments in recent decades have discovered various novel quantum phenomena with different materials and systems. Among these experiments, graphene, discovered at 2004, has attracted a lot of attention in theoretical and experimental studies due to its outstanding electronic properties and excellent stability, which shows a broad application prospect.This work mainly studies the electron transport properties in graphene nano-devices with scattering matrix theory and Green’s function method to provide some theoretical support and ref-erence for the manufacture of nano-device and nanoscale integrated circuits. In this work, we focus on the dynamical current-voltage response of multi-terminal graphene nano-device and dis-cuss the four-terminal, measurement, current rectification, and dissipation. The main contents are as follows:We firstly introduce the electronic properties of graphene. Within the nearest tight-binding approximation, our calculation shows that graphene nanoribbons have different dispersion rela-tion, propagating modes and electrical conductivity due to different widths and edge types. We also present the ac transport theory and Green’s function method for studying the dynamical con-ductance of graphene nano-devices and discuss their relations and advantages.Based on the fundamental properties of graphene nanoribbons and electron transport theories, we study the four-terminal impedance of a graphene nanoribbon based structure. Compared with the conventional two-terminal measurement, four-terminal measurement eliminates the effect of contact resistance between the lead region and the conductor region to provide a more accurate result. According to the ac transport properties of a four-terminal measurement system, we obtain the impedance matrix of the system, which leads to a four-terminal impedance expression related to the dynamic conductance between every two terminals. The results show that at the Dirac point, both the real and imaginary parts of the impedance are negative. As the Fermi energy deviates from the Dirac point, the real part of impedance oscillates with its sign changing frequently, while the imaginary part becomes vanishingly small. It is because that the voltage probes introduce inelastic scattering and change the charge distribution in the graphene conductor region, which reveals the oscillating nature of electrons in the four-terminal measurement result.We also discuss the charge relaxation resistances in graphene nanoribbon field effect transis-tors. Distinguished from the dc Landauer resistance, the charge relaxation resistances accompany with the capacitor in ac circuits and determine the RC time in the circuits. The results demonstrate that the charge relaxation resistances in the gate terminal of graphene nanoribbon field effect tran-sistors have quantized values which vary with the structural details of graphene nanoribbon and gate voltage. When the channel number in the graphene nanoribbon is 0,1, N respectively, the corresponding non-equilibrium charge relaxation resistance at the gate is roughly 1/2,1/4,1/2N resistance quantum(h/e2), whereas the non-equilibrium charge relaxtion resistance is much small-er. Through the analysis the conductance and density of states in the graphene nanoribbon, we find that the charge relaxation resistance is more related to the reservoirs and leads. We can change its values by tuning the gate voltage to control the dissipation and noise at the gate terminal of graphene nanoribbon field effect transistors.