Stable L\'{e}vy diffusion and related model fitting

A fractional advection-dispersion equation (fADE) has been advocated for heavy-tailed flows where the usual Brownian diffusion models fail. A stochastic differential equation (SDE) driven by a stable L\'{e}vy process gives a forward equation that matches the space-fractional advection-dispersion equation and thus gives the stochastic framework of particle tracking for heavy-tailed flows. For constant advection and dispersion coefficient functions, the solution to such SDE itself is a stable process and can be derived easily by least square parameter fitting from the observed flow concentration data. However, in a more generalized scenario, a closed form for the solution to a stable SDE may not exist. We propose a numerical method for solving/generating a stable SDE in a general set-up. The method incorporates a discretized finite volume scheme with the characteristic line to solve the fADE or the forward equation for the Markov process that solves the stable SDE. Then we use a numerical scheme to generate the solution to the governing SDE using the fADE solution. Also, often the functional form of the advection or dispersion coefficients are not known for a given plume concentration data to start with. We use a Levenberg--Marquardt (L-M) regularization method to estimate advection and dispersion coefficient function from the observed data (we present the case for a linear advection) and proceed with the SDE solution construction described above.Comment: Published at https://doi.org/10.15559/18-VMSTA106 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/

Nonequilibrium current driven by a step voltage pulse: an exact solution

One of the most important problems in nanoelectronic device theory is to estimate how fast or how slow a quantum device can turn on/off a current. For an arbitrary noninteracting phase-coherent device scattering region connected to the outside world by leads, we have derived an exact solution for the nonequilibrium, nonlinear, and time-dependent current driven by both up- and down-step pulsed voltages. Our analysis is based on the Keldysh nonequilibrium Green's functions formalism where the electronic structure of the leads as well as the scattering region are treated on an equal footing. A model calculation for a quantum dot with a Lorentzian linewidth function shows that the time-dependent current dynamics display interesting finite-bandwidth effects not captured by the commonly used wideband approximation

Enhancement of parametric pumping due to Andreev reflection

We report properties of parametric electron pumping in the presence of a superconducting lead. Due to a constructive interference between the direct reflection and the multiple Andreev reflection, the pumped current is greatly enhanced. For both quantum point contacts and double barrier structures at resonance, we obtain exact solutions in the weak pumping regime showing that $I_p^{NS} = 4 I_p^N$, which should be compared with the result of conductance $G_{NS} = 2G_N$. Numerical results are also provided for the strong pumping regime showing interesting Andreev assisted pumping behaviour

Structure and Dielectric Properties of Amorphous High-kappa Oxides: HfO2, ZrO2 and their alloys

High-$\kappa$ metal oxides are a class of materials playing an increasingly important role in modern device physics and technology. Here we report theoretical investigations of the properties of structural and lattice dielectric constants of bulk amorphous metal oxides by a combined approach of classical molecular dynamics (MD) - for structure evolution, and quantum mechanical first principles density function theory (DFT) - for electronic structure analysis. Using classical MD based on the Born-Mayer-Buckingham potential function within a melt and quench scheme, amorphous structures of high-$\kappa$ metal oxides Hf$_{1-x}$Zr$_x$O$_2$ with different values of the concentration $x$, are generated. The coordination numbers and the radial distribution functions of the structures are in good agreement with the corresponding experimental data. We then calculate the lattice dielectric constants of the materials from quantum mechanical first principles, and the values averaged over an ensemble of samples agree well with the available experimental data, and are very close to the dielectric constants of their cubic form.Comment: 5 pages, 4 figure

Impact of Edge States on Device Performance of Phosphorene Heterojunction Tunneling Field Effect Transistors

Black phosphorus (BP) tunneling transistors (TFETs) using heterojunction (He) are investigated by atomistic quantum transport simulations. It is observed that edge states have a great impact on transport characteristics of BP He-TFETs, which result in the potential pinning effect and deteriorate the gate control. While, on-state current can be effectively enhanced by using hydrogen to saturate the edge dangling bonds in BP He-TFETs, in which edge states are quenched. By extending layered BP with a smaller band gap to the channel region and modulating the BP thickness, device performance of BP He-TFETs can be further optimized and fulfill the requirements of the international technology road-map for semiconductors (ITRS) 2013 for low power applications. In 15 nm 3L-1L and 4L-1L BP He-TFETs along armchair direction on-state current can reach above 10$^3$ $\mu$A/$\mu$m with the fixed off-state current of 10 $pA/\mu$m. It is also found that ambipolar effect can be effectively suppressed in BP He-TFETs.Comment: 12 pages, 5 figure

The second order nonlinear conductance of a two-dimensional mesoscopic conductor

We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly evaluating the various partial density of states, the sensitivity and the characteristic potential. Interesting spatial structure of these quantities are revealed. We present detailed results concerning the crossover behavior of the second order nonlinear conductance when the conductor changes from geometrically symmetrical to asymmetrical. Other issues of interests such as the gauge invariance are also discussed.Comment: LaTe

Nonlinear I-V Characteristics of a Mesoscopic Conductor

We present a general theoretical formulation, based on nonequilibrium Green's functions, for nonlinear DC transport in multi-probe mesoscopic conductors. The theory is gauge invariant and is useful for the predictions of current-voltage characteristics and the nonequilibrium charge pile-ups inside the conductor. We have provided a detailed comparison between the gauge invariant scattering matrix theory and our theory. We have also given several examples where the I-V curve can be obtained analytically. The effects of exchange and correlation have been considered explicitly