Tiao Lu

Discontinuous galerkin time-domain method for GPR simulation in dispersive media

This paper presents a newly developed high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwells equations in linear dispersive media with UPML boundary treatment. A unified formulation is derived for linear dispersive media of Debye type and the artificial material in the UPML regions with the help of auxiliary differential equations. The DGTD employs finite-element-type meshes, and uses piecewise high-order polynomials for spatial discretization and Runge-Kutta method for time integrations. Arbitrary high-order accuracy can be obtained for scattering of various objects in dispersive media. After validating the numerical convergence of the DGTD method together with the second-order Yees scheme, we apply this new method to the ground-penetrating radar for the detection of buried objects in a lossy half space.

Discontinuous galerkin time domain (DGTD) methods for the study of 2-D waveguide-coupled microring resonators

This paper presents the study of coupling efficiencies between two-dimensional (2-D) waveguides and microring resonators with a newly developed high-order discontinuous Galerkin time domain (DGTD) method for Maxwells equations. The DGTD method is based on a unified formulation for the physical media and the artificial media in the uniaxial perfectly matched layer (UPML) regions used to truncate the computational domain. The DGTD method employs finite element type meshes and uses piecewise high-order polynomials for spatial discretization of the Maxwells equations and Runge-Kutta methods for time integration. After demonstrating the high-order convergence of the DGTD method, the effect of separation gap between the waveguides and one and two microrings on the coupling efficiency and transmittance for pulse propagations is studied.

Quantum hydrodynamic model by moment closure of Wigner equation

In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type first proposed by Grad [“On the kinetic theory of rarefied gases,” Commun. Pure Appl. Math. 2(4), 331–407 (1949)10.1002/cpa.3160020403]. The Grads moment method was originally developed for the Boltzmann equation. Recently, a regularization method for the Grads moment system of the Boltzmann equation was proposed by Cai et al. [Commun. Pure Appl. Math. “Globally hyperbolic regularization of Grads moment system” (in press)] to achieve the global hyperbolicity so that the local well-posedness of the moment system is attained. With the moment expansion of the Wigner function, the drift term in the Wigner equation has exactly the same moment representation as in the Boltzmann equation, thus the regularization applies. The moment expansion of the nonlocal Wigner potential term in the Wigner equation turns out to be a linear source term, which can only...

A device adaptive inflow boundary condition for Wigner equations of quantum transport

In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi-Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.

Stationary Wigner Equation with Inflow Boundary Conditions: Will a Symmetric Potential Yield a Symmetric Solution?

Based on the well-posedness of the stationary Wigner equation with inflow boundary conditions given in [A. Arnold, H. Lange, and P.F. Zweifel, J. Math. Phys., 41 (2000), pp. 7167--7180] we prove without any additional prerequisite conditions that the solution of the Wigner equation with inflow boundary conditions will be symmetric only if the potential is symmetric. This improves the result in [D. Taj, L. Genovese, and F. Rossi, Europhys. Lett., 74 (2006), pp. 1060--1066], which depends on the convergence of the solution formulated in the Neumann series. By numerical studies, we present the convergence of the numerical solution to the symmetric profile for three different numerical schemes. This implies that the upwind schemes can also yield a symmetric numerical solution, contrary to the argument given in [D. Taj, L. Genovese, and F. Rossi, Europhys. Lett., 74 (2006), pp. 1060--1066].

Simulation Study of Quasi-Ballistic Transport in Asymmetric DG-MOSFET by Directly Solving Boltzmann Transport Equation

In this study, we simulate double-gate MOSFET using a 2-D direct Boltzmann transport equation solver. Simulation results are interpreted by quasi-ballistic theory. It is found that the relation between average carrier velocity at virtual source and back-scattering coefficient needs to be modified due to the oversimplified approximations of the original model. A 1-D potential profile model also needs to be extended to better determine the kT-layer length. The key expression for back-scattering coefficient is still valid, but a field-dependent mean free path is needed to be taken into account.

Multi Subband Deterministic Simulation of an Ultra-thin Double Gate MOSFET with 2D Electron Gas

We present a self-consistent multi subband deter- ministic solver of the Boltzmann transport equation of the two dimensional (2D) electron gas. The Sch¨ odinger equation at each slice in the confinement direction and the two dimensional Poisson equation are self-consistently solved with the Boltzmann transport equation. The energy quantization and the scattering of the 2D electron gas are included. We apply this solver to an ultra-thin body double gate MOSFET and show the influence of the 2Dk scattering to the electron transport.

Impact of back biasing in ultra short channel UTBB SOI nMOSFETs

The impact of back biasing on electron transport in extreme short channel Ultra-Thin Body and BOX (UTBB) SOI MOSFETs is investigated by a deterministic multi-subband Boltzmann solver. A 7.5nm channel length UTBB device is simulated, and its transport details are presented in this paper.

Discrete Kernel Preserving Model for 1D Electron---Optical Phonon Scattering

We investigate the discretization of of an electron–optical phonon scattering using a finite volume method. The discretization is conservative in mass and is essentially based on an energy point of view. This results in a discrete scattering system with elegant mathematical features, which are fully clarified. Precisely the discrete scattering matrix is thoroughly studied, including its sparsity pattern and its symmetries, the structure of its eigenvalues and eigenvectors. It makes us reveal the strategy to setup grid points, so that the proper scattering matrix can be obtained to preserve the unique discrete scattering kernel. Numerical results are presented to validate these theoretical findings.

Globally hyperbolic moment method for BTE including phonon scattering

A globally hyperbolic high-order moment method of the Boltzmann transport equation (BTE) is proposed in [1], [2], and here it is extended for the BTE with the electron-phonon scattering term to simulate a silicon nano-wire (SNW). Convergence with respect to the order of the moment system and the characteristics of SNW including the I-V curve are studied.