Sihong Shao

Boundary treatments in non-equilibrium Green's function (NEGF) methods for quantum transport in nano-MOSFETs

Non-equilibrium Greens function (NEGF) is a general method for modeling non-equilibrium quantum transport in open mesoscopic systems with many body scattering effects. In this paper, we present a unified treatment of quantum device boundaries in the framework of NEGF with both finite difference and finite element discretizations. Boundary treatments for both types of numerical methods, and the resulting self-energy @S for the NEGF formulism, representing the dissipative effects of device contacts on the transport, are derived using auxiliary Greens functions for the exterior of the quantum devices. Numerical results with both discretization schemes for an one-dimensional nano-device and a 29nm double gated MOSFET are provided to demonstrate the accuracy and flexibility of the proposed boundary treatments.

An Advective-Spectral-Mixed Method for Time-Dependent Many-Body Wigner Simulations

As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic numerical solutions have been almost exclusively confined to one-dimensional one-body systems and few results are reported even for one-dimensional two-body problems. This paper serves as the first attempt to solve the time-dependent many-body Wigner equation through a grid-based advective-spectral-mixed method. The main feature of the method is to resolve the linear advection in

Accurate calculation of Green's function of the Schrödinger equation in a block layered potential

(\bm{x},t)

Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

-space by an explicit three-step characteristic scheme coupled with the piecewise cubic spline interpolation, while the Chebyshev spectral element method in

Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

\bm k

A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media

-space is adopted for accurate calculation of the nonlocal pseudo-differential term. Not only the time step of the resulting method is not restricted by the usual CFL condition and thus a large time step is allowed, but also the mass conservation can be maintained. In particular, for the system consisting of identical particles, the advective-spectral-mixed method can also rigorously preserve physical symmetry relations. The performance is validated through several typical numerical experiments, like the Gaussian barrier scattering, electron-electron interaction and a Helium-like system, where the third-order accuracy against both grid spacing and time stepping is observed.

A computable branching random walk for the many-body Wigner quantum dynamics

In this paper a new algorithm is presented for calculating the Greens function of the Schrodinger equation in the presence of block layered potentials. Such Greens functions have various and practical applications in quantum modelling of electron transport within nano-MOSFET transistors. The proposed method is based on expansions of the eigenfunctions of the subordinate Sturm-Liouville problems and a collocation matching procedure along possibly curved interfaces of the potential blocks. Accurate numerical results are provided to validate the proposed algorithm.

Numerical Methods for the Wigner Equation with Unbounded Potential

Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.

Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport

We present for the first time an efficient iterative method to directlysolve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCGF method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt2, Au2, TlF, and Bi2Se3 indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy

Numerical methods for nonlinear Dirac equation

In this paper, we propose a parallel Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D complex Helmholtz equations in high frequency wave scattering in dispersive inhomogeneous media. This method is based on the spectral expansion of complex generalized eigen-oscillations for the electromagnetic fields and the Schwarz non-overlapping domain decomposition iteration method. The GeSEM takes advantages of a special real orthogonality property of the complex eigen-oscillations and a new radiation interface condition for the system of equations for the spectral expansion coefficients. Numerical results validate the high resolution and the flexibility of the method for various materials.