Dynamic Multiscale Quantum Mechanics/Electromagnetics Simulation Method

Abstract

A newly developed hybrid quantum mechanics and electromagnetics (QM/EM) method [Yam et al. Phys. Chem. Chem. Phys.2011, 13, 14365] is generalized to simulate the real time dynamics. Instead of the electric and magnetic fields, the scalar and vector potentials are used to integrate Maxwell's equations in the time domain. The TDDFT-NEGF-EOM method [Zheng et al. Phys. Rev. B2007, 75, 195127] is employed to simulate the electronic dynamics in the quantum mechanical region. By allowing the penetration of a classical electromagnetic wave into the quantum mechanical region, the electromagnetic wave for the entire simulating region can be determined consistently by solving Maxwell's equations. The transient potential distributions and current density at the interface between quantum mechanical and classical regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. Charge distribution, current density, and potentials at different temporal steps and spatial scales are integrated seamlessly within a unified computational framework.

A multiscale quantum mechanics/electromagnetics method for device simulations

“…In practice, the system is discretized into regular Cartesian meshes as shown in Fig. 4,19 For the semiconductors, the Scharfetter-Gummel discretization scheme 35 is adopted to solve the drift-diffusion equations numerically. All independent scalar variables are assigned to each node while vector variables are associated with the connections between nodes which are called links hereafter.…”

“…[2][3][4][5][6][7][8][9][10][11] At the nanoscale, details of atomistic disposition can be critical to the overall properties of the system. 7,8 Multiscale approaches have been recently applied to electronic devices, [3][4][5][6] where quantum mechanical models [12][13][14][15][16][17] are solved in conjunction with classical electromagnetics. One way to include appropriate multiple length scales is to connect atomistic models with continuum models.…”

“…One way to include appropriate multiple length scales is to connect atomistic models with continuum models. [3][4][5] The QM/EM method provides a general framework which allows the simultaneous treatment of multiple scales for investigation of interactions between charge carriers and electromagnetic field in different nanoscale devices including field-effect transistors (FETs), photovoltaic and plasmonic devices. In PCM, instead of explicit molecules, the solvent is modeled as a polarizable continuum medium which hosts solute molecules in its cavity.…”

A fast time‐domain EM–TCAD coupled simulation framework via matrix exponential with stiffness reduction

“…The A-V co-simulator has been translated into a series of commercial tools [6] and verified against measurements with a number of industrial examples [7,8]. Meanwhile, the A-V formulation has also been coupled with a quantum-mechanical model to enable a multiscale simulation framework for emerging nano-electronic devices [9,10]. The technique can also be exploited to generate more accurate equivalent circuit models for EM-semiconductor hybrid systems [11].…”

A fast time-domain EM-TCAD coupled simulation framework via matrix exponential

“…The A-V co-simulator has been translated into a series of commercial tools [3], and verified against measurements with a number of industrial examples [4], [5]. Meanwhile, the A-V formulation has also been coupled with a quantum mechanical model to enable a multiscale simulation framework (called QM/EM method) for emerging nano-electronic devices [6], [7]. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”