Mathematical Methods11 Videos

MM01 – Rigorous modal analysis of micro or nanoresonators

Lalanne P.

The most general motion of a system is a superposition of its normal modes, or eigenstates. We report our recent developments of a rigorous modal analysis of electromagnetic resonators, which is accurate even for geometries that have not been analyzed so far, e.g. 3D resonators made of dispersive media and placed in non-homogeneous backgrounds (on […]

MM10 – Full-Vectorial Meshfree Finite Cloud Mode Solver for Fused Fiber-Optic Couplers

Wu X., Xiao J.

A novel full-vectorial meshfree finite cloud mode solver is proposed for analysis of fused optic-fiber couplers, in which the curvilinear coordinate mapping technique is used to map a cloud with curved interface onto a unit square. Numerical results are compared with prior analysis using the finite difference method, showing the validity and utility of the […]

MM07 – Volume exclusion effects in perovskite charge transport modeling

Abdel D., Courtier N., Farrell P.

Due to its flexibility, perovskite materials are a promising candidate for many semiconductor devices. For example, Perovskite Solar Cells (PSCs) have become recently one of the fastest growing photovoltaic technologies. In this work, we take volume exclusion effects into account by formulating two different current densities – either treating the mobility or the diffusion as […]

MM02 – Carrier transport in (In,Ga)N quantum well systems: Connecting atomistic tight-binding electronic structure theory to drift-diffusion simulations

O’Donovan M., Farrell P., Streckenbach T., Koprucki T., Schulz S.

Understanding the impact of the alloy microstructure on carrier transport in (In,Ga)N/GaN quantum well systems is important for aiding device design. We study the impact that alloy fluctuations have on uni-polar carrier transport for both electrons (n-i-n junction) and holes (p-i-p junction) using a multiscale framework. To do so we connect an atomistic tight-binding model […]

MM03 – Implementation of Partially Reflecting Boundary Conditions in the Generalized Maxwell-Bloch Equations

Schreiber M., Popp J., Seitner L., Haider M., Jirauschek C.

Perfectly matched layer (PML) boundary conditions have been used for several decades for the simulation of open domains within the finite difference time domain (FDTD) method. In this paper, we report on a new PML-based partially reflecting boundary condition for the generalized Maxwell-Bloch equations that enables setting a certain value of reflectance R at the […]

MM06 – Dual-Potential Finite-Difference Technique for Computational Electrodynamics

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We present a finite-difference time-domain (FDTD) technique suitable for coupling with quantum-transport solvers. We derive first-order equations for the electric and magnetic vector potentials and the electric scalar potential which, upon the adoption of the Coulomb gauge, decouple into solenoidal and irrotational equation sets and are sourced by the solenoidal and irrotational parts of the […]

MM04 – Simulation of ac conductivity of monolayer MoS2 at terahertz frequencies

Mitra S.,

We present a multiphysics numerical tool for calculating the terahertz (THz) conductivity of transition-metal dichalcogenides (TMDs). The tool combines the ensemble Monte Carlo (EMC) technique for carrier transport with a three-dimensional finite-difference-time-domain (FDTD) solver for electromagnetic fields. We use the coupled EMC–FDTD technique to calculate the frequency-dependent conductivity in the terahertz range for monolayer MoS2, […]

MM05 – Comparison of flux discretizations for varying band edge energies

Moatti J., Farrell P.

Recently, a multiscale framework was developed where drift-diffusion is combined with atomistic tight-binding models. A naive flux discretization was proposed to tackle the problem of heavily fluctuating band edge energies which does not take into account mathematical complications. Here we would like to present several alternatives and compare them.

MM08 – Data-driven doping reconstruction

Piani S., Lei W., Heltai L., Rotundo N., Farrell P.

To reconstruct doping profiles via opto-electronic techniques (e.g. LBIC and LPS), we formulate an inverse problem based on the van Roosbroeck system. To solve it, we use neural networks fed with data created from efficient implementations of the forward model. We discuss errors of the reconstructed doping profiles as well as their robustness with respect […]

MM09 – FiPo FDTD: Computational Electrodynamics Technique Producing Both Fields and Potentials

Avazpour L., King M., Belling S., Knezevic I.

We present the field–potential finite-difference time-domain (FiPo FDTD) algorithm, which solves a set of first-order equations for the electric and magnetic fields (E and H), as well as the magnetic vector potential A and the scalar electric potential φ in the Lorenz gauge. We also present the derivation and implementation of a convolutional perfectly matched […]