Mathematical Methods

Mathematical Methods

MM01–Connecting atomistic and continuum models for (In,Ga)N quantum wells: From tight-binding energy landscapes to electronic structure and carrier transport

Schulz S., O’Donovan M., Chaudhuri D., Patra S. K., Farrell P., Marquardt O., Streckenbach T., Koprucki T.

We present a multi-scale framework for calculating electronic and transport properties of nitride-based devices. Here, an atomistic tight-binding model is connected with continuum based electronic structure and transport models. In a first step, the electronic structure of (In,Ga)N quantum wells is analyzed and compared between atomistic and continuum-based approaches, showing that even though the two […]

MM02–Efficient multi-band k·p calculations of superlattice electronic and optical properties using plane waves

Murphy C., O’Reilly E. P., Broderick C. A.

Solving the multi-band k·p Schrodinger equation for a quantum-confined heterostructure using a reciprocal space plane wave approach presents several advantages compared to conventional real space approaches such as the finite difference or element methods. In addition to allowing analytical derivation of the heterostructure Hamiltonian, a desired level of accuracy in the computed eigenstates can generally […]

MM03–Parameter Estimation of an Ion-Exchange Process Based on a Pseudo Probability Measure

Roth J. P., Kühler T., Griese E.

For the realization of integrated optical waveguide components, needed for integrated photonic circuits, a promising approach to manufacturing is their embedding in thin glass sheets by thermal diffusion processes. Because prototyping or manufacturing small batch series is costly, appropriate numerical simulations are used in order to allow an accurate characterization. However, in practical applications it […]

MM04–Mirror particle effects in kinetic Monte Carlo simulations including Coulomb interaction with periodic boundary conditions

Schwuchow M., Wagner C., Thränhardt A.

We investigate the photoluminescence of low-dimensional disordered materials, as used e.g. in solar cells, by performing kinetic Monte-Carlo simulations of exciton hopping with periodic boundary conditions. In order to perform numerically efficient calculations, the box length Lbox should be as small as possible while maintaining physically meaningful results during the presence of exciton-exciton-interaction. Exciton-exciton interaction […]

MM05–Dynamic Response Prediction of Bi-State Emission of Quantum Dot Lasers Based on Extreme Learning Machine

Santos W.F.S., Simas Filho E. F., Thé G. A. P.

Dual-state emission is an phenomenon which takes place in Quantum Dot Lasers at different temperature and operating conditions. In this study, we investigate that issue from a nonlinear regression model based on Extreme Learning Machine, which revealed to be able to predict the spectrally resolved transient response of InAs/InGaAs quantum dot laser with error performance […]

MM06–Numerical Prediction of Propagation Characteristics for Integrated Optical Couplers

Uebach D., Roth J. P., Kühler T., Griese E.

The field-assisted ion-exchange process for manufacturing integrated optical couplers is multivariate. For this reason, a precise prediction of the optical propagation characteristics of manufactured devices is needed. Two numerical calculation methods are compared with measured results for an integrated coupler to assess its applicability for a precise prediction.

MM07–Optimization of Two-Dimensional Photonic Crystals with Artificial Bee Colony Algorithm

da Silva M. G., Malheiros-Silveira G. N.

We applied the Artificial Bee Colony algorithm for the complete band gap maximization of a two-dimensional photonic crystal. The band diagram and band gap calculation were carried out by the software MIT Photonic Bands, and these results were used in the algorithm’s fitness function. The optimum structure was compared to the literature which used genetic […]

MM08–Controlling Nonlinearities in Semiconductor Superlattice Multipliers

Pereira M.F., Apostolakis A.

A hybrid approach combining Nonequilibrium Green’s Fuctions with solutions of the Boltzman equation, delivers voltage and intrinsic asymmetry control of nonlinearities in semiconductor superlattices. Unexpected nonlinear behavior is predicted for high harmonics as a result of voltage control.