AMaSiS 2018 Workshop: Abstracts

Data-driven electronic structure calculations for nanostructures (DESCANT)

Oliver Marquardt${}^{\mathbf{\text{(1)}}}$, Miguel A. Caro${}^{\mathbf{\text{(2,3)}}}$, Timo Streckenbach${}^{\mathbf{\text{(1)}}}$, Peter Mathé${}^{\mathbf{\text{(1)}}}$,

Jürgen Fuhrmann${}^{\mathbf{\text{(1)}}}$, Morten Willatzen${}^{\mathbf{\text{(4,5)}}}$, and Thomas Koprucki${}^{\mathbf{\text{(1)}}}$

(1) Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin

(2) Aalto University, Department of Electrical Engineering and Automation

(3) Aalto University, Department of Applied Physics Aalto University

(4) Technical University of Denmark, Department of Photonics Engineering

(5) Chinese Academy of Sciences, Beijing Institute of Nanoenergy and Nanosystems

The development of novel electronic devices and light sources requires efficient techniques to model the physical properties of semiconductor nanostructures as accurate as possible. Such models commonly include elastic, piezo- and pyroelectric, electronic, and optical properties which requires the application of a wide range of formalisms during the design process. Continuum formalisms such as linear elasticity theory and six- or eight-band $𝐤\cdot 𝐩$ models in combination with envelope functions represent the back bone of semiconductor device modelling for two decades now and were employed to study semiconductor nanostructures of a wide range of shapes, dimensions, and material compositions [1, 2, 3]. Despite the great successes of these formalisms in the past, they suffer from different shortcomings, such as so-called spurious solutions [4] or the incapability to describe indirect-gap semiconductors. We will discuss these issues in the context of novel heterostructure concepts.

We outline a novel tool kit consisting of a finite-element method (FEM), a multi-band $𝐤\cdot 𝐩$ model, and a fitting scheme to obtain the respective parameters from up-to-date ab initio band structures.

The FEM-based continuum elasticity module allows us to compute the elastic properties of nanostructures of arbitrary material composition, shape, and crystal structure at low computational costs. Once the elastic properties of the system are known, built-in electrostatic potentials are computed by solving the Poisson equation including piezo- and pyroelectric effects. Strain and built-in electrostatic potentials enter a multi-band $𝐤\cdot 𝐩$ model implemented within a plane-wave framework [5]. The number of bands involved and thus the level of sophistication on the one hand and the computational effort on the other can be chosen according to the required accuracy and available computational capabilities. As material parameters for models beyond the eight-band $𝐤\cdot 𝐩$ formalism are rare, we also introduce a parameter fitting scheme for high-dimensional parameter spaces employing Sobol sequences [6, 7] that can employ up-to-date ab initio band structures.

The combination of the above tools allows us to access a much wider range of possible material systems, crystal structures, and heterostructures for the design of novel devices for optoelectronic applications.