A new mathematical interpretation of disordered nanoscale material systems for computational modelling

Jack J Tyson,Tasmiat Rahman,Stuart A Boden

doi:10.1016/j.cpc.2020.107399

Abstract

As the era of microscale technologies becomes increasingly overcome by that of the nanoscale, an ever-increasing emphasis on the accurate modelling of such scaled systems is apparent. This work explores the combination of the finite element method with a new set of statistical algorithms to model the optical properties of disordered nanoscale morphologies. A silicon surface textured with a random distribution of nanowires is created to simulate, as an example study, how it responds to incident light. By averaging over many iterations of the model in which the structural parameters are varied around average values, a good match to experiment is achieved, showcasing an error as low as 1.34% in magnitude against measured data. This research introduces a fresh computational approach to simulating heterogeneous material structures widely applicable for modelling across the field of nanotechnology.

Highlights

Modern computational and mathematical methods permit us to recreate many different physical conditions to model various systems accurately
±2%; below the magnitude of 5% (±2.5%) stated in our simulation methodology. This represented an acceptable degree of uncertainty and was carried forward into the following geometric studies. This convergence point only appears to be affected by the geometric complexity of the model, whereby greater degrees of randomisation and variance between the simulated geometries result in more iterations required for convergence
The convergence point is lower for less complex geometries, the convergence data presented in Fig. 7 is for the most complex geometry, randomness level 3

Summary

Introduction

Modern computational and mathematical methods permit us to recreate many different physical conditions to model various systems accurately. The FEM has been showcased to work well for fluid dynamics, thermal propagation and structural mechanics [3]. Modelling such problems using this method heralded an interest in the late 1990s, whereby increasingly more complex structures need to be modelled, and often in-place of their fabrication [3]. This same level of interest has lingered for the modelling of structures with further complexity at even smaller scales and remained the principal motivation of the work reported here [4]

Methods

Results

Conclusion