A Unified Approach for modeling and control of crystallization of quantum dots (QDs)

Abstract

Recently, quantum dots (QDs) have garnered significant attention due to their superior photoelectronic properties, and widespread applications in high-resolution displays and solar cells. Generally, the optoelectronic properties of QDs are majorly dictated by their bandgap energy (related to their size). Thus, there is a large impetus on accurate modeling and control of size of QD nanocrystals. Unfortunately, unlike traditional protein or sugar crystallization, there are very few models that describe QD crystallization. That said, the existing few QD models are based on computationally demanding multiscale modeling approaches, which (a) makes extrapolation to different QD systems highly resource-intensive; and (b) makes them unsuitable for direct implementation in a controller framework. To address these challenges, we present a unified QD crystallization modeling and control framework. Specifically, mass-energy balance equations, population balance equations (PBEs), and crystallization kinetics are decomposed into a matrix of first-order ordinary differential equations (ODEs) that can be easily computed using native python solvers. Further, a model predictive controller (MPC) module is designed for set-point tracking of crystal size distribution (CSD). Also, unlike the multiscale QD models from the literature, the developed PBE-based QD model has high computational efficiency, and can be directly incorporated within the MPC without the requirement of a surrogate model. Then, to demonstrate the developed unified framework’s capabilities, batch crystallization of CdTe QDs is taken as a case study. It was observed that the simulation results are in good agreement with the experimental results, and the MPC shows effective set-point tracking performance for regulating size of QD crystals.

Keywords

• Population balance modeling
• Model predictive controller
• Unified approach
• Quantum dots