Model Predictive Control of Cadmium Telluride (CdTe) Quantum Dot (QD) Crystallization

Inorganic semiconducting quantum dots (QDs) have emerged as a promising alternative to silicon with widespread applications in next-generation displays and high-efficiency solar cells. Generally, the optoelectronic properties of QDs are majorly dictated by their bandgap energy (related to their size), which makes it important to accurately predict and control size of QD crystals. Unfortunately, unlike protein or sugar crystallization, there are very few models that describe QD crystallization. Moreover, the existing QD models are either based on computationally demanding multiscale modeling approaches making them unsuitable for direct implementation in a controller framework or based on black-box modeling providing little insight into crystallization kinetics. To address this knowledge gap, we present a population balance equation (PBE)-based model for QD crystallization. Specifically, the PBE along with mass and energy balance equations, growth and nucleation kinetics are decomposed into first-order ordinary differential equations (ODEs). Further, a model predictive controller (MPC) is demonstrated for set-point tracking of crystal size and distribution (CSD). Further, the case study of CdTe QDs, which are widely utilized in displays and solar cells, has been investigated. The simulation results are in good agreement with experimental observations, and the proposed MPC demonstrates effective size-control of CdTe QDs by manipulating the solute-concentration using a semi-batch addition operation. Overall, to the best of our knowledge, the current work is the first instance of utilizing well-established PBE-based crystallization model for accurate modeling and MPC-based control of QDs, and will serve as a foundation for modeling other QD systems.