Extreme Ultraviolet lithography is a vital step in the production of cutting edge computer chips that drive emergent technologies like AI, VR and the internet of things [1]. Careful control of Ultraviolet light beams by EUV machine modules such as the Unicom, Uniformity correction module, enable extremely precise printing of nano-scale structures on these chips. This thesis focuses on the construction of a model that predicts the impact of the Unicom on EUV illumination in ASML's lithography machines. Such a model could be used in a predictive maintenance scheme to prevent a fraction of unscheduled machine downtime, which can be estimated to cost ASML's customers around 38 million dollars per machine per year [2-4]. Similar problems have been tackled before [5, 6], but both existing models disregard multiple properties of the EUV machine and are incompatible with the type of measurements obtained by ASML. Therefore, the question remains how an accurate Unicom model can be constructed.
In this thesis, a physics based Unicom model was developed that can be fine-tuned to machine specific measurements. Significant reductions of up to 90.3% of prediction errors were obtained by using the model. Overall, making use of the model provided better or equivalent predictions when compared to not using the model for all but one of the investigated indicators of prediction quality. For the latter indicator errors remained within the desired bound, but further investigation is needed to discover why the Unicom model adversely affected this indicator. With an average execution time of 31.4 s, the created Unicom model in general enables swift and substantial accuracy gains.

Synchronisation is the remarkable phenomenon of in-phase movement of coupled oscillators during a prolonged period of time, which even occurs when these have different natural frequencies. This property is used in many fields like physics, biology and chemistry, to model various system behaviours, for instance: circadian rhythms in the chemistry of the eyes \cite{Rompala2007}.
\newline\noindent This thesis focuses on synchronisation and entanglement in systems consisting of quantum Van der Pol oscillators. After looking at the exemplary properties of the classical VdP oscillator, it follows the methods of \cite{EshaqiSani2020} to explore the behaviour of two coupled QVdPOs, quantum Van der Pol oscillators, using Monte Carlo simulations for trajectories of this system. The system is then expanded to three-oscillator systems with all-to-all and chain coupling. The validity of the extension of the properties found in two QVdPOs in \cite{EshaqiSani2020} with regard to synchronisation and entanglement is tested. Does an Arnold tongue, the region of parameters for which a system shows synchronisation, still exist and if so has its shape changed? Do synchronisation and strong entanglement still show a positive correlation? \newline\noindent Simulations of the 2-oscillator system gave results which were just slightly different from those obtained in\cite{EshaqiSani2020}, validating the occurrence of synchronisation within the Arnold tongue and showing a positive correlation between synchronisation and entanglement of the system. Both the 3-oscillator systems showed synchronisation as well in their respective Arnold tongues, which were increasingly smaller for the all-to-all coupled and the chain coupled system when compared to the 2-oscillator system. Overall, the amount of synchronisation, shown in three oscillators was very close to the amount shown in two oscillators when strongly coupled and just a little less for weak coupling. The correlation between synchronisation and strong entanglement was also found for three oscillators, though for weaker coupling the chain coupled system showed a little more entanglement than before.