Scheduling is a fundamental task in each production facility with implications on the overall efficiency of the facility. While classic job-shop scheduling problems become intractable when the number of machines and jobs increase, the problem gets even more complex in the context of semiconductor manufacturing, where flexible production control and stochastic event handling are required. In this paper, we propose a Deep Reinforcement Learning approach for lot dispatching to minimize the Flow Factor (FF) of a digital twin of a real-world, stochastic, large-scale semiconductor manufacturing facility. We present the first application of Reinforcement Learning to an industrial grade semiconductor manufacturing scenario of that size. Our approach leverages self-attention mechanisms to learn an effective dispatching policy for the manufacturing facility and is able to reduce the global FF of the fab.