Driver monitoring systems (DMS) are a key component of vehicular safety and essential for the transition from semiautonomous to fully autonomous driving. A key task for DMS is to ascertain the cognitive state of a driver and to determine their level of tiredness. Neuromorphic vision systems, based on event camera technology, provide advanced sensing of facial characteristics, in particular the behavior of a driver's eyes. This research explores the potential to extend neuromorphic sensing techniques to analyze the entire facial region, detecting yawning behaviors that give a complimentary indicator of tiredness. A neuromorphic dataset is constructed from 952 video clips (481 yawns, 471 not-yawns) captured with an RGB colour camera, with 37 subjects. A total of 95,200 neuromorphic image frames are generated from this video data using a video-to-event converter. From these data 21 subjects were selected to provide a training dataset, 8 subjects were used for validation data, and the remaining 8 subjects were reserved for an 'unseen' test dataset. An additional 12,300 frames were generated from event simulations of a public dataset to test against other methods. A convolutional neural network (CNN) with self-attention and a recurrent head was trained and tested with these data. Respective precision and recall scores of 95.9% and 94.7% were achieved on our test set, and 89.9% and 91% on the simulated public test set, demonstrating the feasibility to add yawn detection as a sensing component of a neuromorphic DMS.