In this work, we propose Exformer, a time-domain architecture for target speaker extraction. It consists of a pre-trained speaker embedder network and a separator network based on transformer encoder blocks. We study multiple methods to combine speaker information with the input mixture, and the resulting Exformer architecture obtains superior extraction performance compared to prior time-domain networks. Furthermore, we investigate a two-stage procedure to train the model using mixtures without reference signals upon a pre-trained supervised model. Experimental results show that the proposed semi-supervised learning procedure improves the performance of the supervised baselines.