The process engineer you mentioned can be a wafer factory, a packaging and testing factory or a complete machine assembly factory. If you are in a wafer factory, you should study books such as semiconductor physics and integrated circuit technology. If you are in a packaging factory, you can read some books on packaging technology.
In fact, the more downstream the industry, the lower the requirements for professional knowledge. For example, packaging testing and machine assembly are mainly concerned with process problems, and the knowledge of integrated circuits is not high, so they are not used much. Anyone with an engineering background can do it, mainly by accumulating practical experience at work and seeing the theory when encountering problems. A few books are far from enough. Of course, it is impossible to design an integrated circuit without theoretical knowledge.