The goal of this dissertation is to study the application of Bayesian Optimization (BO) algorithms to the design of the Silicon-Germanium Heterojunction Bipolar Transistor. We do this largely through computational means, colloquially known as Technology Computer Aided Design (TCAD). These tools serve to solve the semiconductor equations and offer a means to engineer transistors, diodes, or other semiconducting devices without expensive and time consuming Chapter 1 provides a brief introduction and offers context for the work. Chapter 2 treats theoretical and computational modeling of transport in semiconductors, with a focus on model assumptions and limitations. This is critical as, unlike in circuit design, it is of paramount importance for a device engineer to understand the inner workings of the simulator. Chapter 3 provides a theoretical background for mathematical optimization, as well as details on the Bayesian optimizer we apply in this work. Chapter 4 presents investigations of the Ge profile design in the SiGe base. The evaluation efficiency of the optimization approach is validated. The automatic design of temperature stable profiles is then investigated. Chapter 5 investigates automated design of the collector profile. We first present results showing an improved vertical superjunction. We then present results detailing the Pareto front discovery, or the performance bound discovery, of the collector at cryogenic temperatures. Chapter 6 provides conclusions and future work.