Optimization of Work Function via Bayesian Machine Learning Combined with First-Principles Calculation

Work function is one of the most fundamental and important physical quantities in surface science. Materials with either lower work function or higher work function would find various applications, such as electronic devices and high-performance catalysts. However, it would be challenging to find a material with the optimal work function exploiting the all-search or random approach, whether it is based on an experimental or theoretical method. In this paper, we use the Bayesian optimization (BO) approach, which is one of the most powerful machine-learning tools for optimization, in order to effectively explore a candidate material with a higher or lower work function value out of hundreds of thousands of materials registered in a material database. We introduce a quick measure of the work function based on the depth of the Fermi level calculated from the first-principles computation for the crystalline bulk structure of a material. We call this the approximate work function, treating it as the objective function of our BO scheme. Since we do not need any time-consuming surface calculation with the slab model for the evaluation of the approximate work function, a quick search of a material with the highest or the lowest work function is achieved. As input variables for our BO implementation, we employ some bulk-specific properties of materials, which can be fetched from the database. The demonstration of our BO-based exploration of the database shows that materials with both low and high limits of the approximate work function can be discovered more efficiently in BO than a random exploration. The top 10 lowest work function materials thus found are in line with our chemical intuition in that all of them include either alkali or alkaline earth metal. On the other hand, we found the top 10 highest work function materials with amazement because they also include either alkali or alkaline earth metal and a lanthanide element.