SAT solver-driven approach for validating local electron counting rule

Determining large, complex surface structures is essential for understanding and modeling crystal growth. For semiconductor surfaces, the electron counting (EC) rule is known to be useful for predicting surface stability. In this study, a scheme is proposed to automatically determine if a sampled surface structure locally satisfies the EC rule using a Boolean Satisfiability Problem (SAT) solver. This automatic determination is demonstrated on the GaN(0001)-(6 × 6) surface system with H and Ga adsorption as an example. The scheme is also applicable to the automatic generation of surface structures that are expected to be relatively stable, and is expected to accelerate the study of large and complex surface structures of various semiconductor materials.