Calculation of semiconductor melting temperatures based on Fan-equation approximated by the 37% rule

Abstract

We present a mathematical model capable of the calculation of semiconductor melting temperatures. Notably, and quite different from previous attempts, the procedure does not require specific knowledge about the thermodynamics of the materials and is based on the Fan equation and the 1/e rule, also known as the 37% rule. Employing this new model, we calculated melting temperatures for 14 semiconductors spanning a wide range of bandgap energies. The results found are in good agreement with previous theoretical and experimental values reported in the literature, establishing the strength of the model in spite of its simplicity. The model also unifies elements and compounds with representative linear trends, showcasing the potential for future expansion.