Bonds, bands, and bandgaps in tetrahedrally bonded ternary compounds: the role of group V Lone Pairs

An interesting class of tetrahedrally coordinated ternary compounds have attracted considerable interest because of their potential as good thermoelectrics. These compounds, denoted as I$_3$-V-VI$_4$, contain three monovalent-I (Cu, Ag), one nominally pentavalent-V (P, As, Sb, Bi), and four hexavalent-VI (S, Se, Te) atoms; and can be visualized as ternary derivatives of the II-VI zincblende or wurtzite semiconductors, obtained by starting from four unit cells of (II-VI) and replacing four type II atoms by three type I and one type V atoms. In trying to understand their electronic structures and transport properties, some fundamental questions arise: whether V atoms are indeed pentavalent and if not how do these compounds become semiconductors, what is the role of V lone pair electrons in the origin of band gaps, and what are the general characteristics of states near the valence band maxima and the conduction band minima. We answer some of these questions using ab initio calculations (density functional methods with both local and nonlocal exchange-correlation potential).