  Understanding the structure of ZnO surface reconstructions and their
resultant properties is crucial to the rational design of ZnO-containing
devices ranging from optoelectronics to catalysts. Here, we are motivated by
recent experimental work which showed a new surface reconstruction containing
Zn vacancies ordered in a Zn(3x3) pattern in the subsurface of (0001)-O
terminated ZnO. A reconstruction with Zn vacancies on (0001)-O is surprising
and counterintuitive because Zn vacancies enhance the surface dipole rather
than reduce it. In this work, we show using Density Functional Theory (DFT)
that subsurface Zn vacancies can form on (0001)-O when coupled with adsorption
of surface H and are in fact stable under a wide range of common conditions. We
also show these vacancies have a significant ordering tendency and that
Sb-doping created subsurface inversion domain boundaries (IDBs) enhances the
driving force of Zn vacancy alignment into large domains of the Zn(3x3)
reconstruction.
