Heteroepitaxial
growth of single-crystalline zinc oxide (ZnO) films
on a c-plane sapphire substrate is an important technology
for electronics and optoelectronic devices. Recently, the inverted
Stranski–Krastanov (SK) mode has been demonstrated, and it
has realized the heteroepitaxial growth of ZnO films on a sapphire
substrate by sputtering. In this mode, a 10 nm-thick buffer layer
consisting of three-dimensional islands (3D buffer layers) initially
forms and relaxes the strain, and then, a two-dimensional ZnO film
(2D layer) grows involving small strain. To clarify the correlation
between the structural properties of the 3D buffer layers and the
2D layer, we introduce a figure of merit (FOM) of ZnO films: the reciprocal
of the product of the full width at half-maximum (FWHM) of the (002)
and (101) planes of X-ray rocking curves (XRCs) and root-mean-square
(RMS) roughness. We find that the FOM of the 2D layers correlates
with the RMS roughness, the in-plane orientation, and the lateral
correlation length ξ of the surfaces of the buffer layers. We
observe a surprisingly high correlation coefficient of 0.97. Our results
imply that on the buffer layers with larger ξ, adatoms more
easily reach the thermodynamically favored lattice positions. Thus,
high-quality single-crystalline ZnO films, where the (002) plane XRC-FWHM
and the RMS roughness are 0.05° and 1.5 nm, respectively, are
grown on the buffer layers with a large ξ of 13.7 nm. This finding
provides a useful tool for understanding the mechanism of the inverted
SK mode.