  The dielectric constant or relative permittivity of a dielectric material,
which describes how the net electric field in the medium is reduced with
respect to the external field, is a parameter of critical importance for
charging and screening in electronic devices. Such a fundamental material
property is intimately related to not only the polarizability of individual
atoms, but also the specific atomic arrangement in the crystal lattice. In this
letter, we present both experimental and theoretical investigations on the
dielectric constant of few-layer In2Se3 nano-flakes grown on mica substrates by
van der Waals epitaxy. A nondestructive microwave impedance microscope is
employed to simultaneously quantify the number of layers and local electrical
properties. The measured dielectric constant increases monotonically as a
function of the thickness and saturates to the bulk value at around 6 ~ 8
quintuple layers. The same trend of layer-dependent dielectric constant is also
revealed by first-principle calculations. Our results of the dielectric
response, being ubiquitously applicable to layered 2D semiconductors, are
expected to be significant for this vibrant research field.
