The k value of SiO2 is very small in the visible region, so it is regarded as a dielectric material with a n value close to 1.47. While in the Infrared region, around 8-13 um, its k value is noticeable. Generally, the dielectric constants of materials are measured by using an ellipsometer.
Macroscopic dielectric constant is a lattice-dependent physical quantity (DOI:10.1021/acs.nanolett.9b02982). I don't think the dielectric constant of two-dimensional (2D) materials is reliable in some literatures reported earlier. A recent paper states that the dielectric constant does not define unequivocally the dielectric properties of 2D materials due to the locality of their electrostatic screening. Instead, the electronic polarizability correctly captures the dielectric nature of a 2D material which is united to other physical quantities in an atomically thin layer (DOI:10.1021/acs.nanolett.9b02982).
The dielectric consatnt of SiO2 is about epsilonr~ 4. It slightly depends on the technology used as dry oxidation, wet oxidation or water vapor oxidation. The oxide used as a gate insulator in MOS transistors must be of the best quality which is achieved by dry oxidation. very small percentage of the HCl gas is mixed with oxygen to remove any metal contaminations. If is found that such oxide has very low interface sates between the Si and SiO2.
As the oxide thickness decreases it is probable to form SiO with it.
For more information you can refer to the Book of S. M. Sze titled VLSI technology.