electric current - How are band gap energy, dielectric constant (permittivity) and resistance related to each other?

The following three properties are related to current flow:

1. Band gap energy


2. Dielectric constant


3. Resistance

I would expect them all to have the same trend (i.e. higher band gap energy would cause higher dielectric constant and higher resistance), but this is not the case. For example:

• SiO₂ is a very good insulator (band gap of 9eV), but its dielectric constant is very low ($\epsilon_r=3.9$), compared to many materials. Why so?


• In this ref (page 8) a consistent inverse correlation between $\epsilon$ and $\rho$ for Si is presented. Why is it inverse? I would expect them to rise together.