in order to help, you have to tell me what is HKMG, what is PTM and what is your sample geometry (model geometry).
My guess is that if the oxide is "perfect" (high resistance), the value of eps(relative) of some 3.9 is the value of refractive index^2, measured at low infrared frequencies. If the models in PTM assume the value of 3.9 for all types of oxides, then the model is completly wrong. Different oxides have different optical and electrical properties that are reflected by the dielectric permitivity.
I am sorry, but you do not have to go 2D-3D simulations of SILVACO (AVANTI, SIAM, COMSOL, etc., etc.,...) to answer a simple question how to calculate a capacitance of a thin oxide layer. In fact, in these numerical simulation packages, you have to do a number of approximations in order to be able to manage 2D-3D complexity (in many cases, life is too short when compared to the calculation time needed !). But then you loose some of the important physics.
Sometimes I have a feeling that it would be a very healthy excercise (your students included) to go back to the basics of Classical Electrodynamics to really appreciate space-time-energy aspects of electrical charge (mobile and bound) dynamics.
you are saying that epsrox = 3.9, is same for all models in PTM. I fell that you are possibly somewhere confusing models of PTM with technology node.
If it is not the case, i think Petr Viscor has rightly commented that " If the models in PTM assume the value of 3.9 for all types of oxides, then the model is completly wrong."