electric polarization involves the defect centers in the dielectric

[Silicon]

I konw that the defect centers in a dielectric contribute to the electric polarization and thus affect the permittivity.If there is any microscopic theory can derivate the relationship between the defect centers and the permittivity?

[Gokul43201]

There certainly is. I'm not sure I can find good references on short notice.

Very often - for instance in perovskite structures - an impurity site can be very polar (mostly from electron capture). This strong, oriented dipole "pins" the polarization of the surrounding lattice (in the vicinity) by dipole-dipole interactions. This effect has been studied extensively, in terms of the electrostatic, thermodynamic (the free-energy gains an inhomogeneous strain-energy-like term) and transport (some defects, like oxygen vacancies, can lead to high ionic conductivity) properties of materials.

[marlon]

I konw that the defect centers in a dielectric contribute to the electric polarization and thus affect the permittivity.If there is any microscopic theory can derivate the relationship between the defect centers and the permittivity?

Great question. This is an issue of serious research right now. I will refer you to the home page of Prof Alex Shluger of UCL. He is working in this field and he collaborates with my phd promotor who is working in ESR-caracterization (like Pb-centers,etc).

Here it is http://www.cmmp.ucl.ac.uk/~ayg/group/
Click on "research"

regards
marlon