Continuity of Electric Field at metal-dielectric interface in capacitor

[chuckschuldiner]

Hello Guys
According to Classical electrostatics, when you apply a voltage across a capacitor, +Q and -Q charges are induced on a delta region at the interface of the dielectric and the metal electrode. The electric field inside the dielectric is finite and constant while the electric field in the metal is zero.

However, it has been known for quite some time that due to imperfect electronic screening in real metal electrodes, the charges +Q and -Q are not confined to a delta region at the metal-dielectric interface but are infact distributed in a finite region of space in the metal. This also results in electric field penetration inside the electrodes i.e. due to the distribution of charge inside the metal, electric fields exist inside the metal electrodes.

In addition to this, i have seen some recent ab initio simulation results which seems to show that the electric field is continuos at the metal-dielectric interface (Stengel and Spaldin, Nature 443, 679 (2006)). We know that the potential has to be continuos at the metal-dielectric interface but is it possible that the electric field stays at a nearly constant value inside most of the dielectric but has steep gradients at the metal-dielectric interface so that it also remains continuos at the metal-dielectric interface. Is there any physical argument for this?

 

[Parlyne]

When it comes right down to it, the discontinuous field of an 'ideal' capacitor is really just an approximation in the first place, since it requires that the charge on each plate be a true surface charge distribution; when, in point of fact the charge is in the form of discrete, point or point-like objects. So, in reality, even for an ideal capacitor with real charge-carriers, the field is continuous, with a rather large number of poles at the locations of the charges. It just happens that the changes in the field occur over so small a region that they can be approximated by a discontinuity.

In general, these sorts of behaviors can be best understood by looking at what is occurring microscopically to give a metal or dielectric its properties; then, ignoring those effects that are only relevant at very short distances.

 

[chuckschuldiner]

Thank you for your reply!