Tunneling & Dielectric Constant

[taekcool]

Is there no relationship whatsoever between tunneling and the dielectric constant?
How about breakdown voltage to dielectric constant ?

If not, they on what parameter do they depend on ?

 

[jgruszynski]

There can be statistical correlation in specific cases but not generally.

Tunneling is always dependent on barrier energy height, barrier thickness and barrier band geometry, and that's it. There are no other dependencies for tunneling - such is the world of quantum mechanics. The dielectric constant is only indirectly related to these.

The breakdown of dielectrics can be due to numerous mechanisms. Avalanche currents, Fowler-Nordheim tunneling, trap-assisted Fowler-Nordheim tunneling, ballistic currents and direct tunneling. The exact combination causes breakdown probabilities that can be proportional to exp(-E), exp(1/E) or V^gamma, all depending on the particular material, its manufacture and its dimensions.

There also isn't simply one proven model for breakdown either: hole-trap by impact ionization, trap-assisted field emission, avalanche conduction, etc. And as you cross over from avalanche to quantum currents, breakdown voltage (dielectric strength) can even increase despite having a thinner dielectric.

Remember what dielectric constant physically means: it is the net aggregated ratio of the amount of counter-field generated by the alignment of fixed or mobile electric dipoles in a material due to the application of an external electric field. First there's the specifics of a given material which are quantum mechanical and statistical mechanical (crystallographic, molecular, etc.), and then the aggregate response which is also statistical mechanical (akin to Ising models for permeability in magnetic materials). So lots of ways to break a presumed correlation.

Dielectric constant is a lumped parameter which fails to have meaning as you approach 10s of nm dimensions. Trapping and tunneling responsible for more subtle breakdown effects happen to activate at 10s of nm dimensions and start to dominate electrical behaviors.

Avalanche current breakdown is the closest to anything that is lumped model based but it only applies to fairly thick dielectrics and/or fairly high electric fields (enough energy to cross the band gap of the dielectric) and it is primarily electric field dependent.

Then also consider the coupling to electric field in terms of external electrical parameters like voltage and the effect of carrier concentration and band structure in the metal/semiconductor terminals in terms of that coupling. MOMCAPs are different from MOSCAPs or SOSCAPs because of this.

There can be coupling that would also affect the macro dielectric constant but each has an independent correlation to a shared multitude of "hidden" atomic causes.

 

[htg]

I would like to warn you: quantum mechanics is completely false and based on lies regarding experimental facts.
I do not think there is any tunneling.
I can send you proofs that QM is false.
htg@interia.pl

 

[Kohi_boy]

Interesting... Mind to share them here ?