[extropy-chat] diffraction limit

[Brent Neal]

 (5/30/04 13:05) Dan Clemmensen <dgc at cox.net> wrote:

>HI-K dielectrics are important, but not precisely for this reason. Gate 
>"thickness" is at best loosely related to photolithographic dimensions. 
>The latter are what we have been discussing. Thickness has to do with 
>material depositions, and can already be controlled to within a very few 
>atomic layers.(by analogy, you can easily paint a very thin and uniform 
>thickness of paint with a spraygun, but you cannot paint a narrow sharp 
>line.)  In general, tunneling seems to be designed in and/or accounted 
>for in the vertical dimension. The big problem in this dimension will be 
>when tunneling establishes paths between layers that are not supposed to 
>be there. In the horizontal dimension, as features get smaller, we will 
>reach the point where the same thing happens in this dimension. My 
>uneducated guess is that this imposes a lower bound on feature 
>separation. Consider the "simple" case of two copper paths , or two 
>nanowires, that are supposed to be electrically separate. If you place 
>them close enough together, a tunnel current will flow between them.


Better dielectrics have a lower k, not a higher k. The dielectric constant is the ratio of the permittivity of the material to the permittivity of free space. You want this number to be as low as possible, as free space is actually a pretty damn good conductor of electrons.

And as I pointed out before, the k value of your dielectric is relevant to the tunnelling current. But it is actually more complex than that, as is always the case with quantum mechanics. The permittivity is one parameter in the wave equation, as is the electron energy.  In an infinite well, the electron is confined and goes nowhere. Unfortunately for us, the well isn't infinite, and worse, there is another well nearby. The probability of finding the electron somewhere in the barrier, or on the other side of it tails off to zero, but asymptotically. Essentially, the probability of finding the electron in the next well over (the next trace over...) is given by the value of that probability function.

Because of that, its fairly meaningless to talk about a "minimum dimension above which no tunnelling occurs."  For a given spacing and permittivity, you can talk about the mean time between tunnelling incidents. If that is on the order of 10^10 years, you can safely call that "no tunnelling."  If its 10^-10 seconds, then you can talk about a "tunnelling current." For anywhere in between, you likely care more about whether the tunnelling will allow enough electrons through to cause dielectric breakdown (which is bad) or so few that you can call your device reliable. 

Brent
-- 
Brent Neal
Geek of all Trades
http://brentn.freeshell.org

"Specialization is for insects" -- Robert A. Heinlein