Unaccounted Electrons in Quantum Tunnelling Composites: What Happens to Them?

[willfarquhar96]

I'm creating a simple model of a quantum tunnelling composite component (google for details). Most of the model is simple enough, but I can't think what would happen to the electrons that don't tunnel, as an electron build up would cause current to decrease with time as the plate becomes more and more negatively charged, whereas this does not happen in reality. Also, what would happen to electrons that don't tunnel once inside the composite? Would they remain in the electron trap from which they failed to tunnel?

 

[Nugatory]

If the electrons are allowed to pile up in one area the potential in that area will increase, lowering the potential barrier and increasing the probability of tunneling. Either you have to include the non-constant potential in your model, or you have to limit yourself to situations in which the current in is equal to the tunneling current out.

(If you make the potential barrier high enough the tunneling probability will go to zero and you're modeling a classical capacitor in which the current in does indeed go to zero over time as the electrons pile up on one plate)

 

[willfarquhar96]

I understand the physics of your reply is sound, but do you know if this is the case in components which utilise quantum tunnelling?

It seems like there would have to be a function of time in the model which over complicates things. There would be a probabilistic current due to tunnelling and a complementary probabilistic change in barrier height with respect to time and/or proportion of electrons which reflect.

 

[Nugatory]

It seems like there would have to be a function of time in the model which over complicates things. There would be a probabilistic current due to tunnelling and a complementary probabilistic change in barrier height with respect to time and/or proportion of electrons which reflect.

It does complicate things, but there is no way that you can model a system that changes over time without introducing time into the model.

Depending on exactly what you're trying to do with this model and how accurate it needs to be (probably not very, if it's also going to be simple ), you will probably be able to approximate the height of the potential barrier and the tunneling probability as some fairly straightforward function of the potential difference across the barrier.

If your model is constructed properly and you keep the source and sink voltages constant with respect to time, the system should settle down into a steady state in which the voltage at the trap is equal to the voltage at the source and the current from the source to the trap is equal to the tunneling current out of the trap.

 

[Nugatory]

BTW - the more you tell us about why you're building this model in the first place, the better the answers you'll get.

 

[willfarquhar96]

BTW - the more you tell us about why you're building this model in the first place, the better the answers you'll get.

Thanks for your reply. I have previously started a thread in which I listed all my information, assumptions and approximations and received no answers at all. I thought it best to start small.

So, I am trying to model the relationship between current and compressive strain in Quantum Tunnelling Composites. The component is effectively a capacitor with the difference being the dielectrics resistance decreases exponentially as a compressive strain is applied. This is because 'filler particles', effectively large electron traps, are compressed closer together, decreasing the width of the potential barrier.

My current approximations are:
The filler particles are randomly oriented enough so that I can model a perfect three dimensional array in which each electron travels from trap to trap in a straight line with no more or less optimal paths existing.

The compressive strain on the elastomer is equal to the strain on the average distance between the traps in the array. That is, the strain is perfectly distributed.

The barrier height will be a function of the repelling force on an electron by the elastomer molecules between it and the next trap. I assume that this is a large oversimplification but it is after all a simple model.

The barrier width will be a function of the number of elastomer molecules between two traps and the average width of an elastomer molecule.

The electrons which successively tunnel all the way through do so with no loss in velocity and no time spent 'stationary' in any traps.

 

[willfarquhar96]

The barrier width will be a function of the number of elastomer molecules between two traps and the average width of an elastomer molecule.

I retract this part, the barrier width will be the barrier width - the distance between two traps in the array after a strain is applied

 

[willfarquhar96]

More info/assumptions:

The electrons being modeled as waves do not interfere with each other as they go about their business.

The current when the elastomer is strained will be I(e^-2αl)^t where I is current entering the QTC, l is the barrier width, t is the number of electron traps to be tunnelled to, and alpha is the wavenumber of the electron inside the barrier, (√(2m(V(x)-E)))/hbar.