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This is my first post on PF so forgive any rookie errors. I'm a 17 year old British student. I have just finished a month long placement at Newcastle University researching my chosen topic of quantum tunnelling. The placement itself was very disappointing and I had no interaction with a single physics professional, so I had no one to rely on if I had specific questions to ask. There was also no chance to perform any experiments.

I am now finishing my theoretical research and writing up a report. The aim of my brief project was to obtain a mathematical description of electrical current in relation to compressive strain in Quantum Tunnelling Composites. These components are fairly simple: a silicon rubber elastomer containing conductive filler particles sandwiched by two conductive plates as part of a circuit. In its rest state the elastomer acts as a near perfect insulator. When compressively strained its conductivity increases by many orders of magnitude as a result of Quantum Tunnelling occurring between the filler particles. This means the component may be used to calculate strain by measuring the change in current elsewhere in the circuit, acting as an effective pressure sensor, or as a switch.

There is little more information available on the components as they trademarked by Peratech^{TM}, a UK firm. Their website specifies that they will not reply to academic correspondence and true to their word I have not received a reply.

I really only need help finding an equation which will link the change in current to the strain on the elastomer. Here are the assumptions/approximations I am currently using:

The current entering the elastomer at any time may be calculated using the electron density of the conductor and the cross sectional area of the interface (and possibly the equation linking drift velocity to electron mobility and electric field strength - I have less knowledge of this so some suggestions would be helpful)

The percentage of filler particles in the elastomer may be used to obtain an average distribution and hence an average distance between each conductive particle.

An individual electron entering the elastomer would tunnel from one filler particle to the next with a probability coeffecient which is a function of the distance to the next particle, the energy of the electron (presumably found by its velocity) and and the magnitude of the potential energy barrier created by the elastomer. Again I would appreciate any suggestions regarding this approach.

No time passes during the 'tunnelling' but the probability of an electron which enters the elastomer leaving the elastomer is T^{n}where T is the tunnelling probability coefficient, a function of the electrons energy, the barrier height and the barrier width, and n is the number of particles it must tunnel between to reach the other conducting plate. I've a feeling this is most likely an over simplification as plugging in a high probability coefficient with a relatively low n gives a seemingly low number. But then again it is only a single electron.

The decrease in the width of the elastomer (the compressive strain) will be proportional to average decrease in distance between the metal filler particles, with some constant of proportionality which is beyond my knowledge, so again suggestions are appreciated.

I understand this is a long post and my thoughts are somewhat scattered so please help me by pointing out any glaring mistakes and offering any suggestions you may have. I am most definitely not any sort of expert in quantum mechanics so I imagine I am guilty of approaching this problem too classically.

Thanks in advance,

Will Farquhar

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# Need help modelling Quantum Tunnelling Composites

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