In the derivation of Poole-Frenkel emission (Field assisted thermal emission), the trap barrier is lowered due to applied field and is given as
- Delta U = sqrt((e^3/ pi*\epsilon)*E)
where E is applied field.
The derivation starts from the expression of the electrostatic potential energy due to coulombic trap as
- V = e^2/(4*pi*epsilon*r)
From my understanding of electrostatics, the epsilon used in the potential energy expression is the low frequency permitivity (static permitivity).
But the confusing part is all the papers I have read so far say that the permitivity appearing in Poole-Frenkel coefficient is high frequency component( some say electronic contribution). How can the permitivity introduced in electrostatic potential energy become high frequency part when it goes to Poole-Frenkel?
Can anyone help me understand?
The importance of this is: plotting Poole Frenkel emission of leakage current, the dielectric constant (permitivity) can be approximated. What do you compare it with?
It always depends on the time scale of the phenomenon you are investigating. As electron emission is a relatively fast process, orientation polarization cannot build up, thus the dielectric constant "experienced" by the electron is closer to the atomic polarization component (IR frequency), which is the high frequency end of the radio-wave dielectric spectrum. This is, however, only my guess, if I am not correct, the physicist colleagues will give the right answer.
In most materials dielectric permittivity is frequency dependent - static dielectric permittivity under near DC conditions is different to that at higher frequencies. There is an absorption coefficient for the material which equates to a loss of energy as the frequency increases. This is well covered in the section of Kaye and Laby 'Tables of Physical and Chemical Constants' dealing with the the various physical factors which affect a change in permittivity. .
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