Table C-5: Value of Ea for several materials
|
Material |
Ea |
|
PMMA (perspex) |
1,7 eV |
|
Polythene |
1,0 eV |
|
Glass |
1,3 eV |
C.8.4.3. Electric field-induced dependence
Field enhanced conductivity is attributed to the strong electric field causing the activation of additional carriers as well as increasing the mobility of carriers. The most up-to-date treatment appears to be that of Adamec and Calderwood (A&C, see [31]) in 1975. Even so, their model was not significantly different from earlier work carried out in the 1930s, since A&C showed that their model yielded almost identical results to that of Onsager (1934) (see [32]) over the whole range of field strengths from the Ohmic region up to the breakdown of the dielectric. The A&C relation between electric field and conductivity is
where
• E is electric field,
•
, d is jump
distance (fixed at 10-9 m), and
• e is the charge on an electron.
This formula is essentially theoretical, except that d was chosen to fit experimental data. σ(T) concerns the effect of temperature on conductivity discussed in C.8.4.2.
A&C demonstrated a good correlation between their theoretical predictions of conductivity and experimental measurements.
Polymers demonstrate an increase in conductivity under irradiation and this effect has been subject to much experimental investigation However, most was conducted at very high dose rates by comparison with that seen in space applications. Irradiation excites electrons into the conduction band, generating charge carriers in direct proportion to the energy absorption rate in the polymer i.e. dose rate. This dose rate can be the result of energetic electrons, ions or gamma rays.
The basic equation to describe the conductivity, σ, of irradiated polymers was developed by Fowler (1956) (see [34]). This equation, shown below, is widely used:
[W-1 cm-1]
where
• σo is the dark conductivity [W-1 cm-1],
• kp is the material-dependant co-efficient of prompt radiation induced conductivity [W-1 cm-1 rad-Δ sΔ], and
• Δ is a dimensionless material-dependent exponent (Δ < 1).
It is generally observed that after irradiation is stopped, RIC decays away only slowly (see [34]). The slow decay of RIC is often called ‘delayed’ RIC. In some cases a linear dose-dependent permanent increase in conductivity (confusingly sometimes also called delayed conductivity) is also thought to occur. However, this phenomenon seems to be much less well reported and can be restricted to certain polymers which are prone to undergoing permanent changes under irradiation.
Unlike polymers, electrical conductivity in glasses is ionic i.e. current is carried by the migration of ions as in electrolytes rather than by electron-hole pairs. The sodium ion with a relatively high mobility is responsible for the greater part of the conductivity. Irradiation does not seem to be reported to increase conductivity, presumably because it has no effect on the concentration of the sodium ions (see [19]).