Ingeniero

FIELD ENHANCED CONDUCTION

T

he dielectric properties which we have discussed so far mainly consider the influence of temperature and frequency on &' and s" and relate the observed variation to the structure and morphology by invoking the concept of dielectric relaxation. The magnitude of the macroscopic electric field which we considered was necessarily low since the voltage applied formeasuring the dielectric constant and loss factor are in the range of a few volts.

We shift our orientation to high electric fields, which implies that the frequency under discussion is the power frequency which is 50 Hz or 60 Hz, as the case may be. Since the conduction processes are independent of frequency only direct fields are considered except where the discussion demands reference to higherfrequencies. Conduction current experiments under high electric fields are usually carried out on thin films because the voltages required are low and structurally more uniform samples are easily obtained. In this chapter we describe the various conduction mechanisms and refer to experimental data where the theories are applied. To limit the scope of consideration photoelectric conduction is notincluded.

7.1 SOME GENERAL COMMENTS
Application of a reasonably high voltage -500-1000V to a dielectric generates a current and let's define the macroscopic conductivity, for limited purposes, using Ohm's law. The dc conductivity is given by the simple expression
C7=—

AE

TM

Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved.

330

Chapter?

where a is the conductivityexpressed in (Q m)"1, A the area in m2, and E the electric field in V m"1. The relationship of the conductivity to the dielectric constant has not been theoretically derived though this relationship has been noted for a long time. Fig. 7.1 shows a collection of data1 for a range of materials from gases to metals with the dielectric constant varying over four orders of magnitude, and thetemperature from 15K to 3000K. Note the change in resistivity which ranges from 1026 to 10~14 Q m. Three linear relationships are noticed in barest conformity. For good conductors the relationship is given as

log p + 3 log e' = 7.7
For poor conductors, semi-conductors and insulators the relationship is

(7.2)

(7.3)

2
O
I

2 X

TITANATES

H >
(/>
UJ (E

o >-"

FERRO-ELECTRICS

©GLYCERINE / AT 800° C

CARBON AT 0°C GRAPHITE AT 0°C COPPER AT 500°C SILVER AT 15° K

SUPERCONDUCTORS

Sn-Bi TUNGSTEN AT 3500°K / SILVER AT 0°C COPPER AT 15° K

I02

I03

I04

DIELECTRIC CONSTANT

Fig. 7.1 Relationship between resistivity and dielectric constant (Saums and Pendleton, 1978, with permission of Haydon Book Co.)

Ferro-electrics fall outside the range by a widemargin. The region separating the insulators and semi-conductors is said to show "shot-gun" effect. Ceramics have a higher dielectric constant than that given by equation (7.3) while organic insulators have lower dielectric constant. Gases are asymptotic to the y-axis with very large resistivity and s' is close to one. Ionized gases have resistivity in the semi-conductor region.

TM

Copyrightn 2003 by Marcel Dekker, Inc. All Rights Reserved.

From the definition of complex dielectric constant (ch. 3), we recall the following relationships (Table 7.1): Table 7.1 Summary of definitions for current in alternating voltage Quantity Charging current, Ic Loss current, IL Total current, I Dissipation factor, tan8 Power loss, P Formula
CO C0 8' V

coC 0 s"V co C0 V(s'2 + e"2)1/2
8" / 8'coC 0 e'V 2 tan5

Units amperes amperes amperes none Watts

7.2 MOTION OF CHARGE CARRIERS IN DIELECTRICS Mobility of charge carriers in solids is quite small, in contrast to that in gases, because of the frequent collision with the atoms of the lattice. The frequent exchange of energy does not permit the charges to acquire energy rapidly, unlike in gases. The electrons are trapped and...