Biomedical Engineering Reference
In-Depth Information
particular composition range, manganites undergo insulator to metal
transition on cooling [75-91].
2.5.1 Insulating region
Temperature causes electrons to be excited into the conduction band and
hence resistivity is considered as a thermally activated process. Jonker and
Van Santen [133] measured the resistivity of LaMnO
3
AMnO
3
(where
A=Ca, Sr and Ba) and found that the resistivity plotted as log
ρ
versus 1/T
was linear, showing thermally activated behavior given by the relation:
E
o
k
B
T
rð
T
Þ¼
A exp
½
2
:
3
where E
o
is the activation energy, k
B
is Boltzmann's constant and A is a
constant.
An alternative electrical transport mechanism in the insulating region is
due to the formation of polarons (a strong coupling between an electron and
phonons). Polaron-mediated hopping behavior can be described as:
E
o
k
B
T
rð
Þ¼
½
:
T
BT exp
2
4
where B is a measure of ideal conductivity at elevated temperatures and
depends on polaron concentration. The activation energy for polaron-
mediated conduction can be described using the following equation
proposed by Yeh et al. [145]:
E
o
k
B
T
rð
T
Þ¼r
0
T
a
exp
½
2
:
5
where
equal to 1.6 identifies the
behavior as non-adiabatic small polaron hopping in most cases and
ρ
0
is the residual resistivity at T=0,
α
equals
1 in some cases. Other research suggests that variable range hopping (VRH)
best describes electronic transport. VRH has been suggested by Mott to
describe transport at low temperatures when the electronic states are
localized near the Fermi energy [146-151]:
α
1
=
4
E
o
k
B
T
rð
T
Þ¼r
0
exp
½
2
:
6
Coey et al. [152-155] found that this kind of expression best fitted their data
on a variety of films. To summarize, there is clear evidence in the
paramagnetic insulating region of activated behavior, but there is no
agreement on the exact form of temperature dependence.
