Conduction
Modelling Thermistors
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Modelling
of Conduction in Thermistors:
A plot of Resistance
vs Temperature for a typical NTC
Thermistor is shown in graph #
1. The relationship between Resistance
and Temperature is non-linear
so modelling this relationship
physically and mathematically
can be a complex procedure.
In considering modelling the
Resistance versus Temperature characteristics
of NTC thermistor devices it is
useful to briefly review some of
the principles of solid
state physics associated
with NTC thermistor materials.
At this stage the reader may proceed
directly to where modelling
equations are listed if
an overview of the modelling process
is not required.
Detailed descriptions of the electrical
conduction mechanism for metal-oxide
thermistor materials are beyond
the scope of this catalog, but
a brief overview is adequate to
outline some concepts here.
The exact conduction mechanisms
are not fully understood. The metal
oxide NTC thermistors behave like semiconductors, as
shown in the decrease in resistance
as temperature increases.
The physical
models of electrical
conduction in the major NTC thermistor
materials are generally based on
one of two theories. Detailed treatment
of these models can be found in
reference books on ceramic materials.
Brief summaries of these theories
are outlined below.
A model of conduction called "hopping" is
relevant for some materials,
especially ferrites and manganites
that have a spinel crystal structure.
It is a form of Ionic conductivity
where ions (oxygen ions) "hop" between
point defect sites in a spinel
crystal structure. The probability
of point defects in the crystal
lattice increases as temperature
increases, hence the "hopping" is
more likely to occur and so material
resistivity decreases as temperature
increases.
A second model of conduction is
based on the
band gap model of solid state physics. This
model is of particular relevance
in the semiconductor industry
for materials like Silicon and
Gallium-Arsenide. This model
describes the availability of
charge carriers in terms of the
distribution of physical impurities
in the crystal lattice. This
model works very well for materials
like Silicon which can be produced
in monocrystalline structures
with a high degree of purity.
The silicon can then be "doped" with
required impurities like Boron
or Phosphorous to produce materials
with characteristics that can
be modelled mathematically, from
basic theoretical principles,
with accuracy.
For metal oxide thermistors the
crystal structure is much more
complex. The material structure
is polycrystalline and granular.
The materials are composed of several
metal oxide components and are
generally very difficult to model
from basic principles.
The
approach that is used
for predicting the
behaviour of thermistor
materials, is to make
accurate measurements
of Resistance and Temperature
of components and to
apply curve fitting
techniques to model
the relationship between
them. The
physical models of
conduction are used
in conjunction with
this approach to provide
direction in developing
the mathematical models.
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