Conduction Modelling Thermistors

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Introduction Alpha (Temperature Coefficient) Application Notes BetaCURVE and BetaCHIP Products Chip Configuration Circuit Notes Exponential Model of NTC Thermistors Beta Value,ß , or Sensitivity Index Factors affecting measured resistance value of thermistors Mathematical Modelling of Thermistors Modelling of Conduction in Thermistors	Resistance Self heating effect of thermistors Slope (Resistance Ratio) Specification of thermistors for applications Stability & reliability of thermistors Steinhart Coefficients for BetaTHERM standard part numbers Technical Note from Analog Devices www.analog.com/adn8830 The Steinhart-Hart Thermistor Equation Thermal Time Constant (T.C.)	Thermal Dissipation Constant (D.C.) Tolerance of Thermistors Technical Note from Analog Devices www.analog.com/adn8830 Volume Resistivity Voltage–Current Characteristics Zero-power resistance characteristic

Modelling of Conduction in Thermistors:

Graph 1

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.