Positive temperature coefficient resistors PTC thermistors

PTC resistors could be classified as critical temperature resistors because, in the case of the most widely used type, the positive coefficient is associated with the ferroelectric Curie point. 

A typical PTC characteristic is shown in Fig. 4.20. In the instance illustrated the material has the negative resistivity-temperature characteristic associated with normal semiconductors up to about 100 °C (AB) and above about 200 °C (CD), while between these temperatures (BC) there is an increase of several orders of magnitude in resistivity. The underlying physics of the effect as outlined below draws on the discussions in Sections 2.6.2 and 2.7.3. 

The PTC effect is exhibited by specially doped and processed BaTi03. Because the effect is not observed in the single-crystal form of the material its cause must be assumed to lie in processes associated with grain boundaries. Attention here is focused on lanthanum-doped BaTi03 (BLT), although other donor dopants would be satisfactory, e.g. yttrium (A site) or niobium, tantalum or antimony (B site). 

From Fig. 4.22 pd = 2Vs e where Ns is the surface density of acceptor states near the grain boundary and e is the magnitude of the electronic charge. Therefore the height fi of the barrier to an electron becomes 

The probability that electrons are able to surmount the barrier is measured by the Boltzmann factor exp(—tfi/kT), leading to the following proportionality for the resistance Rgh of a grain boundary  

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