Uses of a silicon semiconductor at high temperatures

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We conducted an experiment in which we found the variation in the resistance of a fairly pure silicon sample between temperatures of about 400K to 600K, and we found a value for the energy gap of silicon of our sample. We were comparing the resistance variation with the model:

##R=R_0e^{\frac{E_g}{2k_BT}}##

Firstly, does anyone know what the name of this model is? I have spent several hours trying to find out about this model (unfortunately it is not possible for me to ask my practical demonstartor) to no avail. This model also predicts that this relationship will only be followed when the temperature of the semiconductor is sufficiently high- within the 'intrinsic region'. However all of my searches about the 'intrinsic region' of a semiconductor simply come back with intrinsic and extrinsic semiconductors. Nothing about the 'intrinsic region'.

Also, I am trying to figure out why such information may be important. I know silicon as a semiconductor has many applications for example in detecting the temperature, however I have not come across any examples of devices that would use the properties of silicon at such a high temperature.
 
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"intrinsic conduction" or something like that could lead to results. The model is simply a pure superconductor with a bandgap, and thermal excitations following a Boltzmann distribution with one state in the valence band and one in the conduction band.

The semiconductor has to be hot for that model to be accurate, at lower temperatures impurities (as doping) dominate the conduction.
 

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