# Uses of a silicon semiconductor and why its resistance at different temperatures

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.

## 1 Answer

It's the energy-band model. The idea is materials have separated conduction and valence bands in which electrons may reside.

Eg is the size of the gap between these bands. In metals, the gap is zero, the bands overlap. In insulators, the gap is so huge that it is impossible for electrons to reach the valence band (temperature >>1000K needed). Semiconductors are inbetween, the gap is a few eV (Si: 1eV@300K).

In think this "intrinsic region" should just mean "temperature-depending conduction" in contrast to the conduction introduced by doping atoms. The latter change the energy niveaus of the bands and the size of the band gap. When the temperature is sufficiently low, there are other effects which govern the resistance measured instead (meaning: it's still there but you cannot measure it independently.)

• Janka- thank you so much for your reply! Searching 'energy-band model' actually yielded many very interesting and useful results! I was wondering though- I keep reading that at higher temperatures, the effects of the impurities are much smaller so the results of experiments approximate the values for pure silicon itself. I was wondering why the effects of the doping/impurities do not become greater to the same extent as that of the silicon when the temperature is raised? – 21joanna12 Dec 29 '16 at 11:36
• Also, am I correct in thinking that the temperature range that we found for the 'intrinsic region' in our experiment would vary depending on what impurities we had in our silicon sample and their percentages in our sample? For instance, I would assume that the general case would be that the purer our silicon sample the lower the temperature at which the 'intrinsic region' would begin (i.e. where the formula above holds). Perhaps if we had 100% pure silicon, this formula would apply for all temparatures (unless there is another physical effect I am not accounting for). – 21joanna12 Dec 29 '16 at 11:49
• Basically, yes. You aren't measuring a single effect but the sum of all effects, which may be dependent on the temperature even in opposite ways. Material science is complicated exactly because of this. – Janka Dec 29 '16 at 14:35