Question

Can the following be used to differentiate between a semiconductor and an insulator? (a) The shape of the conductivity graph versus temperature. (b) The temperature dependence of the conductivity. (c) The band structure.

Short answer

(a) Yes, the shape of the conductivity graph versus temperature can be used to differentiate between a semiconductor and an insulator. Semiconductors show an increase in conductivity with an increase in temperature, whereas insulators have a very low conductivity that remains almost constant across a wide temperature range. (b) Yes, the temperature dependence of conductivity differentiates between a semiconductor and an insulator. Semiconductors show a positive temperature coefficient of conductivity, whereas the conductivity of insulators is very low and almost constant across a range of temperatures. (c) Yes, the band structure can be a discriminator. The energy gap between the valence and conduction bands for semiconductors are relatively small, facilitating electron movement and electrical conduction. In insulators, the energy gap is much larger, making electron excitation and movement to the conduction band difficult, thus restricting electrical conduction.

Step-by-step solution

(a) The shape of the conductivity graph versus temperature.

Yes, the shape of the conductivity graph versus temperature can be used to differentiate between a semiconductor and an insulator. For semiconductors, the electrical conductivity increases with an increase in temperature, showing a positive temperature coefficient. On the other hand, insulators have a very low electrical conductivity that remains almost constant over a wide range of temperatures. Therefore, the shape of the conductivity graph will be significantly different for semiconductors and insulators, allowing us to distinguish between them.

(b) The temperature dependence of the conductivity.

Yes, the temperature dependence of the conductivity can be used to differentiate between a semiconductor and an insulator. As mentioned earlier, semiconductors exhibit a positive temperature coefficient of conductivity, i.e., their conductivity increases with increasing temperature. In contrast, insulators have very low conductivity that remains almost constant over a wide range of temperatures. If we can observe a significant increase in the conductivity with increasing temperature, then it is likely a semiconductor, whereas if the conductivity remains relatively constant, it is likely an insulator.

(c) The band structure.

Yes, the band structure can be used to differentiate between a semiconductor and an insulator. The band structure describes the energy bands in a material and is responsible for determining the electrical properties of that material. In semiconductors, the energy gap between the valence band (highest occupied energy level) and conduction band (lowest unoccupied energy level) is relatively small (typically around 1 eV). This small energy gap allows electrons to be easily excited and move from the valence band to the conduction band, allowing for electrical conduction to occur. On the other hand, insulators have a much larger energy gap between their valence and conduction bands (typically greater than 5 eV). This large energy gap makes it difficult for electrons to be excited and move to the conduction band, thus restricting electrical conduction in insulators. By examining the band structure of a given material, we can determine if it is a semiconductor or an insulator based on the energy gap between its valence and conduction bands.