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Chapter 37: Problem 12

How would you expect the conductivity of an undoped semiconductor to depend on temperature? Why?

Short Answer

Expert verified
The conductivity of an undoped semiconductor would increase with increasing temperature. This is because as temperature rises, more electrons are provided with enough thermal energy to overcome the energy gap between the valence and conduction bands. This creates more charge carriers (both electrons and holes), which in turn, increases the conductivity of the semiconductor.

Step by step solution

01

Understand Basic Semiconductor Physics

An undoped semiconductor typically has a certain number of charge carriers, electrons in the conduction band and holes in the valence band, even at absolute zero temperature. As the temperature rises, thermal energy allows more electrons to overcome the energy gap (or bandgap) between the valence band and the conduction band. When they cross this bandgap, they leave behind holes in the valence band. Both these electrons and holes contribute to increase the conductivity of the semiconductor.
02

Define the Relationship

The increase in temperature provides more thermal energy to the semiconductor. This thermal energy helps the electrons to cross the energy gap. Therefore, with the increasing temperature, more electrons get enough energy to cross the gap, increasing the number of charge carriers and thereby increasing the conductivity. This forms a directly proportional relationship between the temperature and the conductivity of an undoped semiconductor.
03

Summarize the Dependency

Therefore, the conductivity of an undoped semiconductor depends on the temperature in the following way: As temperature increases, the conductivity increases due to the creation of more charge carriers (i.e., electrons and holes). This is because thermal energy allows more electrons to cross the energy gap from the valence band to the conduction band.

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