Question Video: Free Electrons in a Pure Semiconductor as a Function of Temperature | Nagwa Question Video: Free Electrons in a Pure Semiconductor as a Function of Temperature | Nagwa

Question Video: Free Electrons in a Pure Semiconductor as a Function of Temperature Physics • Third Year of Secondary School

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In a pure semiconductor at a temperature of 320 K, the number of free electrons in the semiconductor is ๐‘›. The temperature of the semiconductor is increased to 420 K. Which of the following correctly describes how ๐‘› changes? The semiconductor is in thermal equilibrium at both temperatures. [A] ๐‘› increases. [B] ๐‘› decreases. [C] ๐‘› remains constant.

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Video Transcript

In a pure semiconductor at a temperature of 320 kelvin, the number of free electrons in the semiconductor is ๐‘›. The temperature of the semiconductor is increased to 420 kelvin. Which of the following correctly describes how ๐‘› changes? The semiconductor is in thermal equilibrium at both temperatures. (A) ๐‘› increases. (B) ๐‘› decreases. (C) ๐‘› remains constant.

In this example, weโ€™re working with a pure semiconductor. An example of this is silicon. A neutral atom of silicon has four electrons in its valence shell. This means that when silicon atoms form a lattice, some electron sharing occurs so that interior atoms in that lattice have a full complement of eight valence electrons. From an energy perspective, it doesnโ€™t take the addition of much energy to one of these valence electrons to liberate it and turn it into a free electron.

Our question tells us that when a lattice of silicon atoms has a temperature of 320 kelvin, there are ๐‘› free electrons roaming about through that lattice. The reason there are free electrons at all in such a sample is due to the transfer of thermal energy to valence electrons in the lattice. As weโ€™ve said, if sufficient energy is transferred to such an electron, it becomes free. The thermal energy available for doing this depends on the temperature of the lattice. The higher the temperature, the more thermal energy is available to make valence electrons become free electrons. The higher the temperature then, the more free electrons exist in a lattice.

This shows us then how to answer our question. If the number of free electrons in our semiconductor at a temperature of 320 kelvin is ๐‘›, then that number must increase when we increase the semiconductorโ€™s temperature. We therefore choose answer option (A) ๐‘› increases.

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