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โ and the number of holes in the semiconductor is ๐โ. The temperature of the semiconductor is reduced to 280 K. What is the ratio of ๐โ to ๐โ? The semiconductor is in thermal equilibrium at both temperatures.

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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 minus and the number of holes in the semiconductor is ๐ plus. The temperature of the semiconductor is reduced to 280 kelvin. What is the ratio of ๐ minus to ๐ plus? The semiconductor is in thermal equilibrium at both temperatures.

In this example, weโre working with a pure semiconductor. And letโs say we have a lattice of such semiconductor atoms like this. Each one of these dots then represents the nucleus of such an atom, where we havenโt shown the valence electrons. These electrons are what become free electrons when enough energy is transferred to them so that theyโre liberated from the bonds associated with their respective atoms.

At a temperature of 320 kelvin, there will be some free electrons in our sample. Letโs say those free electrons look like this, moving about all through the lattice. And weโre told that that number of free electrons in our sample at this temperature is ๐ minus. An important thing to note is that each one of these free electrons used to be a valence electron of an atom in this lattice. When a valence electron is liberated to become a free electron, it leaves behind a hole or a vacancy.

Weโre told that the total number of holes in this 320-kelvin semiconductor is ๐ plus. In a pure semiconductor like we have here, the number of holes is always equal to the number of free electrons. Indeed, they canโt exist without one another. If this is our semiconductor at 320 kelvin, if we then decrease its temperature down to 280 kelvin, the result would be that there is less thermal energy available to transfer to valence electrons. And therefore, fewer valence electrons become free electrons.

However, for any electrons that do become free electrons, they also leave behind a hole or a vacancy. So, even though with the temperature decreased the number of free electrons is less, the number of holes is less too by the same amount. Our question asks us about the ratio of ๐ minus to ๐ plus. Regardless of the temperature of a pure semiconductor sample, that ratio is always one. For every free electron in a pure semiconductor, there is one hole. Likewise, for every hole, there is a corresponding free electron. The ratio ๐ minus to ๐ plus is equal to one.

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