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2.5 Digression: Water Analogy

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Suppose you have a large pot of water sitting on the counter at room temperature (25 °C). The water is not moving. Now you place the pot on the stove and increase the temperature to 100 °C, the temperature of boiling water. There are three possibilities:

1 The rim of the pot is much higher than the level of the water. The boiling water remains in the pot. The rim is too high for the water to boil over.

2 The water fills the pot all the way to the top. As soon as the water starts boiling, water spill all over the stove.

3 Now consider an intermediate case. The water level is high, but it does not reach the rim. How much water spills over depends very much on the distance between the original water level and the rim of the pot. The larger the distance between the water level and the rim of the pot, the more water will spill from the pot.

You can immediately recognize the analogy. First, the separation of the water level and the rim of the pot is analogous to the energy gap. Case 1 is the insulator, where there is a large distance between the electrons and the empty conduction band. Case 2 is the conductor, where the electrons start spilling into the conduction band as soon as there is any energy at all. Finally, case 3 is the semiconductor, where the number of electrons in the conduction band depends on the separation between bands. There are more free electrons in silicon at room temperature than in GaAs because the separation of bands is much larger in GaAs.

I hope the analogy helps you understand the effect of the bands in defining the conductive processes of different materials. If you had difficulty in the previous sections, it might be worthwhile to go back and read them again.

Semiconductor Basics

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