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Question Video: Free Electrons in a Pure Semiconductor Physics • 9th Grade

The diagram shows a lattice of Si atoms at a temperature of 300 K. Which of the features labeled in the diagram is a free electron? What is the effective relative charge of the feature labeled 𝐵?

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Video Transcript

The diagram shows a lattice of silicon atoms at a temperature of 300 kelvin. Which of the features labeled in the diagram is a free electron? What is the effective relative charge of the feature labeled 𝐵?

In our diagram, the red circles represent silicon nuclei, and the blue ring around each nucleus represents the electron energy levels below the valence energy level. Along with these features, we see these smaller blue dots and these represent electrons in the valence energy shell. If our lattice of silicon atoms was at a temperature of absolute zero, zero kelvin, then all of the silicon atoms interior to the lattice would have a full complement of eight valence electrons. But because our lattice is at 300 kelvin, about room temperature, enough thermal energy exists in the environment to potentially be absorbed by some of these valence electrons and set them free from the atoms they’re originally bound to.

This is what we see happening in the parts of our diagram labeled 𝐵 and 𝐴. The location marked 𝐵 is where a bound electron, an electron in a valence shell, used to be, while the label 𝐴 identifies the electron that has been liberated from that location, called a free electron. This tells us the answer to the first part of our question. The feature labeled 𝐴 is the free electron. This is the blue dot that’s now in motion and free to move about throughout the lattice.

The next part of our question asks, what is the effective relative charge of the feature labeled 𝐵? We noted that 𝐵 points out the location where the electron used to be. Since an electron used to occupy this spot but no longer does, it’s called a hole or a vacancy. If we think about the electric charge of this location, we’re considering it relative to what it used to be. When the electron was present before it was liberated from the atom, the effective charge of that location was negative one, and that’s the effective charge of one electron. When the electron was liberated from this location, it left behind it an uncharged spot.

Here, we want to figure out what is the charge of this relative to its original charge of negative one. We can see that to get from a charge of negative one to a charge of zero, we need to add plus one. This then we say is the effective relative charge of the vacancy. Compared to what used to be there, the charge of a hole, or a vacancy, is positive one.

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