Question Video: Identifying the Silicon Lattice Best Representing Recombination Physics • 9th Grade

The diagram shows a lattice of Si atoms where a free electron is adjacent to a vacancy. Which of the following diagrams most correctly represents the lattice a short time later? [A] Diagram A [B] Diagram B [C] Diagram C [D] Diagram D [E] Diagram E

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Video Transcript

The diagram below shows a lattice of silicon atoms where a free electron is adjacent to a vacancy. Which of the following diagrams most correctly represents the lattice a short time later?

Among our answers, we have five options, (A), (B), (C), (D), and (E), for the best representation of the moment in time that comes right after that shown in our original diagram. In that original diagram, we have a lattice of silicon atoms where valence shell electrons are represented by blue dots. Those valence electrons are regularly arranged across this lattice except for one location. We notice that right here in our lattice there’s a hole or a vacancy indicated. Along with this, there is a free electron. We can tell this electron is free because it’s in motion as indicated by its blue tail, that we can see is moving directly toward the vacancy.

The relative effective charge of a hole or vacancy is positive one. In that sense, a vacancy is attractive to electrons. Free electrons can combine with holes in a process called recombination. It’s called recombination because for an electron to be free, it had at some point to be liberated from a bound state. In our original diagram though, we see that our free electron is likely to occupy this hole. Among our five answer options then, we’ll look for the one that shows us that hole being occupied by an electron.

In answer choice (A), that location in the diagram is right here. This indeed does show the hole being occupied by an electron, but another hole has opened up right next to it. The problem is this new vacancy appears at a spot in the lattice where no valence electron existed previously. A free electron did exist at this location, but no valence electron that would move and leave a hole behind. For this reason, we won’t choose option (A) as our answer.

In answer choice (B), the location that was marked as a vacancy in our original diagram is no longer there, but now there’s a vacancy over to the left of that spot as well as a liberated or free electron. This doesn’t reflect what would happen a short time after the scenario shown here in our diagram. Therefore, we will eliminate answer option (B) too. In answer option (C), we see that the vacancy, which was vacant in our original state, is still vacant and it seems that the free electron has disappeared entirely. This isn’t what is likely to happen. So, we’ll cross out answer choice (C).

In option (D), the vacancy that was open is now filled by an electron. However, we see that a new vacancy has opened up in between these four valence electrons that are shared by their adjacent silicon atoms. This vacancy, however, doesn’t correspond to the location of any of the valence electrons in our original diagram. We note that this vacancy is located right about here on that diagram where no valence electron exists. Since there’s no electron to leave that location in the first place, no vacancy will open up there.

This brings us to answer option (E), where we see that what was the vacancy in our original diagram is now filled by an electron. At every other location throughout this answer option, the valence electrons have remained in place. Choice (E) then is the best representation for what would happen a short time after the scenario shown to us in our original diagram. The hole in that original diagram would be filled by the free electron, and the result would be a restored valence electron at the location indicated. We choose answer choice (E).