Question Video: Understanding the Motion of Free Electrons and Holes in a Silicon Lattice Physics • 9th Grade

The diagram shows a lattice of silicon atoms in a semiconductor. The left side of the lattice has been doped with donor atoms. This is called the n-side. The right side of the lattice has been doped with acceptor atoms. This is called the p-side. The regions on either side of the dividing line are of equal size and the ion concentration is the same on both sides. The semiconductor is at thermal equilibrium.

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Video Transcript

The diagram shows a lattice of silicon atoms in a semiconductor. The left side of the lattice has been doped with donor atoms. This is called the n-side. The right side of the lattice has been doped with acceptor atoms. This is called the p-side. The regions on either side of the dividing line are of equal size, and the ion concentration is the same on both sides. The semiconductor is at thermal equilibrium.

Alright, before we get to our question, let’s understand this information we’re given here. We’re told that this diagram shows us a lattice of silicon atoms. And we can see that most of the atoms here are indeed silicon, represented by the symbol Si. So we have the silicon lattice, and we’re told that the left side, over here, has been doped with donor atoms. This means that some of the silicon atoms in the lattice have been replaced by what are called impurities. These impurities are called donor atoms because they have one more valence electron in their natural state than silicon does. And therefore, when they’re added into the lattice of silicon, they effectively donate that excess electron to the lattice.

We’re told that this left side of the lattice is called the n-side, so we can label it that way up top. Then, if we look at the right side of our silicon lattice, we’re told that this too has been doped, but this time with acceptor atoms. These are atoms which by themselves have one fewer valence electron than silicon. And therefore, when they’re added into the lattice structure, they create a vacancy or an electron hole. The reason they’re called acceptor atoms is because they tend to accept free electrons into these holes. This right side is the p-side of the semiconductor. Knowing that the p-side and the n-side are of equal size and that they have the same ion concentration and that our semiconductor overall is at thermal equilibrium, let’s now move on to our question.

The first part of our question asks, toward which side of the lattice will free electrons tend to move by diffusion? And then part two says, toward which side of the lattice will holes tend to move by diffusion? Alright, so considering this first part about the movement of free electrons in our semiconductor, we learned earlier that it’s the left side of the semiconductor, the n-side, that features what are called donor atoms. We see these atoms here and here. They’re atoms of phosphorus.

The reason these phosphors atoms are called donors is that while silicon naturally has four electrons in its valence shell, an atom of phosphorus has one more, five, which means that when these phosphorus atoms are inserted into our lattice, each one contributes an extra, we could call it, electron, one more than the silicon atoms they replaced. These extra electrons are separated from the phosphorus atoms and begin to move about freely within the n-side of our semiconductor.

So then, when it comes to which way free electrons will move, we now know what side they’ll begin on. They’ll start on the n-side, contributed by these donor phosphorus atoms. Negatively charged electrons are drawn to positive charges, and it turns out that we can find such positive charges over on the p-side. Here, instead of doping our silicon lattice with phosphorus, we’ve done it with boron. Boron is different from silicon in that it has only three valence electrons, one fewer than silicon. And so, when these boron atoms replace silicon in the lattice, there’s one missing electron, we could say, in their valence shell.

These vacancies are known as holes, and they have an effective positive charge. And that is just what free electrons are drawn to. So over on the n-side, we see this free electron right here and this one here, one each contributed by the phosphorus atoms. And we know that these negatively charged objects will be drawn to the effectively positively charged holes over here on the p-side. So that’s our answer for this first part of our question.

And now let’s think about the second part which asks, toward which side of the lattice will holes tend to move by diffusion? Well, just as the negative free electrons are drawn to the positive holes, so the positive holes will be drawn to the negative free electrons. So the holes then starting out on the p-side, the right side, will be drawn towards the left, and that, as we’ve seen, is the n-side. By diffusion then, holes will be drawn towards the n-side or the left side of our lattice.

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