Video Transcript
The diagram below shows one free electron in a semiconductor diode in which mobile charge carriers diffuse freely. The free electron is shown at three different positions: at the side of the depletion region that borders the n-side of the diode, at the center of the positively charged side of the depletion region, and at the center of the depletion region. At which position is the magnitude of the net force acting on the electron the greatest? (A) Position A, (B) position B, (C) position C, (D) the net force is the same at all the positions.
On the right, we see these three diagrams of a semiconductor diode. All the diagrams are the same, except for the position of the free electron indicated in each one. Our question asks, at which position is the magnitude of the net force acting on the free electron greatest? Because we’re considering an electron, a charge, in order to solve for the net force acting on it, we’d like to know what other charges are around this electron.
To start answering that question, let’s consider our semiconductor diode. This diode we know is the joining, or the junction, of a p-type semiconductor material and an n-type material. These designations tell us that on the n-type side, the mobile charge carriers have a negative charge, that is, the mobile charges are free electrons, whereas on the p-type side, the mobile charge carriers have a positive charge.
Even though we’ve sketched these regions so that it may look like the p-type side has a net positive charge and the n-type side has a net negative charge, in fact, both sides have an overall charge of zero. We just haven’t drawn in the negative charges on the p-type side that balance out the positively charged mobile charge carriers or the positive charges on the n-type side that balance out the free electrons. Despite this, both sides of the semiconductor are electrically neutral. At the place where the p-type material joins up with the n-type material, this is called the junction. Nearby free electrons are able to cross that junction and fill some of the nearby holes on the p-type side.
Several things happen as a result of this. For one, the atoms that were fixed in place in the lattice near this junction but on the p-type side, when these accept a free electron, they become overall negatively charged. Each one of these circles with a minus sign in it then indicates a negatively charged fixed-in-place atom. On the other side, the atoms that the free electrons passed over, say, in order to cross to the p-type side are now positively charged. And these are also fixed in place at certain positions within the lattice. Note, then, that in this region here in our semiconductor diode, there are no longer any mobile charge carriers, either positive or negative. This is called the depletion region, as we see indicated on our diagram.
Notice that on the n-type side of the depletion region, there is a net positive charge. And on the p-type side of that region, there’s a net negative charge. Because there is charge separation, an electric field, we’ll call it 𝐸, forms across the depletion region. One important thing to realize about this electric field is that it’s the result of charge that is distributed over these two parts of the depletion region. That is, it’s different from the way charge is distributed, say, on the plates of a capacitor. We know that an electric field does point from the positive plate of a capacitor to the negative plate. And importantly, that field is uniform.
But that’s different from the situation we have here where our charge is distributed all across the depletion region. Say that we have a graph where the horizontal axis shows us our position in space as we move across our semiconductor diode. On the vertical axis, we plot the magnitude of the electric field. Recall we found earlier that the net charge in the purely p-type region is zero. Therefore, the electric field magnitude in that region would be zero as well. The same thing applies for the net charge of the n-type region. That region is electrically neutral, which means that it too has an overall electric field magnitude of zero. In between these regions though, in the depletion region, the magnitude of the electric field is not zero.
Going back to our capacitor, if the field in this region was like the field in a capacitor, then we could draw it, say, like this dotted line. However, the electric field magnitude within a depletion region is not uniform. Rather, it looks like this, where the peak of that magnitude lines up with the junction of the p-type and n-type materials. In our question, it’s not the electric field magnitude we’re asked about, but rather the net force acting on the free electron of interest. We recall though that the force acting on a charge 𝑞 is equal to that charge multiplied by the electric field 𝐸 in which the charge exists. In all three of our electron’s positions, the charge of the electron is the same.
So the position in which the electron experiences the greatest electric field strength will also be that in which it experiences the greatest net force. We see that when the electron is at position A, it’s actually in a region where the electric field is zero, and therefore it experiences no net force. When the electron is at position B, we would locate that here on our electric field graph, and so the electron there would experience a nonzero net force. But when our electron is at position C, at the junction between these p-type and n-type regions, the electric field magnitude it experiences is greatest. That means the net force it experiences is greatest there as well. For our answer, we choose option (C).
