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Let's say we have a p-type and an n-type semiconductor. I understand that the free electrons in the n-type semiconductor move to the p-type, but why is it said that the holes also move to the n-type semiconductor?

I know that it can sometimes be useful to pretend a hole is actually a particle, like an electron, but wouldn't it be easier to say that the free electrons go to the p-type, leaving behind positive ions in the n-type and creating negative ions in the p-type? Or is this explanation incorrect?

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"to say that the free electrons go to the p-type, leaving behind positive ions in the n-type and creating negative ions in the p-type?"

From your question what I understood is you think hole movement same as electrons movement in opposite direction.

In macroscopic scale your thought might come true. But here we observe the movement of each electron microscopically so there is a little difference. Consider a P-N junction "electron movement" is defined as the movement of a single electron from negative terminal towards depletion region. In "hole movement" a single hole is moving from the positive terminal towards the depletion region. Large number of electrons will be participating in this movement. Therefore we cannot consider hole movement as opposite movement of electron.

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I think the easiest way to visualize this is to think of holes as 'places a an electron could go to' and free electrons as 'electrons that have no place to go'. This leaves a lot of room for bound electrons, eg 'electrons that found a nice place'.

Now, imagine electrons as restless creatures, always looking for a better place to stay by moving to a new location. This would mean a hole would soon be occupied by a previously bound electron, leaving another hole. From the overview this looks like a moving hole.

For free electrons this means that it will try to take the place of a bound electron, leaving a new free electron. Again from the overview this looks like a single electron moving.

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You're totally right, it only confuses people. I think those who explain that way, just kind of copy/paste. Because a professor or someone with a PhD degree said so, others assume that's how you explain.

They also don't explain why free electrons in a neutral state move to the P-type atoms. They often don't know this is a natural reaction because of electron-negativity charge. Atoms with an outer shell of like 7 electrons, want another electron really bad to complete the band. This attracts (steals) free electron from atoms who have just 1 electron in the outer shell and have no problem to loose that 1 electron.

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Electrons can only go where there's a hole for them to go. Suppose there's an electron at the edge of the N-type. If there's a voltage source connected across this junction (+ to P-type), then this electron is pressured by the electric field to move to a hole in the P-type. The electron finds a hole and moves to it - essentially the hole and electron swap positions. Another electron comes along, and it swaps positions with that hole. Looking at it macroscopically, you can look at as a bunch of electrons moving towards the positive terminal, or equally as a bunch of holes moving towards the negative terminal. The latter is used because electrons have negative charge and so they travel opposite to the flow of conventional current which is unintuitive; holes can be seen as the flow of positive charge which is more useful.

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