Why must we consider holes in semiconductors, but not in metals when describing current desnity?

Question

In my undergrad course, current in a semiconductor involves two types of carriers, the electron and empty energy level it leaves behind - aka the hole.

In metals we only consider electrons when solving for the current density.

Why? My professor tells me to just accept it.

Answer 1

It's not true that you must consider holes in semiconductors. It's just an easier way of doing visualization and calculation in a P-type semiconductor, where there is a shortage, rather than a surplus, of free electrons. The best way to appreciate this simplification is to try doing the math without it. Semiconductor behavior is not something that's easy to understand. It might be helpful to read the introductory sections of several different texts on semiconductor physics, since each is likely to explain it in a different way. If your professor just tells you to accept it, then the course isn't thorough enough.

Comparable simplifications might be the motion of a shadow or of an ocean wave.

Answer 2

Dear Matt,

In Metals:
The top energy band is not full. The carriers (electrons) can take up small amounts of kinetic energy and are free to move around and under the influence of external electric fields migrate though the electron sea of the bulk material. Of course the holes left behind act as 'traps' for the electrons and so do migrate as holes but their contribution is small - except in the case of metals like Bismuth where they contribute a lot to the conduction.

In extrinsic P type Semiconductor.
The conduction band is full. We place a band of electron acceptors just above it which is narrow becuse it is a dilute concentration (so doesn't form a wide band)
Thermal electrons jump into this band but can not move because they can not take up small amounts of kinetic energy.(They have very large effective masses). The 'holes they leave behind are filled successively by migrating electron and thus appear to move. They are not as mobile as it is a shuffle process so tend to have a higher mass than in a similar 'n' type semiconductor.
This leads to a difference in carrier mobility in so called matched pairs ot transistors. Look upsome characteristics of a Matched Pair to see this.


I have done the Bismuth part from memory and can not remeber where I read it. Look it up in books etc!

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