Why Are Holes in Semiconductors Heavier and Less Mobile Than Electrons?

[Cheetox]

Homework Statement

give a simple argument which will explain why holes in semiconductors are generally heavier and less mobile than electrons.

Homework Equations

The Attempt at a Solution

Is it something to do with the fact that the hole represents the movements of a lot of electrons rather than just one?

 

[ideasrule]

No, a hole is what's left behind when an electron leaves an atom. It's just a charged atom.

 

[Cheetox]

Ok so how do you then explain why holes are generally heavier?

 

[1Kris]

I'm not sure really but perhaps you should talk about it being an effective mass as opposed to a real mass which is determined by the tendency of an electron to jump from atom to atom (in a particular direction) and that this gives rise to effective masses that are often several times that of a free electron? Sorry if this is too crude an answer but that's the kind of direction I would go in.

Maybe you should back this up with a discussion of the tensor or scalar expressions for the effective mass.

Does anyone disagree?

 

[Mute]

No, a hole is what's left behind when an electron leaves an atom. It's just a charged atom.

The first sentence is correct. The second sentence is not. The hole is not the charged atom, it is the empty space on the charged atom that once contained an electron. When a hole moves it is not the charged atom that is moving; the hole moves by virtue of an electron from another atom leaving that atom to fill the hole, but in effect leaving another hole in its original atom. This is how the hole propagates, so the suggestions that you should compare the electron mass to the mass of the atom it leaves behind is misleading - it gives the impression that the hole mass should be the atom's mass minus an electron, which I doubt is true.