Hole effective mass

1. Dec 28, 2015

SUVAM ROY

Why is it opposite to that of an electron?

2. Dec 28, 2015

ZapperZ

Staff Emeritus
Back up a bit. You haven't told us what you already know.

For instance, do you know how we obtain the 'effective mass' of anything in a solid? For example, the "electron" that is in a metal or semiconductor also has an effective mass. Do you know how that is obtained?

In the future, unless you want your question to drag on for people to figure out what exactly you are asking, you must put SOME effort in elaborating your question, but also what you already know and tried to find out. It is required in the PF Rules.

Zz.

3. Dec 28, 2015

SUVAM ROY

Well I know what is effective mass, how it's expression is obtained, how it varies for electron with wavenumber 'k' (m* vs k graph). But can't understand why for hole the m* vs k graph is opposite to the graph of electron.

4. Dec 29, 2015

DrDu

This is just a matter of reinterpretation: When you remove an electron you can alternatively say that you create a hole and vice versa. Lets say you have n electrons of mass n*m then removing one of it leaves you with mass (n-1)*m. You obtain the same result by saying that you added a hole of mass -m to n*m.

5. Dec 29, 2015

ZapperZ

Staff Emeritus
Then I don't understand why you have your problem.

For example, look at Page 1 of this link at the top figure of a generic band structure of a semiconductor:

The bottom of the conduction band (energy band 1), the second derivative of E vs k is positive, and thus, m* is positive. The top of the valence band (energy band 2) has a negative curvature, and thus, the second derivative is negative, giving a negative m*.

Thus, knowing how m* is derived, and knowing the band structure, you get what m* is. If you know these, why are you still having a problem in understanding it?

Zz.

Last edited by a moderator: May 7, 2017
6. Dec 30, 2015

SUVAM ROY

Thanks. It's just my conception was not that clear. Will you check if I am right or not.

While moving through periodic potential when a electron gets attracted towards a positive center(i.e. zero potential area), it can be said that a hole is created in the high potential area where the electron was previously. So, it can be said that the hole got repelled from the zero potential area producing a (-)ve acceleration. So, in a periodic variation of potential hole motion is opposite to the electron motion.So, their effective masses are also opposite.

Last edited by a moderator: May 7, 2017