# Effective mass

1. Apr 9, 2008

### pwerk

what is effective mass? and how does it effect both the electrical and optical properties of a crystaline structure???

2. Apr 9, 2008

### genneth

Hell pwerk. Welcome to the forums. If this is a homework question, it is best to post it in the homework section. Otherwise:

Assuming that you are talking about electrons in a lattice, the effective mass is a heuristic way to relate the quantum behaviour of these electrons to a semi-classical picture. For example, you can say things like the momentum of the electron is the mass * velocity -- for suitably defined notions of velocity. Similarly, many classical electrodynamics results, e.g. optical response of plasmas, can be directly applied, by substituting the effective mass in.

3. Apr 12, 2008

### marlon

Intuitively, effective mass is a concept that uncouples one many body problem into a set of one body problems that are more easy to solve (i mean, of which the Schrödinger equation, ie the SE, is easier to solve).

Suppose you have 100 electrons mutually interacting through a coulombic potential. The SE cannot be solved exactly because of the mutual coupling between all the electrons (electron 1 interacts with electron 2,3, etc). To uncouple this many body system, we convert it into a system where you have "new electrons" interacting in a background potential. So, you look at the problem as if the new electrons are no longer interacting with each other but with some background potential. Since both systems need to be equivalent (ie you need to describe the same physical reality) you need to compare both systems : the original system as mutually interacting electrons, the new system has non interacting electrons in a certain potential well. To make sure that both systems are equivalent, we change the mass of the electrons in the second system, in such a way that both SE are describing the same reality. This new mass is the effective mass, which can be defined as the electron mass + some interactions (ie energy of those interactions) to uncouple the many body problem into many one body problems.

That is the philosophy behind effective mass.

marlon

4. Apr 22, 2008

### LydiaAC

In vacuum you have Newton's second law relating force, velocity (through acceleration) and mass.

In a crystal you have a similar relationship between an external force, a group velocity and an effective mass.

To get more profound you will need quantum mechanics.

Lydia Alvarez

5. Apr 22, 2008

### olgranpappy

In band structure calculations the effective mass is basically the curvature of the energy-band near the bottom.

In (isotropic homogeneous) fermi liquid theory the effective mass is due to particle interactions.

If you want to take into account both the periodic crystal potential (thus band structure) and particle interactions then the effective mass depends on both and can't be separated in a simple way.

cheers.