# Effective mass of electrons in metals

• joel.martens
In summary, the conversation discusses the concept of effective mass of electrons and its applications, particularly in semiconductors. The concept is closely related to mobility and can be understood through fermionic renormalisation methods. The effective mass is seen as a curvature of the electronic dispersion relation, where in a crystalline solid, the mass is 'renormalized' and can be lower than the free electron mass. There is a discussion on the physical explanation for this phenomenon.

#### joel.martens

The literature i have on the origins / need for an effective mass of electrons seems only to relate it to the explanation of heat capacity of metals but it seems like the concept has applications far beyond this. Can someone pls provide a more general summary of its derivation and applications?
Cheers.

Effective mass of holes and electrons in semiconductors is closely related to mobility. See
http://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics [Broken])

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The cleanest understanding of effective mass in Fermi liquids comes from a solid understanding of fermionic renormalisation methods. See any number of papers by Shankar on the topic.

I think of effective mass as a curvature of the electronic dispersion relation. I.e. for a free electron:
E = hbar^2 k^2 / 2m

where m is the mass of free electron.

Now, in a crystalline solid, where electronic band diagram applies, any band (near a symmetry point) can be represented as parabolic in k space, with its own curvature, i.e.:

E = hbar^2 k^2 / 2m*

where m* is the 'renormalized' mass of an particle in band (electron or a hole).

What is puzzling to me is why in for example semiconductors the effective mass is lower than the free electron mass? If I apply an external electric field, these electrons will reach steady state velocity larger than the free ones... what is physically happening that electron acts as if its inertia is lowered?

## 1. What is the effective mass of electrons in metals?

The effective mass of electrons in metals refers to the mass of an electron in a metal that behaves as if it were free from the influence of other particles. It is a measure of how easily an electron can move through a metal's atomic lattice structure.

## 2. Why is the effective mass of electrons important in metals?

The effective mass of electrons is important because it affects the electrical and thermal conductivity of metals. It also plays a role in other properties such as the specific heat and magnetic susceptibility of metals.

## 3. How is the effective mass of electrons in metals determined?

The effective mass of electrons is determined through experimental measurements, such as the Hall effect or cyclotron resonance. Theoretical models, such as the nearly free electron model, can also be used to calculate the effective mass.

## 4. Can the effective mass of electrons vary in different metals?

Yes, the effective mass of electrons can vary in different metals. This is because it is dependent on the atomic structure and composition of the metal, as well as external factors such as temperature and pressure.

## 5. How does the effective mass of electrons change with temperature?

The effective mass of electrons typically increases with temperature in metals. This is due to the increased thermal vibrations of the atomic lattice, which makes it more difficult for electrons to move through the metal.