# E-k diagram what is k?

In the E-k diagrams for a semiconductor material,what exactly is k?
I have read that it is a propagation constant,a wave vector.
But does movement in the semiconductor material represent corresponding changes in k?
I mean to ask if changes in k represent the physical movement in the semiconductor material(from an observer's point of view).

Also does that parabolic shape in E-k diagrams repeat itself with k periodically?
Most of the texts I have seen give only one parabola(though another one for the valence band).

Is it arbitrarily chosen that the top of the valence band has an energy equal to 0?
In Bohr's model we took the energy at an infinite distance from the atom to have an energy equal to 0.

## Answers and Replies

The k in E-k diagram is related to the momentum of the electron or hole.

you can take any solids and the property of that solid is determined by two qualities, one the energy of the electron, which is dependent on the other quality, momentum, since it is the electron that do all the work, for example electricity, so E is the energy and k, usually denoted as state vector is the momentum of the electron. the formula for k is planck's constant times p. hopes this clears you doubt

As you said, the k in a crystalline solid is a wave vector, much like the wave vector in a propagating electromagnetic wave. In the case of an E-k diagram, k corresponds to the wave vector of the electronic wave function.

You can create a wave-packet by adding a number of waves with different wave vector. In this case, the wave packet will move through the crystal with a velocity given by the group velocity, which is proportional to the slope in the E-k diagram.

k is the wave number, or momentum of the electron/hole. I am assuming you are looking at the digram showing the difference between direct and indirect semiconductors?