What are e-k diagrams ?
What does they represent?
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You can think of k being the momentum and E as the energy. From a mathematical point of view it is the wavevector. The E vs k is a dispersion diagram.
For example the probability of a photon emission indirect band gap semiconductor is much much lower than than of the a direct band gap semiconductor. In the direct band gap the minimum of the conduction band and the maximum of the valence band are at the same k =0, so momentum is conserved and when the hole and electron recombine both energy and momentum conservation requirements are met. In the indirect semiconductor the momentum mismatch needs to be made up by a phonon which is unlikely.
Since it is a dispersion diagram you can look at the curvature of the diagram and determine other parameters such as the electron mobility, effective mass.
Without getting into a lot detail, a crystal is a multi-body problem with forces from huge numbers of atoms. When they are organized likely as in a crystal we consider the electron as a wave with the wavevector etc. This allows one to conveniently think about the electron as some sort of billiard ball model as being simple and having a mass and if we apply a field acceleration etc. The band diagrams let us she how the effective mass etc change as the electron travels in different directions.
For example the probability of a photon emission indirect band gap semiconductor is much much lower than than of the a direct band gap semiconductor. In the direct band gap the minimum of the conduction band and the maximum of the valence band are at the same k =0, so momentum is conserved and when the hole and electron recombine both energy and momentum conservation requirements are met. In the indirect semiconductor the momentum mismatch needs to be made up by a phonon which is unlikely.
Since it is a dispersion diagram you can look at the curvature of the diagram and determine other parameters such as the electron mobility, effective mass.
Without getting into a lot detail, a crystal is a multi-body problem with forces from huge numbers of atoms. When they are organized likely as in a crystal we consider the electron as a wave with the wavevector etc. This allows one to conveniently think about the electron as some sort of billiard ball model as being simple and having a mass and if we apply a field acceleration etc. The band diagrams let us she how the effective mass etc change as the electron travels in different directions.
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