The quantum well density of states step function?

[jeebs]

I'm trying to get my head around the step function and the energy states of the quantum well. What I've got so far is this:

The density of states for an electron confined in one direction by the potential barriers of the well, but free to move in the other two directions in the place of the layer, is not dependent on the energy of those states, but rather on the electron's effective mass, ie. $$D = m*/ \hbar \pi$$

This means that, say the energy of incoming photons is above the band gap threshold is increased further, there will be no increase in the number of electrons being promoted/photons being absorbed, because there is no increase in the number of available states (unlike in a bulk semiconductor, where the density of states varies as E^(1/2).
*I am aware that quantum well absorption threshold actually happens slightly above the band edge, but the rest of the question will explain my issues with this*.

However, here is where my confusion lies. The only thing that can affect the density of states is the effective mass, m*. What is it that makes m* increase?

More to the point, why does the increase in m* coincide with the quantized levels associated with the 1D confinement?

I mean, it clearly does, and I get why the steps are flat and the absorption remains constant between the steps (as there is a continuum of states available for the directions that are unconfined), I just do not get what the reason for the step increase / m* change is in the first place.

Why do we see steps at the quantized levels in the density of states / absorption graphs?

 

[eljose79]

I can see that you are trying to understand the step function and the energy states of the quantum well. Let me try to explain it to you in simpler terms.

Firstly, the density of states for an electron in a quantum well is determined by the electron's effective mass, which is a measure of how easily an electron can move in a particular material. In a quantum well, the electron is confined in one direction by potential barriers, but is free to move in the other two directions. This means that the density of states is not dependent on the energy of the states, but rather on the effective mass of the electron.

Now, let's consider the case of incoming photons with energy above the band gap threshold. In a bulk semiconductor, the density of states increases as the energy of the states increases. However, in a quantum well, the density of states remains constant because there is no increase in the number of available states. This is because the density of states in a quantum well is only affected by the electron's effective mass, which does not change with increasing energy.

Now, let's address your confusion about why the effective mass increases at the quantized energy levels associated with the 1D confinement. This is because the electron is confined in one dimension, and this confinement leads to a change in the electron's effective mass. This change in effective mass is what causes the step increase in the density of states and absorption graphs at the quantized energy levels.

In summary, the reason for the step increase in the density of states and absorption graphs at the quantized energy levels is due to the change in the electron's effective mass caused by the 1D confinement. I hope this helps to clarify your confusion.