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An electron-hole is just a free electron state in a quantum system. Is this right? For example, let's say that there are 2 electrons with opposite spins in the fundamental state of a quantum well. If one electron with spin up is excited to the first excited state now you have a free spin up spot at the fundamental level an electron can take, which can be interpreted as an electron-hole with spin up.

Now let me change the scenario to that of a quantum dot. If you have a quantum dot operating with electrons in a quantum well you may load 1 electron into it. If you irradiate it with an appropriate photon it might get enough energy to jump from the valence band to the conduction one.

If you have, however, a quantum dot operating with electron-holes and you irradiate it with a photon, what happens to the hole? The quantum dot in this case is a region of the crystal which a perfect balance between positive and negative charges except for one open spot for an electron of a particular energy, which we call a hole. If you give energy to the system through light irradiation you might send an electron to the conduction band and just place one more hole in your quantum dot. So what happens to the hole in the quantum dot if you irradiate it?

And a follow up question... what happens to the electron in the first case? If you give it energy enough to go to the conduction band wouldn't it just scape from the quantum dot? So why is the energy band gap important at all other than a way to know how to empty your quantum dot thought light irradiation?

Thank you very much for your time.

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There are many different types of quantum dots, depending on their size and how they are fabricated.

In the context of optics one usually talks about QDs that are drops of a semiconductor material (e.g., colloidal QDs), i.e. little pieces of a semiconductor, which have a valence and a conduction band. Removing an electron from a valence band and placing it into the conduction band creates and electron-hole pair. However, the finite size of the dot means that a) the electron and hole levels might be quantized, and b) the distance between the electron and the hole is controlled by the size of the dot, i.e. we cannot meaningfully talk neither about an exciton, nor about a free electron and a free hole.

In the context of electronic transport one usually speak of quantum dots formed by a split-gate technique, i.e., by the electric potential applied to the gates, deposited near a degenerate two-dimensional electron gas. We are essentially talking about a metal here (although it is in practice a heavily doped n-semiconductor), and there are no holes in sight. The zero-dimensional regions formed in such a way (i.e., the QDs) possess discrete energy levels, either due to their very small size or the strong Coulomb repulsion between the electrons. One occasionally uses electron-hole description for such cases, but these are not the same holes as in the case. Importantly, they do not have much to offer in terms of interaction with photons: due to small energy spacing (compared to optical wavelengths), small spatial extension (i.E. small dipole moment), due to strong Coulomb effects (washing out optical resonances, like in metals), and due to the metallic gates shielding the dot from the rest of the world. One one does talk about "photons" in this context, one really means radio-frequency ac field applied to some of the metallic gates.

There are exist some other types of QDs - e.g., due to cracks on a surface of a material or big molecules suspended between leads - they usually fall into one of the two categories described above.

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