I understand that the quantum confinement effect is observed when the wavelength of an electron is smaller than the wavelength of a material. I have also read that Quantum Dots have energy band gaps, because of the semiconductor material that makes them. For an exciton to be created an electron must jump from the valence band to the conduction band, generally in semiconductors this occurs from light absorption. If electrons are not permitted to move, from the confinement effect then how are they going from the valence to the conduction band? Am I picturing this wrong in my head, or is just that even quantum dots have some free electrons?
Confinement means that the possible electron states are discrete in energy, rather than continuous, NOT that the electron cannot move between these states. Creation of an exciton is an electron transition from a state in the valence band to one in the conduction band, induced by the optical field. This is similar to electron transitions in an atom.