In a semi conductor, for an electron in valence band to transfer to conduction band, it needs energy which can be provided by applying an electric field such that a force is applied on it until it breaks free from its parent atom. Now till the time it is at rest no change in kinetic energy is there. Hence, the energy that it gained and transfered to conduction band is electric potential energy. But this electric potential energy is stored in the field configuration i.e. The number at every point in space. And when u change that number you have to give off energy. N when the number is reverted back. It gives back to you the same energy.
Now my question is that this case of the electron breaking free requires that the electric potential energy be localised at the electron like the electron's kinetic energy and not be stored in the field configuration. How is this happening? Is electric potential energy stored in electron or the electric field configuration at each point in space? And if in the field then how does the electron jump the energy gap and enter the conduction band, where does it get the energy from? Is kinetic energy locally stored in the particle or it is also a field configuration kind of thing? Is there a field associated with kinetic energy ?
Or my understanding is wrong in which case please explain what is meant by electric potential energy is stored in electric field? And what is electric field energy density?
edit: leaving the semiconductor example aside. Suppose i have an atom and i apply external electric field and that causes the atom to ionise. Where did the electron that flew away got the energy from?