Why insulators do not conduct electicity when they are negatively charged?

Question

The following excerpt is from Young and Freedman 13th edition:

Most metals are good conductors, while most nonmetals are insulators. Within a solid metal such as copper, one or more outer electrons in each atom become detached and can move freely throughout the material, just as the molecules of a gas can move through the spaces between the grains in a bucket of sand. The other electrons remain bound to the positively charged nuclei, which themselves are bound in nearly fixed positions within the material. In an insulator, there are no, or very few, free electrons, and electric charge cannot move freely through the material. Some materials called semiconductors are intermediate in their properties between good conductors and good insulators.

So what I understand is, conduction of electricity is simply the movement of electrons through a body. As the excerpt states, for some reason not yet explained in the book, metals do not cause many problems to give up a couple of their outer electrons (which makes them become positive ions). This results in free electrons in the body, which makes the body a conductor.

On the other hand, the excerpt states that there are no or very few free electrons in an insulator, which AFAIK is due to the reluctance of insulators to give up a couple of their outer electrons.

If what is written up here is correct, then why doesn't an insulator conduct electricity when it is negatively charged? (let's assume the insulating body is composed of a single type of atom for simplicity) The reason I think why it should do this is: When a body is negatively charged, it has an excess of electrons. Then numerically, every atom in the body can own as many electrons as their number of protons. If every atom owns the same number of electrons as its protons, then there will be free electrons in the body. Hence, by definition, the body will be a conductor.

But AFAIK this is not the case. Then one possibility is, atoms in the insulator keep excess electrons and become negative ions when the body is negatively charged. If that's true, why this is the case? Why do insulators keep electrons more than their number of protons?

Answer 1

Few things from quantum mechanics are needed to explain this: 1. Pauli exclusion principle, no two electron can occupy a same state. 2. Band theory of solids. There is an energy gap in the density of states in semiconductors and insulators, but none for metals. 3. And then that conduction can be explained by scattering from occupied states to unoccupied.

What it essentially means that electrons are free is that there is "plenty of room" for an electron from occupied valence band to scatter to a very close by unoccupied state (in conduction band). There are no such "close-by" states available in an insulator, so the conductivity will be very poor.

Now for your question about charging an insulator. Yes, it works. You have essentially reinvented the doping of semiconductors, resulting into development of transistors. The only practical difference is that it is impossible to charge an insulator to required charge (and the charge would probably be at the surface only). However, by introducing defects into an insulator/semiconductor one can effectively charge the conduction band with electrons (or remove electrons from valence band with other types of defects). This happends in finite temperatures, since the defects are easily ionized and donating electrons. And here, the system will remain electrically neutral, since the defects are charged positively and they donated their negative electrons to the conduction band. There is room for electrons in the conduction band to scatter to empty conduction band states and conductance is increased.

There is also intrinsic semiconductivity, where no doping is required, and there also, the conduction band is "thermally chared".