Do you remember the law of Ohm, I=V/R ?

Do you remember that the resistance R decreases when the transversal section through the conductor increases, R ~ 1/S?

If the charges would flow only through the external surface of a conductor, the perimeter of the transversal section would matter, not the surface.

Now, the situation that in a metal the charges are spread only on the external surface, is correct only in an equilibrium state. If, for instance, there are electrical discharges in the close vicinity of the metal, transient currents may cross the metal.

Band theory is good, to explain. Metals are having no forbidden band between valence and conduction band, semiconductor with 1 to 2 ev forbidden band and insulating material with higher than 2ev. Conduction in material could be carried out by exciting(applying potential(voltage)) electrons in outer most orbit(valance band). For semiconductor, measurable(0.3 to0.7V), and for insulator considerable, potential different is needed and almost nil(depending on resistivity, R=(resistivity)(length)/(cross sec. area) for conducting material......

Dear colleague,

inside of metal conductors is free of negative charges just in the statical case when all the free electrons are gathered on the conductor surface.

For the case of direct current we have uniform current density, i.e. uniform distribution of electrons (charges) in conductor's cross-section. For the case of alternating current the distribution of electrons (charges) is determined by skin-effect. Thus, in the presence of a voltage source compensating for Joule losses in the directed motion of electrons, charges inside the conductor will exist.

You may see the corresponding chapters in the courses of Landau or Feynman.

Regards

The charges in the metal is neutral. The metal has an equal number of negative and positive. When current flows on it, the charges move because of the flow of electron. Remember, opposite charges attract and similar charges repel.

From Wikipédia :

" An electric current is a flow of electric charge.... In electric circuits this charge is often carried by moving electrons in a wire The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors...

In a conductive material, the moving charged particles which constitute the electric current are called charge carriers. In metals, which make up the wires and other conductors in most electrical circuits, the positively charged atomic nuclei are held in a fixed position, and the negatively charged electrons are free to move, carrying their charge from one place to another. In other materials, notably the semiconductors, the charge carriers can be positive or negative, depending on the dopant used. "

Please, take a look to the whole article in the following link :

https://en.wikipedia.org/wiki/Electric_current