Free electrons are those electrons in the conduction band. They’ve thrown off the shackles of their nucleus and can move wherever they want. It’s time to party!
Electron that can move freely from one atom to the next.
Grob’s Basic Electronics, 11th Edition by Mitchel E. Schultz
An electron that has acquired enough energy to break away from the valance band of the parent atom; also called a conduction electron.
Electronic Devices : Conventional Current Version, 9th Edition by Thomas L. Floyd
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. In non-metals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it.
The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.