Final answer:
An electron in the conduction band of a semiconductor does not behave like a completely free electron due to the residual interactions with the semiconductor lattice, despite being more free than when in the valence band. The free electron model's assumptions do not fully apply to semiconductors.
Step-by-step explanation:
It is not entirely accurate to say that an electron in the conduction band of a semiconductor behaves like a "free electron" as it would in a metal. Although electrons in the conduction band of a semiconductor are more free to move compared to when they are in the valence band, they are not completely free of interactions with the lattice ions or impurities within the semiconductor material. The free electron model assumes a constant potential energy environment for electrons, which is not the scenario in a real semiconductor. The periodic Coulomb potential seen within a semiconductor lattice points to the fact that electrons still interact with the atomic potentials, although these interactions are weaker in the conduction band.
In a semiconductor, the band gap is smaller than in an insulator, meaning electrons can be easily excited from the valence band to the conduction band with little energy, such as thermal energy at room temperature. This allows for the movement of electrons and creation of holes in the valence band, both of which contribute to electrical conductivity. However, this capability does not equate to the electron being entirely free like those in metals, where the loosely bound electrons form a sea in which they can move very freely.