In the isolated atomic structure there are discrete or individual energy levels associated with each orbiting electron, as shown in Figure below. Each material has its own set of permissible energy levels for the electrons in its atomic structure.
If we take the reference to infinity for the sake of measurement of potential energy of electron i.e. if we consider the potential energy of electron to be zero at infinity then the more distant the electron from the nucleus, the higher the energy level associated with that electron, and any electron that has left its parent atom has a higher energy state than any electron in the atomic structure.
As can be seen from the figure above, between the discrete energy levels there are gaps in which no electrons in the isolated atomic structure can appear. This energy gap is called Forbidden Energy Gap. As the atoms of a material are brought closer together to form the crystal lattice structure, there is an interaction between atoms that will result in the electrons in a particular orbit of one atom having slightly different energy levels from electrons in the same orbit of an adjoining atom. The net result is an expansion of the discrete energy levels of valance band electrons as shown in figure (b) above. Thus the gap between the two energy levels of valance band and conduction band i.e. forbidden energy gap decreases.
Any material conducts electricity only if the material has electrons in its conduction band. In case of insulator as the forbidden energy gap Eg is quite high, therefore no electrons can jump to conduction band from valance band.
At 0 K or absolute zero (273.15°C), all the valence electrons of semiconductor materials find themselves locked in their outermost shell of the atom with energy levels associated with the valence band. However, at room temperature (300 K, 25°C) a large number of valence electrons have acquired sufficient energy to leave the valence band and cross the energy gap defined by Eg in figure above and enters the conduction band. For silicon Eg is 1.1 eV, for germanium 0.67 eV, and for gallium arsenide 1.41 eV. The obviously lower Eg for germanium accounts for the increased number of carriers in that material as compared to silicon at room temperature.
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Note for the insulator that the energy gap or forbidden energy gap is typically 5 eV or more, which severely limits the number of electrons that can enter the conduction band at room temperature.
The conductor has electrons in the conduction band even at 0 K. Mind here that conduction band and valance band are overlapping for conductor. Therefore, at room temperature there are more than enough free carriers to sustain a heavy flow of charge, or current in a conductor.
Thus the concept of conductor, semiconductor and insulator can be well explained using energy levels theory.