Q.What is the importance of energy gap in a semiconductor?

[!TLDR] The size of the band gap decides whether a solid conducts as a metal, a semiconductor, or an insulator, since it sets how easily electrons can be thermally excited from the valence band into the conduction band. [!ANSWER] A small band gap lets a solid behave as a semiconductor; the gap's size is the key factor separating metals, semiconductors and insulators.

The band gap (or energy gap) is the separation, in energy, between the top of the valence band and the bottom of the conduction band. In a metal there is no gap at all -- the valence and conduction bands overlap -- so electrons need almost no extra energy to become available for conduction, and metals conduct very well at all temperatures. In an insulator the gap is wide (about 5.0 eV for diamond, for example), so electrons essentially never gain enough thermal energy at ordinary temperatures to cross it, and the material conducts extremely poorly. A semiconductor sits in between: its gap is fairly small, of the order of one electron-volt or less (1.12 eV for silicon, 0.66 eV for germanium), which is small enough that a workable number of electrons ARE thermally excited across it at room temperature, giving the material a usable, and importantly TUNEABLE, conductivity. The size of the gap therefore directly explains why semiconductor conductivity rises so strongly with temperature (more thermal energy excites more electrons across the same fixed gap), and why doping -- which adds donor or acceptor levels much closer to a band edge than the full gap width -- can dramatically increase conductivity with only a very small amount of impurity. [!ANSWER] A small band gap lets a solid behave as a semiconductor; the gap's size is the key factor separating metals, semiconductors and insulators.

Connect the band gap's size to the ease of thermally exciting a valence electron into the conduction band, and use that to explain the metal/semiconductor/insulator classification and temperature dependence.

Treating the band gap as just one more fact to memorise rather than the single physical quantity that explains both WHY semiconductors sit between metals and insulators AND why their conductivity rises with temperature.