The band gap generally refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is also closely related to the HOMO/LUMO gap. The electrochemical and optical properties not only depends on band gap value but also HOMO/LUMO potentials.
It is the bandgap that gives semiconductors the ability to switch currents on and off as desired in order to achieve a given electrical function; after all, a transistor is just a very tiny switch embedded in a silicon-based substrate. A higher energy bandgap imparts characteristics that make wide bandgap (WBG) materials superior to silicon as a semiconductor. WBG-based devices tolerate much higher operating temperatures in a smaller size than the equivalent silicon-based device, enabling previously impossible applications. For example, silicon possesses a bandgap of 1.1 electronvolts (eV), SiC and GaN have a bandgap of 3.3 eV and 3.4 eV, respectively. Insulators are materials with very large bandgaps, typically greater than 4 electronvolts (eV), and high resistivity. In general, they are not useful as semiconductors except in the case of diamond (C). Though technically an insulator with a bandgap of 5.5 eV, diamond exhibits properties that actually make it the ultimate semiconductor.
Hence, the advantages of WBG semiconductors over Si in power electronics include lower losses for higher efficiency, higher switching frequencies for more compact designs, higher operating temperature (far beyond 150° C, the approximate maximum of Si), robustness in harsh environments, and high breakdown voltages.
For further references you can see at: web.eecs.utk.edu/~tolbert/publications/iasted_2003_wide_bandgap.pdf
The main disadvantage of large wide bandgap semiconductors possess low photoadsorption activity, thus resulting in decreases in catalyst activity compare to narrow bandgap semiconductors like CuO, Fe2O3, etc. The smaller bandgap which shows good results in releasing of reactive oxygen species.
In wide bandgap semiconductors, the light energy is insufficient to ejection of electrons from valence band to conduction band. In such case, these materials can be form Composites with other supporting materials.