The increase in band gap of a semiconductor has drastic changes in electrical and optical properties. For example, if a semiconductor was transparent in infrared region, on increasing band gap it may be transparent in visible region. Electrical conductivity may decrease on increase in band gap. Use of a semiconductor in solar cells also depend on band gap. Optimum value for this purpose is 1.4 eV. It may not be showing photo luminescence at low band gap but may show photoluminescence when band gap becomes higher. In conclusion one can say that band gap is a critical parameter from application point of view.

Whether there will be any application for a higher band gap, will depend upon the current band gap and the relevant properties of the semiconductor for an application. Say the application is solar cell and the current band gap is less than the optimal band gap, which is in the range of 1.4 - 1.5 eV. But, if the absorption coefficient of the semiconductor is not attractive, then there is not much sense in increasing its ban gap, say, by alloying with other semiconductors. 

Effects of increase in semiconductor bandgap: 

The increases of the energy gap for semiconductors lead to decreases the absorption region and the substance may be transparency and the absorption edge shifted toward low wavelengths. This may be useful for solar cell applications .   

Thanks for all Bandgap experts.

Could anyone specify the applications with respect to band gap ranging from 0 to 5 eV, please?