Could anyone specify bandgaps with respect to applications or vice versa, please? For example, a semiconductor within some specified lower and upper limit may give highest performance as a solar cell, or field effect transistor, etc....
Semiconductors are generally used to generate energy (PV panel) and for electronic applications (diode, transistor, etc.). Each semiconductor material has energetic capacities (depending on the bandgap) on which are used.
For more help see the attached papers.
Article Optical band gaps of organic semiconductor materials
This depends on the many parameters which effect on the performance of a device, and this mean you should take all parameters for device in your consideration, because or may be another reason not only energy gap effect on the performance of a device, such as optical, electrical, structural properties,..etc.
I do agree with you that other parameters also play vital role in the performance of device. But other parameters are of secondary concern, the most important is the energy/optical gap of the materials for some specific application.