Well, the criterion is not directly the gap value but "dopability" (is there a way to make it n-type or p-type conducting by doping?). Usually large-gap materials possess small dielectric constants and usually also more and more "flat" bands with high effective masses (because usually the bonding is more ionic than covalent). Thinking about the simple quasi-H impurity model for donors and acceptors giving donor/acceptor binding energies of Ry*m_eff/epsilon^2, you quickly end up with a value of about 1 eV or more if entering large masses around 1 electron mass or more and small dielectric constants epsilon around 2-5. Only if this binding energy is not  larger than about 0.1 eV there will still be some n- or p-type conductivity (at room temperature, kT=25meV). But there are few exceptions like Ga compounds (or also ZnO) which still possess at least  a very small conduction band mass (typically about order of 0.1 electron masses ) giving rise to rather "small" donor binding energies of about 0.1 eV (n-type doping) and even "intrinsic n-type conductivity" (somehow a self-doping by defects). And as long as you can make a material weakly conductive (by doping) people still like to call it a "semiconductor" (though there is often the problem that most of these large-gap semiconductors can be found n-type conductive but not p-type because their valence band masses are much higher and there don't exist shallow acceptor levels). So, the borderline is not sharp in terms of gap energies (but with increasing gap it becomes harder and harder to find anything you could still call semiconductor and I think latest beyond 5-6  eV  you will not find anything else than insulators).

They are a wide-bandgap semiconductors that can operate at extreme conditions (voltage, temperature etc.). Size of gap is not main criterion (also above)

Thank you everyone!

Finally, I came to know that effective mass also plays an important role in this regard.

I think that your question points to a general aspect which is a fundamental necessity for doing research in natural sciences: Do not be biased by assumptions or theory or general belief! Instead, start from facts.

This means here that if you have a material which shows a certain conductivity, at least at high-enough temperatures, then it's not an insulator, obviously -- no matter how large its band-gap may be! It's just a matter of conductivity (and of the temperature dependence of the conductivity) if some material is called "metal" or "semiconductor" or "insulator".

So, as a conclusion, what does this mean for statements like "Generally material having the bandgap more than 3 eV is called an insulator"? In my opinion, this is just arbitrariness.