What is the limiting value of band gap that makes a material semiconductor?
The transition of electron from the valence band to the conduction band is a probabilistic event.  Electrons get this excess energy equivalent to the band gap ($\Delta E$) from the thermal energy ($kT$, where $k$ is the Boltzmann constant and $T$, temperature in Kelvin). Hence, the probability of such an event will be proportional to $e^{-\Delta E/kT}$.

Answering your question, although there is no standard defined value of band gap, you can see since it's an exponentially falling smooth curve that one can define a cutoff $\Delta E$, saying that for band gap $&gt; \Delta E$ there are practically no electrons transiting to the conduction band, qualifying the material as an insulator (i.e., exhibiting insulator-like properties).