Question

Why is the energy required to create an electron-hole pair in semiconductors higher than their band gap energy?

Answer 1

As far as i know the minimum energy required to produce an electron hole pair is equal or slightly greater than the energy gap in case of direct gap and indirect energy gap material, respectively. The difference comes from the momentum offset which can affect a difference of energy of about kT of about 26 mev at 300K.

n case of substitutional diffusion of impurities in silicon such as Boron atoms, the activation energy of such process is about 3 electron volts that is about breaking three covalent bonds. 

If you specify the process more precisely, one could explain this number. But this number is sufficient to break three covalent  bonds and release 3 electron hole pairs.