Doping of a semiconductor will have the effect of narrowing the band gap, however, if the dopant concentration exceeded a certain limit, problems start to appear. For example, the scattering of conduction electrons will increase as the field inside the crystal is fluctuated due to the existence of high concentration of impurity atoms. This might lead to widening of the band gap.
There is some literature available on this topic, you can go through it. With my knowledge, I can say that if there is a significant change in the lattice parameter after doping then you can expect a change in the band gap also including the intermediate state arising from the dopant.
As Manuel pointed out there will be huge effect at high doping concentrations. One phenomenon is "Burstein–Moss effect" where the band gap increases significantly, which is different from size effect (as B-M effect will happen in bulk also). Rest Google will tell......
Doping of a semiconductor will have the effect of narrowing the band gap, however, if the dopant concentration exceeded a certain limit, problems start to appear. For example, the scattering of conduction electrons will increase as the field inside the crystal is fluctuated due to the existence of high concentration of impurity atoms. This might lead to widening of the band gap.