I prepared non doped PbTe and Yb, Nd doped PbTe by hydrothermal method, then I found the bandgap energy increases by enhancing level doped , the particle size of them is same (PbTe and doped PbTe), how is it possible ?
Stronger is the bond, higher is the band gap. Electronegativity difference, ionic size (oxidation state) and crystal structure type play important role in increasing or decreasing the bandgaps in semiconductor. Compare these values for Pb2+, Nd3+ and Yb3+ to get the answer.
If you are talking about the optical band gap, that is, the band gap you measured from optical absorption spectroscopy (e.g. UV/Vis), increased band gap is likely due to higher carrier concentration, referred to as Burstein−Moss band filling effect. This is quite common actually. Briefly, for an n-type semiconductor, because electrons take up the lower energy levels in the conduction band, electrons from valence band have to take extra energy in order to be excited to the energy levels higher than the conduction band minimum, which results in a blue shift from undoped sample in the optical absorption spectrum.
If you have doped a non metal element, because it has pn electrons, it is a donor and so decrease the band gap. for example, TiO2 doped with C, S has a smaller band gap comparing to the pure TiO2. And, for decreasing the band gap without using the dopant, a usual method is decreasing the material size.