You can't affect the bands structure by moderate doping levels. However, the presence of doping introduces electronic states inside the bandgap.
Impurities may be of acceptor type or donor type.
- Acceptors (as the name suggests) may accept one additional electron. If the acceptors' energy level is just above the valence band edge, electrons from valence band may be captured by acceptors when excited by relatively low energies (relative to the energy required to excite an electron from valence band to conduction band). The electron becomes trapped in the acceptor until it "falls" back to valence band, but, meanwhile, the hole which emerged in valence band can contribute to current.
- Donors may donate one additional electron. If the donors' energy level is just below the conduction band edge, electrons from donors may be excited to conduction band by relatively low energies. These electrons become conduction electrons until they "fall" back to donors' level.
The above described "shallow states" introduced by impurities - very low excitation energies. Sometimes you want to introduce "deep states" - higher excitation energies required, but still less than exciting over bandgap.
Do these impurities change the conductivity of the SC? Well, first of all they allow for easier change of conductivity (by reducing the required excitation energy). It means that they allow for more control over SC's electrical behavior. They can also change SC's resistance regardless of externally controlled excitations, but it depends on the rate of ionized impurities at a given temperature.