Why do n-type materials have a smaller conduction energy band?
Your thinking is on the right track, but it misses a few small details. One way to visualize the process you're interested in is via the Fermi level -- this however is in some ways a post hoc rationalization of the end-result, rather than an explanation from first principles.
Notice the dashed line for the Fermi level, marked \$E_f\$ on the band diagram. It is flat because the structure is in thermodynamic equilibrium, and represents (among other interpretations) the energy level of a hypothetical electron level that is 50% likely to be occupied.
The consequence of doping is that the bands move relative to the Fermi level -- in a P-type semiconductor, the valence band is likely to have openings and the conduction band is likely to be near-empty, putting the Fermi level close to the valence band; in an N-type semiconductor the valence band is full and states are likely to be occupied in the conduction band, thus putting the Fermi level close to the conduction band. However, once the materials are connected and brought into equilibrium, the conduction and valence bands themselves must be aligned to maintain the Fermi level as flat.