Electronic band structures are caused by electron-electron interactions between neighboring atoms. The greater the degree of interaction, the wider the band generally becomes. For this reason, atoms with high coordination numbers tend to form wider bands, since more bonds are formed when coordination number is higher. If the bands are wider, the band gaps become smaller because the band covers more energy values. Base on this knowledge, if you made a single-atom layer thin film out of a semiconductor, what would you expect the bandgap of this film to be compared to a bulk (large in all 3 dimensions) semiconductor made out of the same material? Please explain why.